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Frost Closure of Roof Vents

in Plumbing Systems

United States Department of Commerce

National Bureau of Standards

Building Materials and Structures Report 142
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UNITED STATES DEPARTMENT OF COMMERCE • Sinclair Weeks, Secretary NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Frost Closure of Roof Vents

in Plumbing Systems

Herbert N. Eaton and Robert S. Wyly

Building Materials and Structures Report 142

Issued October 25, 1954-

For sale by the Superintendent of Documents, U. S. Government Printing Office, Washington 25, D. C. Price 25 cents

Foreword

For several years the National Bureau of Standards conducted for the

Housing and Home Finance Agency of the Federal Government a series of

investigations of the physical aspects of the flow phenomena in the sanitary

drainage systems of buildings. Problems of venting were involved in these in- vestigations, and this led naturally later to a consideration of how the partial or complete closure of roof vents by frost in cold weather might affect the

venting of a building drainage system. Very little information as to the conditions under which frost closure might occur is available, and, as a result, the

requirements in plumbing codes have generally been based on local practices

without any regard to the consideration of the factors that affect its occurrence. Because of the importance of the problem, the Housing and Home Finance

Agency requested the National Bureau of Standards to undertake an experimental investigation of this phenomenon as part of a broad investigation of

building drainage systems, the physics of the closure of vents by frost being

emphasized, rather than the effects of such closure on the drainage system.

Experimental studies were conducted in which the roof vent of a simulated

building drainage system was enclosed in a low-temperature chamber, and

vents as large as 3 inches in diameter were completely closed by frost. Later, when the report was being written, a theoretical analysis was made

of the heat-transfer processes that are involved in the freezing of a roof vent,

and this analysis made it possible to predict to what extent an exposed roof

vent of any given diameter will freeze up under any given conditions.

The experimental part of the investigation was undertaken for the Housing

and Home Finance Agency as part of the research program of that Agency

under its statutory authority. The analysis of the problem and the writing

of this report were sponsored by the National Bureau of Standards.

A. V. Astin, Director.

iii
Contents

Page Foreword i in

1. Introduction 1 2. Purpose and scope of the investigation 2

3. Previous investigation of the problem 2

4. Analysis of conditions in service and test installations 5

4.1. Analysis of service installation 5

4.2. Test apparatus 6

4.3. Analysis of test installation 8

a. Conditions outside of system 8

b. Conditions inside of system 8

c. Conditions in manometer line 8

5. Friction losses involved in the upward flow of air in the system 9

5.1. Head loss at transition from street sewer to building sewer 9

5.2. Head loss in building sewer and drain 9

5.3. Bend loss at entrance to stack 9

5.4. Head loss at contraction, upper end of bend 9

5.5. Head loss due to friction in stack 10

5.6. Head loss at transition to roof vent 10

5.7. Head loss due to friction in roof vent 10

5.8. Head loss at outlet of roof vent 10

6. Physics of frost closure of roof vents 12

6.1. General considerations 1 12

6.2. Heat transfer in a roof vent 13

a. Transfer of heat from air stream in vent to inner wall of vent 13

b. Transfer of heat through ice layer and pipe wall 14

c. Transfer of heat from outer wall of vent to outer air 14

d. Computation of the temperature of the ice-air surface in the vent 15

7. Test procedure 21

8. Test results 23

8.1. Tests on system with house trap 23

8.2. Tests on system with air flow up stack 23

9. Discussion of frost closure—field reports 26

10. Methods of retarding or preventing closure of roof vents by frost 28

11. Conclusions 30

12. References 31

IV
Frost Closure of Roof Vents in Plumbing Systems

Herbert N. Eaton and Robert S. Wyly

Results are reported of a laboratory investigation of the freezing up of roof vents in extremely cold weather and an analysis is given of the heat-transfer process that leads to the partial or complete closure of these vents by frost under sufficiently severe condition- information as to the occurrence of frost closure in Canada and methods used there to avoid

or minimize the freezing up of roof vents is also included.

1. Introduction

It lias been recognized for years that in severely

I cold weather the roof-vent pipes of building drainI age systems may be rendered ineffective as a re-

: suit of the accumulation of frost inside the vent- pipe. When waste water flows down a stack, it carries air with it because of the friction exerted

! by the falling water on the core of air in the middle

of the pipe cross section, and this air is carried

i away through the building drain or through vents

connecting to the lower portion of the stack or to

the building drain. The air thus removed must

be replaced, and this occiu’s normally by means of inflow through the roof vent. Hence if this inflow

is prevented or restricted because the roof vent is

! wholly or partly blocked by frost, the pneumatic

pressure in the system may fall, when fixtures are discharging into the stack, until air is sucked into

the system through the trap seals of the fixtures

attached to the system. This may lead to suffi- cient losses of water in the trap seals of fixtures to allow slight excesses of pneumatic pressure that occur when fixtures are discharging to force sewer

air through the reduced trap seals into the rooms

!

of the building.

Occurrences of partial or complete closure during

very cold weather have been reported from northern states in this country and from Canada [l]. 1 Various -expedients, such as requiring the use of minimum sizes of roof vents larger than those that

would be required for adequate venting in normal

weather; the requirement that the vents be enlarged at or a little below the roof line; and the

reduction of the exposed length of vent to the

minimum that is feasible have been proposed and

are being used successfully in Canada.

The formation of ice or frost in a roof vent results from the condensation and freezing of the moisture

carried by the relatively warm air that rises in the

stack during periods of cold weather at times when

there is little or no flow of waste water down the

1 Figures in brackets indicate the literature references at the end of this

stack. When this warm moist air comes in contact with the cold inner surface of the vent pipe

above the roof of the building, some of its moisture

condenses on the wall of the vent pipe, where it may freeze if the outdoor air temperature is low

enough. The formation of frost or ice inside of the vent pipe becomes possible whenever the temperature of the inner wall drops at least to the

freezing point and remains there for some time,

provided there is a stream of warm moist air rising

through the vent constantly or intermittently.

In very cold weather it may happen that the vem

pipe will be at a temperature below 32° F for some

distance from its upper end; for example, when ii extends down through an unheated attic or similar

space beneath the roof. Moisture is carried to the cold portion of the

vent pipe by several means, any or all of which

may be going on simultaneously:

1. The principal cause is the existence of an upward current of air in the stack or vent due to temperature differences between the outside at- mosphere and the air in the stack and sewer. In systems connected directly to a street sewer or a septic tank without the insertion of a house trap,

the weight of the heavier cold air outdoors a< • t - through the manholes or other openings, causing an upward motion of moisture-laden, warmer

and hence lighter—air inside the house drainage

system. This convection can take place also in systems having a house trap with a fresh-air vent on the building side of the trap, but to a lesser extent, since the air entering through this vent is at the temperature of the outdoor air and cannot

rise in the stack until it is warmed somewhat.

2. Diffusion of water vapor in the stack may

be a minor factor. Whenever fixtures are Tscharged, water vapor is introduced into the stack

in high concentration, especially if very hot water

is discharged. This water vapor tends to did use through the stack and venting system and may

this way come in contact with the cold surtaee m

the vent pipe.
3. Air currents are set up by the intermittent

discharge of the fixtures owing to the displacement

of the air in the drainage system and to friction between the air and the water. This may temporarily reverse the direction of the normal convective current and tend to chill the stack and

roof vent by drawing cold outdoor air into the

system through the roof vent.

4. Pressure changes in the vent pipe induced by

wind blowing past the vent or by gusts strikingdown on the opening in the vent owing to the

presence of nearby buildings may increase or decrease the rate of flow of air in the vent. It has

also been suggested that the frosting of the vent

will be affected by the tendency of cold outdoor

air to force its way into the vent near the wall of the pipe, where the velocity of the rising air is least. As will be shown later in this paper, frost closure of a roof vent may assume either of two

general forms, or a combination of the two. The

first form, the one that is analyzed in this paper,

is that of a layer of ice or frost which builds up

annularly on the interior wall of the vent, until,

if conditions are severe enough and last long

enough, the vent pipe may be completely blocked

by frost. The other way in which the vent may

be blocked by frost is through the building up

from the rim of the vent pipe of a frost cap which

may assume various forms. As this cap builds up,

a hole remains in the center of the cap, permitting

air from the stack to flow up through it. However, under sufficiently severe conditions, this hole gets smaller and smaller, until the frost cap

may completely close the vent. A photograph of such a frost cap is shown in figure 1.

Figure 1 . Frost cap.

2 . Purpose and Scope of the

Investigation

This investigation was undertaken at the sug-'

gestion of the Housing and Home Finance Agency

as a result of questions that arose in meetings of; the Uniform Plumbing Code Committee when1 that Committee was preparing its report. Doubt

was expressed that complete frost closure could

occur. Owing to the scarcity of information as to actual cases of the occurrence of this phenomenon, it was proposed that, if possible, experiments

be made to determine whether roof vents could be1 completely closed by frost under any reasonably

conceivable conditions, and the Hydraulics Section

of the National Bureau of Standards was asked to, look into the matter. Obviously it was impossible to conduct such a study on actual installations in the District of Columbia because of the mild winter temperatures

that prevail here. However, the possibility of simulating actual service conditions by extending!

the roof vent of a laboratory plumbing stack up! into a cold chamber in which low temperatures,

could be maintained was considered. Such an

installation was constructed as shown in figure 4. It was necessary to use a blower to provide!

artificially the updraft of air in the stack that

ordinarily would result from “chimney action”

in an untrapped stack in winter. In the tests the

updraft rate was adjusted to correspond to the rate! computed for the assumed service conditions.

This problem is analyzed in a later section of this paper. Because of the limited purpose of the investigation when it was started, the desirability ol simulating closely an actual installation, and the limited time and funds that were then available,

the experimental investigation was of a practical

nature rather than of a broad, scientific nature. However, it did demonstrate certain basic principles and pointed the way in which a more!

scientific study of the problem can be made at some later date. Over a period of time subsequent to the ex-j perimental investigation, an analysis of the fros closure of vents was made on the basis of heat- transfer relationships at the vent section. The1 analysis yielded results in general agreemenl

with observations of frost closure in the field, ane|

is presented in some detail to indicate the natun

of the phenomenon.

Previous Investigation of the

Problem

The late Roy B. Hunter of the Nationa

Bureau of Standards considered the question o the effect of frost closure on trap seals in BH13

“Recommended Minimum Requirements fo; Plumbing” [2], Tests simulating conditions o

partial closure of roof vents by frost were made by
!

reducing the openings in the tops of stacks and

roof vents by replacing the topmost portion of the

vents with pipes of smaller diameters. Thus,

ij Hunter was interested in the effect of partial

j closure of the roof vent on the drainage system,

(

not in how the phenomenon of frost closure occurs. Other unpublished material relating to later tests made at the National Bureau of Standards also

j deals with this effect. Hunter states: “Frost

' closure was simulated by setting sections of pipes

,( of various diameters and lengths into the stack top.

Xo measurable effect was produced by setting a

, lb-in. pipe 20 in. long into the tops of the 3-in. stacks of the different systems. A 1-in. pipe 12

in. long set in the 3-in. stack only slightly in- creased the vacuum produced by a heavy dis1 charge from the fixtures. Xo doubt the effect

I would be felt more with an increase in the volume

of discharge. With a complete closure of the

stack top. the water was sucked from one or more

traps by the discharge of a single water closet on

the system."

Tests made at a later date have confirmed these

conclusions and have indicated that, if the top

opening in a 3-in. stack is reduced to 1 in. in

diameter, undesirable reductions in trap seal may

I

occur in the fixture traps in a one- or two-storv- and-basement installation.

Hunter states further: “Chief reliance for

j ventilation of the drainage system and for the

relief of pressure changes set up by fixture dis- charge is placed upon a free course of air from

street sewer to roof terminal. Effects of frost closure as determined bv experiments apparently

are so slight as to be negligible if a clear opening is left at the top of the stack equal in area to a circle of lb in. in diameter.” It is assumed that the

diameter of opening referred to applies in the case

of a 3-in. stack.

A vent diameter of 4 in. at the roof line has been

found adequate under most conditions, but, in some parts of the United States and in Canada,

the severe climatic conditions encountered have

led to the use of increasers 2 in. larger in diameter

than the pipe below the roof. It has also been

found that vent pipes that extend but a few inches

above the roof are less subject to frost closure than

longer lengths. This, however, may increase the

effect of wind pressure on trap seals. Extension

of such pipes above the elevation of possible snowdrifts has been found unnecessary, as the escaping warm air “honeycombs” the snow sufficiently to prevent serious obstruction.

Gray [3] states that a system connecting

directly to the street sewer and having no trap in the house drain “favors high humidity and

closure of vents by frost in winter”. He also indicates that a system having back circuits or

loop vents provides considerably greater heating

surface for the air passing through it, which tends

to make the temperature of the air higher as it passes- tlrrough the roof vent than would be the

case for a stack-vented system. His conclusion

appears to indicate that a stack-vented -v-w-m

connected directly to the street sewer is more

likely to be affected by frost closure than are othei

systems, other factors being equal.

Gray points out that beat from the roof may

cause the temperature of the air surrounding tie roof vent to be somewhat higher than the average

outdoor air temperature on windless days. Thi~ heat

may come either from the attic space fas. for example, from a heated atticj or from the absorption and reflection of the sunlight. Furthermore,

lie states that although at night, the temperature

of the air around the roof vent will usually be

lower than in the daytime, the infrequent use of the plumbing fixtures during the late evening and

early morning hours results in lower humidity of the air passing through the system. Gray suggests that it is desirable to enlarge the stack, not

at- the roof line, but at some distance below the

roof, in order to take advantage of the large

heating surface of the increaser below the root

line. Evidently he assumes here that the temperature of the air in the space immediately below the

roof would be higher than the temperature of the

air in the stack. If this were not true, it is obvious

that heat would be lost by the air stream instead

of gained.

The authors have received much interesting

and significant information on the subject of

frost closure from Canadian sources, and this > summarized later in the paper.

Valuable information on instances of frost closure has also been found in a report of the

Canadian Institute of Sanitary Engineers [tj This report contains a lengthy discussion of the

problem of frost closure of roof vents in various

parts of Canada and gives the results of observations at Winnipeg, Manitoba, during a cold spell

in January and February of an earlier year. Figure 2 gives the daily minimum temperature at Winnipeg during this period and also the changes

in closure of three stacks by frost, a 6-in. >ta. k and an 8-in. stack at the Grain Exchange and a 6-in. stack at the Civic Curling Rink. Unfortunately, we do not know how the daily minimum temperatures had varied just prior to tin- period in question, nor do we know what fixtures

discharged into the stacks, nor what wind velocities prevailed. It will be noted from figure 2 that the stack at the Curling Rink was enlarged

from 4 to 6 in. in diameter just before passing

through the roof, which in this case had a steep

slope. This roof vent extended only 1 in

above the roof on the high side. The other two

stacks at the Grain Exchange were not enlarged

before passing through the roof and extended 12

in. above the level of the flat roof. They were exposed on all sides. The opening in the S-in. roof vent was about

'

in. in diameter on January 24, the beginning ot the period of observation, and the daily minimum

temperature at this time was —25° F. Although

the temperature rose shortly after this date
Figure 2. Observations of frost closure at Winnipeg,

Canada.

reaching a value of +4° F on February 2, falling

thereafter to —32° F on February 6, the vent

continued to close up, until on February 6 it was completely closed. The daily minimum

temperature remained below —30° F until February 12, when the stack was next observed and was found to be still completely closed. Following this the temperature again rose, until on February 16 it was — 1° F, when it again

commenced to fall. The vent was observed on February 1 7 and was found to have opened partially,

the diameter of the opening being about 5.4 in. Thereafter the temperature fell erratically, ending

at —31° F on February 23, the last day of the

period of observation. At this time the opening

in the vent was about 5 inches.

The 6-in. roof vent at the Grain Exchange

showed similar tendencies to those of the 8-in. vent, but it closed up sooner than the latter. It

is, of course, possible that this vent might have

opened up a little between the January 29 and the

February 6 observations as a result of the warm

spell during the latter part of this period.

The 6-in. roof vent at the Curling Rink, which was enlarged from 4 to 6 in. in diameter below the

roof and which extended only a very short distance

above the roof, did not close completely at any

time during the period of observation, and the

diameter of the opening in the vent followed in a general way the fluctuations of temperature.

These observations of the frost closure of roof

vents are the most detailed of any that have, come

to the attention of the authors and tend to support

the conclusions given later in this paper as to the

behavior of roof vents in very cold weather.

Another unusual and interesting case of frost closure will be described here, although it relates

to the closure of a smoke stack from a stove rather

than the closure of a roof vent. The instance was

brought to the attention of the authors by Robert

F. Legget, Director, Division of Building Research,;

National Research Council of Canada. The; following is quoted from a letter from Mr. Legget:

Even though the record may sound fantastic, it may be of interest to you if I record the worst case 1 that has come to my attention. The winter of 1945-46 ji was an unusually severe one in the North of Canada. At a small place called Baker Lake, which you will find at the end of Chesterfield Inlet on the West side

of Hudson Bay, there are a few small buildings. One

j

5 of these is occupied by a Roman Catholic mission, i It is heated by an open stove with a metal smoke

stack extending through the roof and protected outside the roof in the usual way by a caribou hide. This is especially effective against the high winds that always I

1 blow at this location. One night during this bad winter the combination

of temperature and wind was such that the water ! vapor in the smoke stack coming from the fire started

to freeze on the sides of the chimney. Once having

started, it built up rapidly and eventually sealed the chimney tight, even though the fire was burning below. Two priests were severely gassed, but fortunately

got out of the building in time.

Ill response to a further inquiry, Mr. Legge

stated that this phenomenon occurred at least! twice in this building and that the fuel being1 burned was coal. Another example of frost closure has been called: to the attention of the authors through L. Glen

Shields, Chief Plumbing Inspector for the City

of Detroit, Mich. This instance occurred at the1 Hotel St. James in Ironwood, Michigan. This

hotel has 20 4-in. and 2-in. stacks of cast-iron soil pipe. The vents extend .about 2 ft above a flat' roof and are of the same diameter as the stacks.' The building drain did not contain a house trap!

On January 18, 1950, when the outside air tempera-l1 ture was —23° F, several of the 4-in. vents were1 observed to be completely closed by frost, and all' of the 2-in. vents were completely closed. All of

the other 4-in. stacks were partially closed. The

inspector who made the observations estimated

that at that time probably from 30 to 40 percent1 of all the vent stacks in Ironwood were partially! or completely closed by frost (see fig. 1). At the time of the observation the outside air, temperature was —23° F, and the temperatures^ on the preceding days had been as follows:

Preceding day Maximum Minimum

° F ° F

1st _ 0 -20

2d 5 -15

3d 20 + 5

The fixtures discharging into a typical 4-in. stack in the hotel were listed as follows: 4 bath- room groups and hot and cold process water. Although much consideration has been given to

1 the problem of frost closure of roof vents in Canada, and although the phenomenon has been ob-f

4
served, but not much commented upon, in the

United States, apparently no laboratory tests have been made to study the problem previously,

J nor does any analysis of the physical factors in- volved appear to have been made. Perhaps this

j may be due in part to the fact that, where frost closure is frequent and severe, methods of minii raizing it have been developed by empirical methods,

; some of which have proved very effective. Another

[ reason may be the difficulty involved in simulating

j service conditions in a laboratory test. Some of

these difficulties are not apparent at first sight,

I and the tests reported in this paper required a

j quite complicated setup before service conditions

could be simulated successfully.

4. Analysis of Conditions in Service

and Test Installations

The tendency for air to flow upward in plumbing

stacks and vents in cold weather, at least when

there is little or no water flowing down the stack,

j is due to the same principle as is involved in the

I action of a chimney. The phenomenon is due to the fact that the static pressure differential between the bottom and the top of the stack is

| greater outside of the building than it is inside of the stack, since the air temperature outside of the building is lower in winter than the temperai tore of the ah' inside the stack.

The static pressure difference outside of the

i building between the levels of the top and bottom

of the stack is determined by the weight of an air column of unit cross section extending between

these two levels outside of the building. The air

i inside of the stack, being at a higher temperature

than the air outside of the building during cold

weather, weighs less than the air outside of the

| building. Hence the column of air in the stack

will exert a smaller pressure at the bottom of the

| stack than the column of air outside of the stack,

or at least it would if it were stationary. The

result is that this difference in pressure of the two

columns, due to difference in density, is available

to create an upward flow of air in the stack, and

this flow is of such magnitude that the sum of the

pressure losses within the stack due to wall friction

to increases and decreases of diameter of the line, to bends in the line and to the creation of velocity

of flow', is equal to this pressure difference. In what follows it will be assumed that no

water is flowing in the stack. This condition will

exist in many buildings during a large part of the

time. Any small flow' of water down the stack

will decrease the convective flow' of air up the

stack, and for larger flowr s the direction of the

air current will be reversed, at least a portion of

this air ultimately being carried out through the

building drain and sewer to the street sewer. However, except in quite large buildings, the

probability of finding an appreciable flow' of water in the drainage stack at an arbitrarily chosen

instant of observation is rather small.

In this paper no account is taken of the -.light variation in density of the air vertically in a col- umn of uniform temperature. Taking this variation into account would scarcely change the remit - and would complicate the computations. Sine*

the tests conducted in this investigation -howf-d

that the air raising through the stack was nearly

saturated with water vapor, the densities assumed

for the relatively warm air inside the system were

those given for saturated air. On the other hand,

since air at temperatures far below the freezing

point of water can contain only a negligible

amount of water vapor, the densities assumed

for the cold outside air were those given for dry

air.For the sake of simplicity it has been assumed

that the building drain and the building sewer have the same diameter and the same coefficient of friction per unit length.2

4.1. Analysis of Service Installation

Figure 3 shows a stack with a short enlarged sec- tion at the top (the roof vent) and with a building drain and building sewer connecting to the

street sewer. The building drain and sewer are assumed to be of the same diameter, so that no

distinction is made between them in this drawing.

The following considerations govern the assumptions made as to the different air densities involved.

It is assumed that the temperature of the at- mosphere outside of the building is below freezing, so that the mass density Pis

3 of the air outside of the building is relatively high. Actually, as has

already been mentioned, the density varies a

little from the level of the top of the stack to the

ground level, but for simplicity an average value of pi3 is assumed to exist over this distance.

2 According to the Report of the. Coordinating Committee for a Xatioi Plumbing Code, the building drain extends from the base of the stack to . point 3 ft outside of the inner face of the building wall. The building ». u

extends from this point to the street sewer.

3 The subscripts “s” and “t” will be used to distinguish between tin service and the test systems discussed in this paper.

303316- .54 2
The temperature of the air in the street sewer,

the building sewer, and the building drain is as- sumed to be somewhat higher than that of the

outdoor air. Actually it may increase a little as the air flows from the street sewer, through the

building sewer and drain to the stack, but again

for simplicity we assume that the mass density

p2s of the ah' in this part of the system is constant

from the top of the manhole in the street sewer through the building sewer and drain to the base

of the stack.

Similarly, as the air rises through the stack and

roof vent, its temperature increases still further

until it reaches the exposed part of the roof vent,

where it will be cooled somewhat. However, for simplicity, it will be assumed that the mass density

pls of the ah in the stack and roof vent is constant. With these assumptions in mind, one can easily see that the pressure increase outdoors from the

level of the point “b” at the top of the roof vent

to the point “a” in the street sewer is given by

Pas pbs Pi sfi^lsT” P2s<7 Lys Lis) A

p

s . (la)

But as Ap= PyigAh, (2)

where pw is the mass density of water, and Ah is the height of water column in a manometer

corresponding to the pressure Ap, eq (la) may be

expressed as

h as — h bs —hLr Lis -\~— (Zis+Tiss —A-is) —Ahs. (lb)

P w Pw

If r is used for the ratio of the air density to the

water density, eq (lb) becomes

has hbs 7 4s-i'4s -

!-

?’2s (.Lis

~\~ L$s L4S ) Ahs

. (lc)

Now, as the ah in the stack is at a higher

temperature than the outside atmosphere, the

pressure difference between points “a” and “b”

under purely static conditions in the stack would

be less than that which actually exists between

these two levels in the outside atmosphere. As a result of this, air flows from the street sewer into

the building sewer (if there is no house trap in

the building drain), through the building sewer and drain, and up the stack at such a rate that

the pressure loss his due to wall friction, expansion

and contraction, and the creation of velocity

head, added to the static pressure difference

between the points “a” and “b,” measured inside

the system, is equal to the pressure difference

measured outside of the system.

Consideration of conditions inside the system

indicates that

has hfr s h f S T? lsfAig -

!- L^s ) . (3)

i

After substituting in eq (3) the value of haS —hhs from eq (lc) and reducing, the following expression for h ts is obtained:

h Is (.L] S -\~L^S Lis) C 2s 1 1s) d

- LiS {> 4s /is)- (4)

Thus we have derived formally the fact that

could have been predicted a priori, that the head

available to produce flow of air up the stack is determined by the difference in density of the

two static air columns between points “a” and

“b,” one inside the stack and the other outside

the building, and by the height of the system.

4.2. Test Apparatus

Figure 4 shows the arrangement of the test apparatus that was used for the experimental

work. A 3-in. stack-vented, single-story-withbasement sj'stem was erected, complete with

water closet, bathtub, lavatory, and kitchen sink.

A pump supplied water for discharge through the

bathtub at a constant rate and at anv desired

H

Figure 4 . Test apparatus.

A, Orifice plate; B, damper; C, large fan: D, device for measuring carbon

dioxide content of air; E, inclined manometers; F. thermostat for automatic

control of large fan, C; G, small fan; H, remote temperature indicator;

I, electrical connections to thermocouples at points 1 to 10; J. manometer

tube; K, small ice chamber; L, lavatory; M, wet- and dry-bulb thermometers; X', bathtub; O, sink; P, water pump; Q, water supply; R, roof vent;

S, spill basin; T, thermometer; U. immersion heater with thermostatic

control; V, drain; W, water closet; X, air blower; Y, exhaust pipe; Z, overflow weir.

6
temperature. An automatic device connected to the water closet flushed the closet at regular

intervals of time. At the top of the stack an

insulated cold chamber in the form of a cube

approximately 3 ft on a side (inside dimensions)

surrounded the stack terminal or roof vent. This

chamber was fitted with windows for making

observations and with a door for maintenance of the test equipment located in the test chamber and

for checking the accumulation of frost in the vent

pipe. A rack was provided on which approximately 200 lb of “dry ice” (solid carbon dioxide)

could be placed. This provided the means by

which a very low temperature could be maintained in the chamber.

A fan mounted above the dry ice, actuated bv means of a thermostatic control unit mounted

near the terminal of the stack, circulated air in the chamber whenever required to maintain the

temperature approximately constant at the value

determined by the setting of the control unit.

The control unit stopped the circulating fan

whenever the temperature of the air in the chamber

was reduced to the value to which the control

unit was adjusted.

A smaller fail nearer the stack was run continually in order to simulate a breeze blowing over

the rooftop and to cause a more nearly uniform

temperature distribution along the portion of the

stack inside the cold chamber. A section of 3-in.- diameter plastic pipe about 5 ft long was set in the top of the cold chamber to provide means by

which the air from the stack and the gaseous

carbon dioxide from the dry ice could pass freely

from the cold chamber to the external atmosphere;

otherwise the chamber was made as nearly air- tight as possible in order to prevent undue heat

loss and to make it possible to measure the flow

of au in the stack. This section of pipe contained an orifice for the purpose of measuring the rate of

air flow through the system; and, since the orifice could be observed through the transparent plastic

pipe, it could be kept free of frost in order that the

readings might be reasonably accurate. A closed chamber surrounded a perforated section of the house drain. A blower discharged air through a valve into this chamber, and by appropriate adjustment of this valve the desired pressure

differential could be maintained and the rate of

air flow through the system could be controlled.

The air entered the house drain through a number

of %-in. -diameter holes having a total cross- sectional area equal to the cross-sectional area of

the 3-in. house drain. In this way the frictional resistance due to the air entering the drain was

probably greater than if it had entered through

an open end of the 3-in. drain, since the entrance was through a number of small orifices in a direction at right angles to the direction of flow in the

drain. This, of course, resulted in a head loss as

a result of the change in direction of the inflowingair through an angle of 90°, similar to the effect of introducing the air through a 90° elbow of small

radius of curvature. In effect, this arrangement

probably simulated a house drain and sewer of a length that might be expected in service, but whieh

space limitations prevented in the test installation. Water occupied the part of the chamber belov. the drain. The temperature of the water was

controlled by means of an immersion heater, -o that any desired temperature above room tomperature could be maintained. Some of this hot

water was pumped up to the bathtub from which

it flowed in a steady stream at a rate of about 1 .8 gal/min into the stack and returned through tin- drain to the supply chamber.

A slot was cut in the bottom of the drain, so that

the flow of hot water from the bathtub would b<- returned to the supply chamber without loss, whereas a large flow of cold water, such as tin- discharge of the water closet, would for the most

part pass on through the drain into the spill basin,

so that there would be no great amount of cooling

of the warmer water in the supply chamber dm

to the addition of relatively large quantities of cold water. The house drain terminated in a 90° bend

turned downward into the spill basin to form a water seal, which prevented the escape of air from

the drain by this route. During very hot weather it was found that it was impossible to keep the average temperature

of the air in the stack as low as was desired in some of the tests, and, if the weather turned hot

during a test run, it was sometimes impossible for the existing apparatus to keep the stack temperature at the value selected at the beginning of a run. Hence an additional chamber was mounted

near the blower and was filled with dry ice, so that

by proper valve adjustment part of the air supplied by the blower passed through this chamber

By using this source of cooling, it was found possible to maintain the temperature of the air in the

stack at the desired degree.

Inclined differential monometers were used to measure pressure differences between the pressure

chamber enclosing the house drain and the chamber enclosing the roof vent and between opposite

sides of the orifice plate in the outlet tube from

the cold chamber.

The concentration of carbon dioxide in the

mixture of air and carbon dioxide passing through

the orifice was measured by a device that operated on the principle of absorption of the carbon dioxidt

from the mixture by means of a potassium hydroxide solution.

Temperatures inside the cold chamber, at five points in the air stream in the stack, at one point

in the air stream passing through the orifice plate,

and at two points in the wall of the section of vent pipe inside of the cold chamber, were measured

by means of a remote recording device connected

to thermocouples placed at the various points s< fig. 4). Temperatures of the room air surrounding the test setup and water temperatures wet measured by means of ordinary mercury-in gla<s

thermometers. Humidity determinations insuh
the stack were based on wet- and dry-bulb

thermometer readings taken at a point about 5 ft above the level at which the bathtub drain con- nected to the stack. These thermometers were

fitted with rubber bushings, which were inserted

into holes in the stack wall. Humidity deter

minations of the air in the room surrounding the

installation were also based on wet- and dry-bulb

thermometer readings.

In this connection, it is quite likely that the

humidities obtained for the air in the stack were somewhat greater than the actual values, since

the velocities in the stack probably were inadequate to lower the wet-bulb temperatures to their

full extent. However, this possibility Avas over- looked at the time the tests were made.

4.3. Analysis of Test Installation

There are three sets of conditions to consider in connection with the test installation: (1) conditions outside of the system, (2) conditions inside

of the system (i. e., inside of the stack and buildingdrain), and (3) conditions in the manometer line

(see fig. 5).

a. Conditions Outside of System

Corresponding to eq (lc) applying to the

sendee system, the following equation applies to the test system:

^ at' Kt~ +>2 1 (-£ 1 1 +-^3t = Ah t . (5) However, in the tests made in this investigation

the stack was mounted inside of a building at

'

ordinary room temperatures and thus Avas not

subject to as great a difference in static head as would exist under service conditions in cold

weather betAveen the outlet of the building sewer ; and the top of the roof vent, OAving to the lesser density of the air at room temperature compared

with that of air at, say, —30° F. Hence, to pro- duce a floAv of air through the test system comparable to that Avhich would occur in actual Avinter service, it Avas necessary to create artificially an

additional difference in pressure head, he , between

points “a” and “b” through the stack. In the

test installation this Avas done by means of a

bloAver, as has been explained earlier. The head

produced by the bloAver ranged from a few liun- 1 dredths to a few tenths of an inch of water column. [ In order to produce the same difference in static pressure between points “a” and “b” as Avould

exist in a similar installation in cold-Aveather I

service, the folloAving relation must be satisfied:

it

hjat [ he

- A'bt ^ as hbs

. (0) ;

b. Conditions Inside of System

Corresponding to eq (3) for the service installation, AA’e have for the test installation:

i ha.t-\-he —hbt =htt-\-rlt (LWrL3t ). (7) >

£ We can substitute in this the value of hat —hbt from eq (5) and sol\T e for h u , obtaining:

t

htt = (Ln-\-

3 t t rlt ) +Litifix, ^it)T^e- ;jj (8) b

ti c. Conditions in Manometer Line

f The auxiliary pressure created by the blower

Avas measured by a manometer mounted on a level with the top of the roof vent. A relation between

the reading hm of the manometer and the pressure , head he will next be derived. We can see intuitively

j

• that he must be approximately equal to hmt but, ;

if Ave Avish to demonstrate this formally, we note j from a consideration of figure 5 that the folloAving

relation holds for the manometer line:

hstt —hbt -\-h e —hm

-\- r4 ,i4t +r2t {Ln

J

\r L3t —

4t)

(9)

!

Actually the value of r4t inside of the manometer line will be a little greater than in the outside ah because of the slightly higher pressure in

the manometer line. Consideration of this pres- sure difference, using the gas laAv, shoAvs, hoAvever,

that the difference was not more than 0.1 percent

in any of the tests, so the effect will be neglected,

j Hence, if Ave subtract eq (5) from eq (9), we obtain:

he =hm . (10)

| 8
Figure 6. Air-water density ratios for different temperatures.

Figure 6, giving the values of r over the range

of temperature in which we are interested, has

been prepared for convenience in computing. As

has been stated, for the lower temperatures the

ah- was assumed to be dry, while for the higher

temperatures inside the stack the air was assumed

to be saturated.

5. Friction Losses Involved in the

Upward Flow of Air in the System

In what follows it should be remembered that we are considering only the case hi which no water

is flowing in the drainage system. In order to evaluate the losses of head, h ts and hit , it is neces- sary to consider the drainage system in detail

(see fig. 3). The head losses in the system can be considered

as belonging to three classes: (1) losses due to the

frictional resistance to flow hi straight pipes; (2) losses due to change in direction or to changes in cross-sectional area; and (3) losses required to create velocity of the ah’ in the system. The

first of these can be computed from the DarcyWeisbach equation:

Ah=f

7i d < lla) where

Ah =the head loss hi terms of height of the

fluid flowing—in this case, air /=the dimensionless Darcy-Weisbach fric- tion coefficient

L =the length of the pipe

d=the internal diameter of the pipe

r=the mean velocity of flow in the pipe

.9 =the acceleration of gravity.

The second class of losses can be expressed b\ >i coefficient multiplied by the velocity head; so. again multiplying by r in order to obtain A// in height of water column:

ah=rK^, (12)

where A is a constant. The third type of loss is that due to the kinetic

energy of the air issuing from the roof vent and

can be expressed by an equation similar to eq 12

5.1.

Head Loss at Transition From Street

Sewer to Building Sewer

We assume that the energy loss, expressed as head of air, is equal to half the velocity head, as

is customary where a square-cornered entrance is involved. The loss of head required to create the

velocity v2 , the mean velocity of air flow in the

building sewer and building drain, will not be

added, since, if we take account of the energy

losses (not transformations of energy) from point

to point along the system, we need only to allow

for the head loss required to create the velocit

v3 of the ah’ issuing from the roof vent. Herne

the loss of energy head at entrance to the building sewer is given by

or, since we shall find it convenient to express all losses in terms of the velocity head in the stack

Ah=

l

r2 (|) Yg

(13a

5.2.

Head Loss In Building Sewer and Drain

Usually the building sewer and building drain

comprise a single line of the same diameter and

slope, being physically indistinguishable from each

other. The distinction is made solely for administrative purposes. Hence, in what follows they

will be treated as a unit, the line having the diameter d2 and the length L2 . The loss due to friction

in this line is given by

Ah=r2f

U I diV v'i

</_. ' d 2g

(13b)

In order that Ah may be measured in height of water column, it is necessary to multiply the

right member by the ratio r of the density of air under the assumed conditions to the density of

water, since a water manometer was used to measure values of Ah. Thus, when Ah is measured in height of water column, we have

Ah=rf 7ihi

(llb)

5.3.

Bend Loss at Entrance to Stack

5.4.

Head Loss at Contraction, Upper End of

Bend

In general the stack may be smaller in diamcici

than the building drain. Then the lo<> due to
contraction is

Ah—/'

i ( ( v\ 2 9

(13d)

CQ , the contraction coefficient, can be evaluated

from tables given in various hydraulics textbooks,

for example, Dodge and Thompson, Fluid mechanics, first edition, page 215.

5.5. Head Loss Due to Friction in Stack

(13e)

. , , Li v\ Ah=r' f dt W

5.6. Head Loss at Transition to Roof Vent

The transition from the stack to the roof vent

if they are not both of the same diameter—may

be either a contraction or an expansion. If it is a contraction, the loss is given by

(13f)

and Cc can be evaluated as explained above. If

it is an expansion, it is given by

(13g)

where Ce =[l —(di/d3)

2

] 2

.

5.7. Head Loss Due to Friction in Roof Vent

(13h)

where d3 is the diameter of the opening in the vent,

which depends on the thickness of the layer of

frost, if such a layer is present.

5.8. Head Loss at Outlet of Roof Vent

Because the outlet is square-cornered, it will be

assumed that all of the kinetic energy of the issuing

air is lost. That is, there is no recovery of head at

exit. However, we must include in the equation

for the loss of head in the system the velocity head

of the air issuing from the roof vent because a loss of head was required to create this velocity.

Hence

(13i)

This procedure is not strictly correct because some of the changes of velocity in the system occur

at the temperature d2 and some at temperature 6 U under the assumptions made. However, the dif- ferences involved are so small as to be neglibible

in the problem.

The total loss of head in the system is the sum

of the above head losses, or

h

+r i ^ u—h D, m

L,

<r3/ ; J

vi 2 g

Table 1. Pressure differentials h/ in feet of water column tending to -produce convection in stacks of different heights

Height

of stack

L\-{-Li b

“Temperature differences (°F)

110 100 90 80 70 60 50 40 30 20

ft 20 0. 0056 0. 0050 0. 0044 0. 0039 0. 0034 0. 0030 0. 0025 0. 0020 0. 0016 0. 0012

30 . 0093 .0082 .0072 .0064 . 0056 .0048 . 0036 . 0033 .0026 .0019

40 .0130 .0115 .0100 .0089 .0077 .0067 .0056 .0045 .0035 .0026

50 .0166 .0147 .0128 .0114 .0099 .0085 .0072 .0057 .0045 .0032

60 . 0203 .0179 .0156 .0139 . 0120 .0104 .0087 . 0069 .0054 .0039

70 .0239 .0211 .0184 .0165 .0142 . 0122 .0103 .0082 .0064 .0046

80 .0276 . 0243 .0212 . 0189 .0163 .0141 .0118 .0094 .0073 . 0053

90 .0312 .0276 .0240 .0214 . 0185 .0159 . 0134 .0106 .0083 .0060

100 . 0349 . 0308 .0286 .0239 .0206 .0178 .0149 .0119 .0092 .0066

» Temperature of the air in the stack and vent is taken as 60° F. Temperature of the air in the street sewer, manhole,

building sewer, and building drain is taken as 50° F. The temperature difference is the algebraic difference between the temperature of the air in the stack and that of the outside air.

b L\-\-Li— Li=5 ft.

(14)

(In this equation, Ce is to be replaced by Ccbh/dg)4

if there is a contraction instead of an expansion.

If neither, Ce and Cc are both equal to zero.)

Now, inserting the proper values for the density

ratios, the lengths, the diameters, and the coeffi- cients, and computing ht from eq (4), we can solve

eq (14) for vx

. The following assumptions are made in the

computations that follow: The diameters of the

house sewer, the house drain, the stack, and the

roof vent are all the same and will be represented

by di. Of course, as the vent frosts up, its diameter Avill decrease, and, under these conditions will be represented by d3

. The total length of house

sewer and drain is 50 ft. We adopt the following

10
HEIGHT OF STACK , FEET Figure 7. Pressure differentials tending to cause convection due to temperature difference between outside air and air in

stack.

(See footnote to table 1 for air temperatures assumed.)

values: /= 0.03, (?b =0.23, and g=32.2 ft/sec

squared.

Values of h t computed from eq (4) are tabulated

in table 1 and are plotted in figure 7 for various

differences in temperature between that of the

outside air and the air in the stack and for heights

1 of stack up to 1,000 ft.

(

Table 2 gives velocities of air flow in systems in which the building sewer, building drain, stack,

and roof vent are all 3 in. in diameter for stacks

up to 60 ft in height and for temperature differ- ences ranging from 30 to 90 deg F. In this and

all the following cases for which computed velocities are given, it is assumed that the total length

of building drain is 50 ft. The temperature of the

air in the building drain and sewer is assunied to be 50° F. and that in the stack is assumed to be

60° F. Outside air temperatures are selected to give the desired temperature differences.

Tables 3, 4, 5, and 6 give air velocities in 4-in.,

6-in., 8-in., and 12-in. systems for stack heights

!

up to 1,000 ft in the case of the 8-in. and 12-in. stacks.

Table 2. Air velocities in stacks due to convection

Pipe diameter throughout system, 3 in. a

Height of stack L1+L3

Temperature difference (° F)

30 40 50 60 70 80 90

ft fps fps fps fps fps fps fps

20 2.9 3.2 3.6 3.9 4. 2 4.5 4.8

40 3.8 4.4 4.9 5.3 5. 7 6. 1 6.5

60 4.4 5.0 5.6 6.1 6.5 7.0 7.4

a Length of house sewer and house drain, 50 ft.

Table 3. Air velocities in stacks due to ccmvectir/n Pipe diameter throughout system, 4 in. >

Height of stack

Temperature difference (° F)

30 40 50 60 70 80 90

ft fps fps fps fps fps fps fps

20 3.2 3.6 4. 1 4.4 4.7 5.

5. 4 40 4.3 4.9 5. 5 6.0 6.4 6.9 7.3

60 4.9 5.6 6.3 6.9 7.4 8.0 8.4

80 5.4 6. 1 6.8 /. O 8.0 8.6 9.2

100 5.7 6.4 7.2 7.9 8.5 9.1 9.7

“ Length of house sewer and house drain, 50 ft. Table 4. Air velocities in slacks due to convection

Pipe diameter throughout system was 0 in.

Height of stack

Temperature difference (° F) L1 +L3 30 40 50 60 70 80 90

ft fps fps fps fps fps ' fps fPS

50 5.5 6.3 7.0 7.6 8. 2 8.

9.4

100 6.8 7. 7 8.6 9.4 10. 1 10. 9 11.5 200 7. 7 8.8 9.8 10.8 11.6 12.5 13.2 300 8.

9.3 10.4 11.3 12.2 ! 13.2 13.9 400 8.4 9.6 10.7 11.7 12. 6 I 13.

14.4

500 8.5 9.7 10.9 11.9 12.8 13.8 14.6

“ Length of house sewer and house drain, 50 ft. Table 5. Air velocities in stacks due to convection

Pipe diameter throughout system, 8 in. J

Height of stack L1 +L3

Temperature difference (° F)

30 40 50 60 70 80 90

ft fps fps fps fps fps fps fps

50 6. 1 7.0 7.8 8.5 9. 1 9.9 10.4

100 7.6 8.6 9.7 10.5 11.4 12. 2 13.0 200 8.8 10.0 11.2 12.2 13.2 14.2 15.0

300 9.3 10.6 11.8 12.9 13.9 15.0 15.9

400 9.6 10.9 12.2 13.4 14.4 15. 5 16. 4 500 9.8 11.

12.5 13.6 14.7 15.

16.7

600 9.9 11.3 12.6 13.8 14.9 16.0 17.0 700 10.0 11.4 12.8 13.9 15.0 16.2 17. 1 800 10. 1 11.5 12.9 14.0 15.

16.3 17.3 900 10. 1 11.5 12.9 14. 1 15.2 16.4 17.4 1,000 10.2 11.6 13.0 14.2 15.3 16. 5 17. 5

» Length of house sewer and house drain, 50 ft. Table 6. Air velocities in stacks due to con’-

Pipe diameter throughout system, 12 in.’

Height of stack

L\-\-Lz

Temperature difference (° F)

30 40 50 60 70 so 90

ft fps fps fps fps fps fps fps

50 7. 1 s.o 8.9 9. 8 10.

11.3 12.

100 8.9 10. 1 11.3 12. 3 13.

14.3 15. 1 200 10.4 11.8 13.3 14.5 15.6 16.8 17.8 300 11. 1 12. 6 14.2 15. 5 16. 7 18. 0 19.0 400 11. 5 13. 1 14.7 16.0 1 17.3 IS. 6 19.7 500 11.8 13.4 15. 0 16.4 17.7 19. 1 20. 2

600 12.0 13. 6 15.3 16. 7 1 IS. 0 19.4 20. 5

700 12. 1 13.8 15.4 16. 9 18. 2 19. 6 20. 7 800 12.2 13.9 15.6 17.0 18.3 19. S 20.

900 12.3 14.0 15.7 17.1 18* 5 19* 9 21. 1 1,000 12.4 14. 1 15. S 17.2 18.6 20.

21.2

" Length of house sewer and house drain, 50 ft.

11
Table 7. Air velocities in stacks due to convection Data from Gray

Temperature

differ- ence

Height of stack

Stack diameter (in.)

2 3- 4 a 6

deg F ft fps fps fps • fps fps

20 20 1.88 2. 25 2. 47 2.80 3. 17 20 50 2. 78 3. 55 3. 90 — —

25 20 1.97 2. 52 2. 77 3. 12 3. 53

25 50 3. 07 3. 97 4.37 4.95 5. 58

30 20 2.15 2.75 3.02 3. 42 3. 87

30 50 3. 40 4. 33 4. 78 5. 42 6. 12

By comparison, the data given by Gray [3] on

the velocity of flow of ah' in stacks due to con- vection are given in table 7. He does not state

all of the assumptions he made in computing these

values, but it will be observed that his results fit very well the results given in the tables referred

to above.

It should be emphasized that the values given

in tables 2 to 6, inclusive, apply only when no

water is being discharged into the stack and when

there is no closure of the vent by frost. In

addition, these values have been computed on the

assumption of straight stacks without horizontal

branch or vent connections. Obviously these

assumptions give computed velocities somewhat

greater than those that occur sometimes in service.

However, owing to the many variables inherent in the many types of plumbing drainage systems in service, it is necessary to make certain simplifying

assumptions in connection with such computations. It is believed that the values in the tables

above give at least a rough estimate of the maximum convective velocities to be expected in stacks.

6. Physics of Frost Closure of Roof

Vents

6.1. General Considerations

The closure of a roof vent by the formation of a layer of frost on the inner surface of the vent is a complicated process which it is not feasible to discuss with any great degree of accuracy. However, the general physics of the process is quite

clear and leads to certain conclusions, some of which are at variance with commonly accepted

ideas today. The process will be discussed at considerable length here, therefore, both for the

purpose of achieving a clear understanding of the

principles involved in the process and for pointing

out the way in which any further investigation

might best be carried out. The partial or complete closure of a roof vent

by frost in cold weather requires that a more or

less steady current of warm moist air flow up

through the stack and roof vent. If the system

does not contain a house trap, then this air comes

from the street sewer and is relatively moist and

warm. If there is a house trap in the building

drain, then a fresh-air inlet is ordinarily required on the house side of the trap ; and in this case the | current of air flowing up the stack is much cooler

than in the first-mentioned case and is less pro- nounced. It is also much drier when it enters the

system.

When water is discharged intermittently from i fixtures that drain into the stack, the upward cur- rent of air may become quite erratic, and, at times when considerable water is discharging, its direction may be reversed. However, during

many hours of each day little or no use is made of

the plumbing fixtures, and the upward current is fairly steady.

The air flowing upward through the stack,

partially or completely saturated with water

vapor, is chilled by heat loss to the cold interior

surface of the roof vent. This causes condensation or deposition of water on or the adhering of

ice particles to the surface. If the inner surface

of the vent is below 32° F, the water freezes or the

ice particles adhere, forming an ice or frost deposit ; if it is above 32° F, the deposited water

runs down the inner surface of the stack. The

temperature of the inner surface of the vent, j exposed to the current of air flowing upward in

the stack, is thus a controlling factor in the for- < mation of a frost deposit. Under steady conditions of outdoor weather and air temperature in the stack, the temperature of the inner surface of the vent depends on the temperature of the outside air and the wind velocity, on the insulating

effect of the vent pipe and the frost deposit, and

on the temperature and velocity of the air flowing- in the vent pipe.

As the frost deposit builds up, it acts as insulation to reduce the flow of heat from the stack air to the outdoor air and consequently to raise the

j temperature of the frost deposit exposed to the

stack air. If the ice-air surface rises in temperature to 32° F, further moisture deposits will remain

liquid and will drain down the stack, and the frost deposit will not thicken any further. The calculations presented in this paper are for the purpose of estimating for any particular stack vent under | steady temperature conditions the extent to which j frost deposits may be expected to build up in the

vent pipe.

The rate at which moisture or frost particles may

be deposited, and, therefore, the rate at which a. frost deposit may thicken, increases, other things

being equal, as the humidity of the air stream

increases. Whether a given vent will freeze closed

during a particular spell of cold weather may thus j depend on the rate of moisture deposition and so, to a considerable extent, on the humidity of the

stack air. The exposed length of the vent pipe is of obvious

importance in connection with this phenomenon,

since the available area for chilling the stack air and, therefore, for abstracting its accompanying

moisture, is increased with increased length of vent.

12
while the effect of conduction of heat upward in the

wall of the vent pipe from the warmer length below

| is Reduced.

6.2. Heat Transfer in a Roof Vent

It is assumed that warm air at the temperature

. 9i. saturated with water vapor, is flowing upward

through the vent with velocity r3 . From the

standpoint of heat transfer, the general problem is that of a warm fluid flowing in a cylindrical pipe or

shell, with heat transfer to the shell, and thence

through the shell to the colder air or wind beyond

it. The heat transfer phenomenon is a complicated one, partly because of the existence of a boundary layer near the pipe wall in the air stream

and partly because changes of state occur in the

air stream as it loses its moisture in passing through

the vent.

It has already been stated that, as the saturated

or nearly saturated air chills while passing up

' through the roof vent, some of the water condenses

; to form drops of moisture. Under some conditions

| some of this moisture may freeze while still in the

i ail- stream. As the layer of ice in the vent

increases in thickness, the resistance that the vent

1 offers to the flow of air increases, with the result

that there is a decrease in the velocity of the air stream in the stack, but an increase in the velocity

of the air stream in the vent (see fig. 8). When

this happens, a smaller amount of moisture passes

through the vent in a given time than when the

latter is unobstructed, but, on the other hand, the area of the surface on which moisture can deposit

is reduced to a greater extent than is the volume of

flow. Owing to these facts and to the further fact that

there are two changes in state occurring in the vent

pipe, i. e., from vapor to liquid and from liquid to

DIAMETER OF OPENING IN VENT, INCHES Figure 8. Changes in air velocities in a 3-in. stack and

vent as the vent freezes up.

Height of stack, 40 ft; length of vent affected by frost, 1 ft; and temperature difference, 90 deg F. (See footnote to table 1 for air temperature

assumed.)

solid, with consequent release of heat, it is obviouthat it would be an extremely difficult and complicated task to compute accurately the rate of beat transfer from the air stream to the inner call of the vent, nor do the practical aspects of the

problem warrant such an attempt. However,

formulas are available for the transfer of heat

from an air stream to a chilled pipe wall when no

changes of state occur, and one of these formulas

will be used here, an estimate being included for the effect of the changes of state that occur. Figure 9, showing the cross section of a vent, gives

the nomenclature used in what follows.

a. Transfer of Heat From Air Stream in Vent to Inner Wall of Vent

The general equation for the transfer of heat

from the air stream to the wall is [4, p. 3]: q=KSAd, ( 15) where

2= the rate of heat transfer through the sur- face involved

ix =the coefficient of heat transfer, which

varies with the velocity of air flow and

other quantities (see eq 17 and 24)

5*= the area of the surface in question

A0=the difference in temperature producing

the flow of heat.

Applying this equation to the transfer of heat

from the stream of air in the vent to the wall of the

pipe or to the ice surface, as the case may be, we

write eq (15) as follows:

2s3 =-^s3$30s3 =27T/'3.K’33083, (16 I

Figure 9. Nomenclature used in heat tra> s

303.316—54 3 13
where

gS3— the rate of heat transfer from the air stream to the wall Kb3 =the coefficient of heat transfer from the

air stream to the wall

1the 1 aclius of the cylindrical opening in the vent ^3 = the area of the inner wall= 27rr3 , since

., unit length of vent is being considered ^3—the difference m temperature between the

wall and the air stream. lo evaluate #s3 , the equation given by Mc- Adam applying to this case is used [4, p. 168]:

T*-0.028(*lT(¥T' <'7)

the notation being adapted to the present problem in this equation

d3 =the diameter of the cylindrical opening in the vent, in feet /f=the coefficient of thermal conductivity of the air, in Btu/(hr) (ft) (deg F)

(

i> the specific heat of the air at constant

pressure, in Btu/(lb) air (deg F)

Pi =the weight density of the air in the stack

and vent, in lb/ft 3 the absolute viscosity of the air in lb/'(hr)

«3 =the velocity of air flow through the vent m ft/hr.

Equation 17 gives the value of the coefficient

of heat transfer As3 for the case of a fluid flowing through a chilled pipe, under the conditions that

the viscosity of the fluid is not more than twice that of water and for Reynolds numbers exceed- mg .,100, in other words, for turbulent flow.

1 hese two conditions are fulfilled in the problem under consideration, except that, for very low velocities m the smallest vents, the Reynolds number

above ^ somewhat ,ess than the value specified va

j uc, °f 0.78 can be taken as an average for

Cpn/k. Substituting this in eq (17), we obtain

#83 = 0.027

c p (p iP 3)°-V- 2 dV ’ (18)

which is in agreement with McAdam [4, p. 1741. the coefficient 0.027 will be increased to 0 030 ar- bitrarily m an attempt to allow for heat generated bv the changes m state referred to earlier. If this change is made, an average value of 0.0435 is as- sumecl for M, and a value of 0.25 is assumed for c„ eq (18) reduces to the form

Ks .0.004 ( Pl v 3) 0 - 8

If this value of As3 is substituted in eq (16) the' following expression is obtained:

2s3 =0.004 S

(p iv 3)°-

3 dV dB3 — 0.0047r(p : p 3 d3)

0 - 8

i9 8 3. (20);

This last equation gives the rate of heat transfer

le tween the air stream in the vent and the inside I surface of the vent (metal or ice) in British ther- 1 mal units per hour per foot length of vent.

b. Transfer of Heat Through Ice Layer and Pipe Wall

The equation for the transfer of heat through

a cylindrical shell is [4, p. 8]: S

2=i

2-k k,„L

AO,

(21 \n(x ) 0/xi) where

£m = the mean thermal conductivity of the material of the shell L=the length of the cylindrical surface of the

shell Av* i = the radii of the outer and inner walls re- spectively, of the shell A0=the difference in temperature between the

inner and outer walls of the shell. Using eq (21), and taking the length of the cyl- inder, L as unity, 2si> the rate of heat transfer

c finder1Ce aye1'’ bec0meS) Per unit length of

27t/l 31 4!l=Eyy3e”- (22)

Similaily, (/jo, the rate of heat transfer through I the pipe wall, becomes

2 io = ln(r0/r,) (23)

c. Transfer of Heat From Outer Wall of Vent to Outer

Air

I he roof vent, extending vertically upward from a flat roof, may be looked upon as a single heated cylinder in a stream of cooler air flowing

at light angles to its axis. The flow of air thus

represents the wind blowing past the vent For

this condition McAdam [4, p. 221] gives a curve

of the relation between Kdjk plotted against the Reynolds number, r/0

?>4p4 /p, which applies to this case and extends to nearly the highest values

of the Reynolds number that will be involved in the following computations. In the above Reynolds number, v4 is the velocity of the wind in feet per hour, and p4 is the weight density of the out- door air in pounds per cubic foot. This curve was used in the computations that follow, and the

relation that it gives can be represented by the

equation, J

where \p is a functional symbol.

(19)
Substituting the value of A'oa given by eq (24)

in eq (15), we have for tlie rate of heat transfer

from the outer wall of the vent pipe to the outer atmosphere:

q 0>=S0 ~ i 0oa=2x/.Ji oa 0 oa) (25)

where q0

and 6> oa are the rate of heat transfer per

unit length of pipe, and the temperature difference

between the outer wall and the air, respectively,

S0 is the area of the surface of unit length of the outer wall of the vt nt, d0 is the outside diameter,

and r„ the outside adius of the vent.

d. Computation of the Temperature of the Ice-Air

Surface in the Vent

The problem is to compute the variation of the

temperature of the ice-air surface in a given vent

for any set of assumed conditions as the vent

freezes up. If, at any stage of the icing prove-- the temperature of this surface rises to .‘52' F

the freezing will not continue further, and the pipe

will remain only partly closed. If, on the other

hand, the temperature of this surface doe- riot n-e

as high as 32° F during the process of freezing,

then the freezing will continue to complete

closure, provided the conditions remain constant

for a sufficiently long period.

The computations will be given in detail for a 3-in. vent in what follows. We assume a particular system in which the building drain and

sewer, the stack, and the vent are all 3 in. in diameter. It will be assumed that the building sewer and drain together are 50 ft long and that

the stack, including the roof vent, is 40 ft high.

For the sake of concreteness, it will be further

assumed that the vent projects 1 ft above the

roof, although this assumption is not essential

to the problem. The air temperature in the

Table 8. Computation of coefficient of heat transfer from air stream in 3-in. vent to inner wall of vent

Temperature of air in vent, 60° F; weight density of air in vent, p\, 0.075 lb/ft8

; ir8 3=0.004

(3,6QOpif 3 ) 0 - 8 Ms) 0 ' 2

Diameter opening in vent, dz

Temperature of outside air

Velocity of

air in vent 3,600pifl3 (dz) »-2 A',3 n

To 11

T\

in.

3. 07

ft

0. 256

° F

-30

fps

6. 49

Ibiffthr 1,750 395 0. 762 2. 08 0.877 1.00

3. 07 .256 -20 6. 13 1,655 375 . 762 2. 00 .877 1.00 3.07 .256 -10 5. 75 1,555 360 .762 1.89 .877 1.00 3.07 .256 0 5.31 1,435 335 .762 1.78 .877 1.00 3.07 .256 +10 4.90 1, 325 315 . 762 1. 66 .877 1.00

3. 07 .256 +20 4. 35 1, 175 285 . 762 1. 50 .877 1.00

2.5 .208 -30 9. 23 2, 490 520 .731 2. 85 .714 0.814

2.5 .208 -20 8. 80 2, 375 500 .731 2. 73 .714 .814 2.5 .208 -10 8. 25 2,230 475 .731 2.60 .714 .814 2.5 .208 0 7. 57 2, 045 450 .731 2. 44 .714 .814 2.5 .208 +10 6. 92 1.870 415 .731 2.28 .714 .814 2.5 .208 +20 6. 22 1,680 380 .731 2. 08 .714 .814

2.0 . 167 -30 12. 85 3, 470 680 .699 3.90 .571 .651 2.0 . 167 -20 12. 15 3,280 650 . 699 3. 72 .571 .651 2.0 . 167 -10 11.30 3. 050 615 .699 3. 52 .571 .651 2.0 . 167 0 10. 50 2, 835 580 .699 3. 32 .571 .651 2.0 . 167 +10 9. 62 2,600 540 .699 3.09 .571 .651 2.0 . 167 +20 8. 63 2, 330 495 .699 2. 84 .571 .651

1.5 . 125 -30 17. 25 4, 660 860 .660 5.20 .429 .489

1. 5 . 125 -20 16.15 4, 360 820 .660 4. 96 .429 . 489 1.5 .125 -10 15. 15 4, 090 775 .660 4.68 .429 . 4S9

1.5 .125 0 14. 10 3,810 730 . 660 4. 42 .429 .489

1.

.125 +10 12. 90 3, 480 680 .660 4. 12 .429 .489

1.5 . 125 +20 11.60 3, 130 625 .660 3.88 .429 .489

1.0 .0833 -30 20. 55 5, 550 990 .608 6.51 .286 .326

1.0 .0833 -20 19. 35 5, 225 945 .608 6.21 .286 .326

1.0 . 0833 -10 18. 15 4,900 895 .608 5. 88 .286 . 326

1.0 .0833 0 16. 80 4, 535 845 .608 5. 56 . 286 .326

1.0 . 0833 +10 15. 40 4,160 785 . 608 5. 16 . 286 .326

1.0 .0833 +20 13. 75 3, 720 720 .608 4. 74 .286 . 326

0.75 .0625 -30 21.40 5,780 1,025 .575 7. 12 .214 .244

.75 .0625 -20 20.20 5,455 975 .575 6. 78 .214 .244 .75 .0625 -10 18. 75 5, 065 920 . 575 6. 40 .214 . 244 .75 .0625 0 17. 55 4, 740 875 .575 6. 08 .214 . 244

.75 .0625 +10 16. 10 4, 350 815 .575 5. 68 .214 . 244

.75 .0625 +20 14. 30 3, 860 740 .575 5. 15 .214 .244

.50 .0417 -30 22. 10 5, 970 1,050 .530 7. 92 . 143 . 163 .50 .0417 -20 20. 80 5, 615 1,000 . 530 7. 55 . 143 . 163 .50 .0417 -10 19. 35 5, 225 945 . 530 7. 12 . 143 . 163 .50 .0417 0 18. 10 4,890 895 . 530 6. 75 . 143 . 163

.50 .0417 +10 16.60 4, 485 835 .530 6. 28 . 143 . 163 .50 .0417 +20 14. 85 4,010 765 .530 5. 76 . 143 . 163

.25 .0208 -30 22. 60 6, 100 1,070 . 461 9.28 .0714 . (1814 .25 . 0208 -20 21. 20 5, 725 1,015 . 461 8. 82 . 0714 .11814 .25 .0208 -10 19. 95 5, 390 965 .461 8. 36 . 0714 . (1814 .25 .0208 0 18. 45 4. 985 910 .461 7. 90 .0714 .0814 .25 .0208 +10 16. 95 4, .580 850 . 461 7. 36 .0714 .0814

.25 .0208 +20 5. 35 4, 145 785 . 461 6. 82 .071

. l>814
building sewer and drain will be taken as 50° F

and that in the stack as 60° F. With these assumptions we can compute the

velocity of air flow upward through the vent for

different degrees of closure of the vent, once we have assumed the temperature of the outdoor

air. This temperature will be given successive

values ranging from —30° F to + 20°Fby 10-deg

steps.

The first step in the computation is to determine

values of v3 for these different outdoor air temperatures for different degrees of closure of the

vent. In order to do this we first compute the

corresponding values of i\ by using eq (14), which

takes on the following simple form for the case assumed:

1 i /• L'2 /i-f— I r2 \ ^

Jrf [> +>’i Li~\-L 3 dr is M' (26)

Once the value of Vi has been computed, v3 can

be found from the relation:

'•=(1

)' <27>

The results of this computation for an outdoor

air temperature of —30° F are given in figure 8. In computing the value of Ks3 from eq (19),

v3 must be expressed in feet per hour, whereas

in the computations dealing with pipe friction,

the velocities have been expressed in feet per

second. Hence we multiply the values of v3 taken from figure 8 and similar figures not shown,

by 3,600. The successive steps of the computation

are given in table 8. The value of k3l , the coefficient of thermal conductivity of the ice was taken as 1.0 Btu/(hr)(ft)

(deg F) for ice that is assumed to be part granular

and part solid. It seems probable that the layer

of ice in the vent is neither entirely solid nor

entirely granular; and a computation based on the

assumption that the ice was solid, in which case k3i would be about 1.3 Btu/(hr) (ft) (deg F), gave

temperature curves that seemed to be too low.

Furthermore, a computation based on a value of ^3 i = 0.6 Btu/(hr) (ft) (deg F), which would be approximately correct for granular ice, gave curves

that were too high to agree well with the Winnipeg

data used later in this paper as a check on the

analysis. No allowance was made for the small

effect of temperature on the value of k3i . In order to compute /v oa , the coefficient of heat

transfer from the outer wall of the pipe to the

wind blowing past it, the curve given by klcAdam

[4, fig. Ill] was used. Values of 3,600 p4y4 were

first computed for various wind velocities iu and

outdoor temperatures 04 (or d0). Values of the

Reynolds number, 3,600 d0 p4r4/p), were next computed under the assumption that p has the constant value, 0.0435 lb/ (hr) (ft) , regardless of the

temperature. Next, values of 'P(d0pivi/p.) were

read from McAdam’s curve and were multiplied

by k/d0. The values of k used for the different

assumed air temperatures are indicated in table

j 9, together with the details of the computation of

the values of Koa for the 3-in. vent.

Table 9. Computation of coefficient of heat transfer from ! outer wall of 3-in. vent to wind stream

Outdoor

air a tem3,000 pi Wind

velocity, Vt 3,600 P1 V4 3,600 dopiV*

jp UF) k pera- Koo

ture, 0 a P do

°F

-30

Ib/ft* 334.8 fps

2 670 4, 490 37.5 0. 0429 1.61 -30 334.8 5 1,676 11, 215 60.2 .0429 2.58 -30 334. 8 10 3, 350 22, 430 88.0 .0429 3.78 -30 334.8 20 6, 695 44, 860 137.0 .0429 5.88 -30 334.8 40 13, 390 89, 725 227 .0429 9.75 -30 334. 8 60 20, 290 134, 600 312 .0429 13.4 -30 334.8 100 33, 480 224, 310 470 .0429 20.

-20 327.6 2 655 4, 390 37.

.0435 1.61 -20 327.6 5 1, 640 10, 975 59.5 .0435 2. 59 -20 327.6 10 3, 275 21, 950 87.0 .0435 3.79 -20 327.6 20 6, 550 43, 900 134. 0 .0435 5. 83 -20 327.6 40 13. 100 87, 800 223 .0435 9.70 -20 327.6 60 19, 660 131, 700 307 .0435 13.4 -20 327.6 100 32, 750 219, 500 460 .0435 20.0 -10 320.4 2 640 4, 295 36.8 .0442 1. 63 -10 320.4 5 1,600 10, 730 59.0 .0442 2.61 -10 320.4 10 3,205 21, 470 86.

.0442 3.81 -10 320.4 20 6, 410 42, 930 132.0 .0442 5. 84 -10 320.4 40 12, 820 85, 870 220 .0442 9. 72 -10 320.4 60 19, 225 128, 800 298 .0442 13.2 -10 320.4 100 32, 040 214, 670 453 .0442 20.0

0 313.2 2 625 4, 195 36.4 . 0453 1.65

0 313. 2 5 1.525 10, 500 58.3 .0453 2. 64

0 313.2 10 3, 130 20, 980 84.7 .0453 3. 83

0 313.2 20 6, 260 41, 970 131.0 .0453 5.93

0 313. 2 40 12. 530 83, 940 215 .0453 9. 74

0 313.2 60 18, 800 125, 900 294 .0453 13.3

0 313.2 100 31, 320 209, 850 443 .0453 20.

+10 306.4 2 612 4, 100 36.0 .0459 1.65 +10 306.4 5 1.530 10, 250 57.5 .0459 2.64 +10 300.4 10 3, 060 20, 500 84. 0 .0459 3.86 +10 306.4 20 6, 120 41, 000 128.0 .0459 5.88 +10 306.4 40 12, 240 82, 000 212 .0459 9. 74 +10 306. 4 60 18, 360 123,000 290 . 0459 13.3 +10 306.4 100 30, 600 205, 000 437 .0459 20.

+20 298.8 2 598 4,005 35.6 .0470 1.67 +20 298.8 5 1,495 10, 010 56.3 .0470 2. 64 +20 298.8 10 2, 990 20, 020 82.8 .0470 3. 88 +20 298.8 20 5, 980 40, 040 127.0 .0470 5. 97 +20 298.8 40 11,950 80. 080 208 .0470 9. 77 +20 298.8 60 17, 930 120, 200 284 .0470 13.3 +20 298.8 100 29, 900 200, 200 430 .0470 20.2

a Assumed characteristics of outdoor air:

0a, (04) Pi k M

°F Ib/ft* Btu!(hr) (ft) (deg F) Mkr)m

-30 0. 093 0.0125 0. 0435 -20 .091 .0127 .0435 -10 .089 .0129 .0435

0 .087 .0132 .0435 +10 .085 .0134 .0435 +20 .083 .0137 .0435

d„=3.5 in. =0.2917 ft; S„=0.916 ft2

.

With the required values of Ks3 , k3i , k l0 , and

/v oa determined,4 the procedure of computing the ! temperatures of the ice-air surface under various

assumed conditions is as follows: First, eq (20,

4 Eq (19) and (24) give the methods for determining Kt 3 and KOB, respectively. *31 is assumed to be 1.0 Btu/(hr)(ft)(deg F) for partly granular ice.

k-,o is about 0.3 Btu/(hr)(ft)(deg F) for asbestos cement, and about. 30 Btu/

(hr) (ft) (deg F) for steel or cast iron. 16
22. 23. and 25) are adopted in the form Then

2s3 —2 irr^Kssd^j (20a)

23i = (27rA"3i)/ln(r 1 /r3

^ 03 j, (22a)

Q io (2 irk i 0) / 111 ( / 0

( ^ i) ^io? (23a;

Qosl 2 7T/ o-^-oa^oa* (25a)

These equations are next written in the form

0s3 p

1 2 s 3 2 irr3ifs3 (20b)

03i p — ln(ri/r 3) =n3i— —- r—> 1/31 2wk3l (22b)

0io p ln(f0

/r,)

2,o

10 2wki0

’ (23b)

^oa d

(Zoa 7T/ 0-^- oa (25b)

Adding

Y)-=ZR=— ^q

2ir r 1 ln(r i/r 3 ) ln(r 0/r,) r

1 1

[_r3.Ks3 &31 k l0 /•oFCoaJ

(28)

Since q^ —$31 —310 — 2oa and 4 0 10 —

)— — 0sa

6S —0a , then

0s3=0s-03 = (0s-0a) §§’ (29)

where

6S =t he temperature of the airstream in the

vent in degrees Fahrenheit

0a =the temperature of the outdoor air in degrees Fahrenheit ( =04 ) 03 =the temperature of the ice-air surface in the vent in degrees Fahrenheit.

From eq (28) and (29) the following expression

is obtained

03 h?s3 -. T es -e~xR~

ln(ri/r3)

l n(r 0/r t ) 1_ 1 r3Ks3

(

^

3 i ^ io ^3 TCa3 t o-hoa and

1 t/ rin(ri/r3) , ln(r0/r,) , 1 N

aKs3

L h[

-+^r+r^ Ks3

r3 Ks3 k3 i In(r,/r3) r3 Ka3 k to ln(r 0/r 1) +

-f r3 Ks3

t o-R-oa (31)

h~ 1 =t=^rf'nlr:,r ' K-'‘ \_h

lnfr,/r,)

+ In (>„;>,) + 1, (;J2) r° io • oxlL 0a_J

since, from eq (30), iV= (08 —03)/(0

? —0a). For a given 0a and 0a , freezing will continue, and

r3/r, will decrease, until 03 increases to 32° f That is, the vent will continue to freeze up until N decreases below a value,

N= (03 —32)/(0s —

a). (33)

The temperature of the ice-air surface can now

be computed from eq (32) for any assumed conditions. The results of this computation for a 3-in. metal vent are given in table 10 for a wind velocity

Table 10. Computation of temperature of ice-air surface

in 3-inch vent. !„= 1.75 in. = 0.146 ft; 0, =60° F; n = 1.53 in.=0.128 ft; £3, = 1.0 Btu Uinffr !• _ F); i>4 = 10 fps.

2n 0 a 03-0*

08-03 03 r3/ri

in . 3. 07

0 F

-30 2.08 3. 78 0. 482

0 p

-0.7 1.00

3. 07 -20 2.00 3. 79 .463 +5.3 1.00

3. 07 -10 1.89 3.81 .435 11. 2 1.00

3. 07 0 1. 78 3.83 . 407 17.4 1.00

3. 07 +10 1.66 3. 86 . 377 23.7 1.00

3. 07 +20 1.50 3.88 .339 30. 1 1.00

2. 50 -30 2. 85 3.78 .600 +3.7 0.814

2.50 -20 2. 73 3. 79 .574 9.2 .814 2.50 -10 2. 60 3.81 .543 14.6 .814

2. 50 0 2. 44 3. 83 .508 20. 2 .814

2.50 +10 2. 28 3. 86 .471 26.0 .814

2. 50 +20 2.08 3. 88 .428 32.0 .814

2.00 -30 3.90 3.78 .731 +8.0 . 651

2. 00 -20 3. 72 3. 79 . 697 12.9 . 651 2.00 -10 3. 52 3.81 .651 17.6 .651

2. 00 0 3. 32 3.83 .617 22.9 . 651

2. 00 +10 3. 09 3.86 .568 28.

. 651

2. 00 +20 2. 84 3. 88 .520 33.7 . 651

1. 50 -30 5.20 3.78 .828 +10.8 .489

1. 50 -20 4. 96 3.79 . /86 15.2 . 4S9

1. 50 - 10 4. 68 3.81 .738 19.7 .489

1.50 0 4.42 3.83 .692 24.6 .489

1. 50 +10 4. 12 3. 86 .644 29. 6 .489

1.50 +20 3. 88 3.88 .601 35.0 .489

1.00 -30 6.51 3.78 .798 -f-9. 9 .326

1.00 -20 6. 21 3. 79 . 761 14. 6 . 326

1.00 -10 5.88 3.81 . 715 19.

.326

1.00 0 5. 56 3. 83 . 675 24. 2 . 326

1.00 +10 5. 16 3.86 .623 29. 2 . 326

1.00 +20 4. 74 3.8S . 569 34.5 .326

0. 75 -30 7. 12 3. 78 . 715 +"• 5 . 244

.75 -20 6. 78 3. 79 .681 12.4 .244

. 75 -10 6. 40 3. SI . 642 17.4 . 244

. 75 0 6. 08 3. S3 . 608 22. 7 . 244

.75 +10 5. 68 3. 86 . 565 28. 1 . 244

.75 +20 5. 16 3.8S .512 33.5 . 244

.50 -30 7. 92 3. 78 .601 +3.S . 163

. 50 -20 7. 56 3. 79 . 579. 1 . 163

. 50 -10 7. 12 3. SI . 536 14. 4 . 163 .50 0 6. 74 3. S3 . 507 20.

. 163

. 50 +10 6. 28 3.86 . 471 26.

. 163 .50 +20 5. 76 3.88 . 430 32.

. 163

.25 -30 9. 28 3.7S . 418 —3*5 . 0814

.25 -20 8. 82 3. 79 . 397 +2.8 .25 —10 8. 36 3. SI . 375 9.

. 0814

.25 0 7. 90 3. 83 3.M 15.7 . 0814

.25 + 10 7. 36 3. 86 . 329 22. 4 N .25 +20 6. 82 3. 88 .304 29. 3 8

17
of 10 ft/sec and are plotted in figure 11. Similar

temperature curves are shown in figures 10, 12,

13, 14, and 15 for 1 %, 4, 6, 8, and 12-in. vents,

respectively. The numbers appearing on the curves refer to the corresponding outdoor temperatures in degrees Fahrenheit. Because of the

high thermal conductivity of a metallic vent and

the negligible temperature drop through the wall

of such a vent, the term (l/A, l0 )ln(r0/r 1 ) in eq (32) can be omitted without appreciable error. This

has been done in computing the temperature

curves shown in the above-mentioned figures.

The heights of stack and vent assumed for diameters of 1 y2 , 4, 6, 8, and 12-in. stacks were 30, 60,

100, 150, and 200 ft, respectively. The total length of the building sewer and building drain was taken as 50 ft in all cases. The assumed air temperatures in the building sewer, drain, and

stack were the same as for the 3-in. stack.

Returning now to figure 11, it will be observed

that the curve for an outside air temperature of 20° F crosses the line representing a temperature

of 32° for the ice-air surface. Hence the vent

would frost up until the diameter of the opening

corresponds to the ratio, r3

/r,-, for which this occurs. The moisture deposited on the ice surface

DIAMETER OPENING IN VENT

INSIDE DIAMETER OF VENT Figure 10. Temperatures of the ice-air surface in a l]4-in. vent for different outside air temperatures and for a wind

velocity of 10 ft/sec as the vent freezes up.

Figure 11. Temperatures of the ice-air surface in a 3-in. vent for different outside air temperatures and for a wind

velocity of 10 ft/sec as the vent freezes up.

I

thereafter will not freeze but will run down the , surface. Thus the dashed portion of the curve , lying above the intersection of the 20° curve I with the 32° line represents conditions that are ; physically impossible. In fact, the solid portion

of the curve lying to the right of the dashed portion

is also physically impossible for a vent that is ! freezing up. However, it may represent physical | facts for a vent that is thawing.

To illustrate the effect of different wind velocities on the temperature of the ice-air surface as , the vent freezes up, figure 16 was prepared for a 3-in. vent, an outside air temperature of —30°

F and different wind velocities from 2 to 90 ft/sec

kia

if#

nl

F

lit

itsi

sis' *

i

Figure 12. Temperatures of the ice-air surface in a J/-in. vent for different outside air temperatures and for a wind

velocity of 10 ft/sec as the vent freezes up.

Figure 13. Temperatures of the ice-air surface in a 6-in. vent for different outside air temperatures and for a wind

velocity of 10 ft/sec as the vent freezes up.

18
being asssumed. None of these curves crosses the

; 32° F line; hence it is concluded that, given an

I outside air temperature of —30° F, a 3-in. vent

will always freeze up solid, given sufficient time.

Finally, in order to show the effect of using for the vent pipe a material offering considerable

| resistance to the flow of heat, instead of the

I customary metal pipe, there are shown in figure 17

j curves of the temperature of the ice-air surface

in a 4-in. vent, first when the vent pipe is metal,

and second when it is asbestos-cement. AsbestosINSIDE DIAMETER OF VENT Figure 14. Temperatures of the ice-air surface in an 8-in.

vent for different outside air temperatures and for a wind

velocity of 10 ft!sec as the vent freezes up.

DIAMETER OPENING IN VENT

INSIDE DIAMETER OF VENT Figure 15. Temperatures of the ice-air surface in a 12-in.

vent for different outside air temperatures and for a. wind

velocity of 10 ft/ sec as the vent ferezes up.

cement, having a thermal conductivity of 0.3 Btu/(hr) (ft) (deg F), was used for this comparison

because this pipe is coming into use for dry vents. In computing the temperature curves for asbestoscement, it was necessary to take into account

the second term in the bracket iri eq (32j involving

the heat transfer through the wall of the vent

pipe. The improvement in conditions attained

by using this material in place of steel or cast iron (or any other metal) is definite. Evidently

very heavy thermal insulation is necessary if complete protection against frost closure is to be

achieved by this means, however.

The temperature curves bring out one puzzling

feature of the phenomenon. The frost in a completely closed vent will presumably begin to thaw

outward from the center when the outside air

INSIDE DIAMETER OF VENT Figure 16. Temperatures of the ice-air surface in a 3- in. vent for an outside air temperature of — 30° F and for

different wind velocities as the vent freezes up.

Figure 17. Temperatures of the ice-air $u -fact vent for different outside air temperatures and 'a- velocity of 10 ft/scc. Comparison of stool and asbostoe-coment vont pipos.
temperature rises. For example, referring to figure 12, which gives the temperature of the

ice-air surface in a 4-in. vent for different outside

air temperatures and for a wind velocity of 10

ft/sec, it is clear that, if the outside air temperature

is —10° F, for example, frosting will continue

until complete closure results, given sufficient time, because the temperature of this surface

remains below 32° F for all degrees of closure of the vent. Now suppose that the outside air temperature

rises to and remains at 20° F. Since, when the

vent is completely filled with frost, the temperature of the frost in the vent is equal to the temperature of the outside air, the temperature of the

frost will rise with the outside air temperature to 20° F and should remain there. Thus it would

seem at first sight as if the vent should not start

to thaw out until the temperature of the outside air had risen above 32° F. Yet there is evidence

that this is not the case. The data from Winnipeg,

presented earlier in this paper, appear to contradict

this. Further consideration of the problem leads to a possible explanation of the phenomenon. It is very likely that there does not exist in the exposed

part of the vent a layer of ice of uniform thickness.

When the vent is completely closed for some dis- tance down from the top, it is likely that the

thickness of the layer of ice tapers off in the downward direction, as shown in figure 18. Whether

there exists a very small opening through the vent

when what has been assumed to be complete clos- ure exists is not known. However, when the ex- perimental vents that were presumably completely

closed were inspected visually from the top, a small opening was seen, which apparently tapered

off to zero a short distance down from the top.

It may be, however, that this small opening merely

deviated sidewise until it was lost to view.

If figure 18 represents the actual conditions,

then there would be a current of warm air rising

in the center of the vent, coming in contact with

Figure 18. Conjectured form of so-called complete closure of a roof vent by frost.

the ice, chilling, and then flowing downward in

the neighborhood of the ice layer. A condition of approximate equilibrium would be attained as long as the outside air temperature remained low,

say —10° F, with the ice in the portion of the vent

that is frozen up completely attaining this same

temperature.

Suppose now that the outside air temperature

rises to 20° F. Then the ice in the completely frozen

part of the vent would soon attain this latter temperature (see fig. 18). The condition of

equilibrium that had been established would then

be upset, and the current of warm air would begin

to melt some of the ice with which it comes in contact. The upper point of the conical cavity [' shown in figure 18 would move upward until a clear opening might be established, air would 1 then begin to pass upward and out of the vent,

and the conditions assumed earlier for the freezing

of vents in general would be established once more. Under these conditions, presumably the

appropriate curve shown by the solid fine at the

right-hand edge of the appropriate figure (fig. 12

for a 4-in. vent) would be valid. The Winnipeg data shown in figure 2 afford a rough check on the analysis made in this paper. The comparison is shown in figure 19. The curves

in this figure were obtained as follows: From figure

1 1 we see that the 20° F curve for the 3 -in. vent

crosses the 32° F line at a value of the ratio r3 fr

\

of

approximately 0.86, or for a diameter of opening

of 2.6 in. That is, if the outside air temperature

is 20° F, the vent would freeze to this point and

then stop. This establishes the point plotted on

the line in figure 19 for the 3-in. vent. Furthermore, it is estimated from figure 11 that, if the

temperature of the outside air should fall to about

14° F, the temperature curve (if plotted in figure

11) would just miss reaching a temperature of

-

11

i

TEMPERATURE OF OUTSIDE AIR , °FAHR. Figure 19. Comparison of computed temperatures of

ice-air surface with data from Canada for 6- and 8-in.

vents.

1

(

j

'

;

I I

!i

i

20
I

1

32° F at its highest point. In other words, the vent would freeze up completely for air temperatures of 14° F and below, given sufficient time.

This is indicated by the vertical line drawn in figure 10 through a temperature of 14° F.

Similarly, we see from figure 12 for the 4-in.

I vent that the vent barely starts to freeze if the

i temperature of the outside air is 20° F. This

j establishes a point on the line for the 4-in. vent in

! figure 10. Another point is established by observ-

| mg that, if the temperature of the outdoor air is

: 10° F. the vent will stop freezing when the ratio

r

3 r , takes on a value of about 0.73 (diameter of

[ opening about 3.0 in.). This establishes the other

I point plotted in figure 10 for this diameter vent.

! We note also from figure 12 that the highest outj door air temperature for which the curve (if

I plotted 1 would miss touching the 32° F line is about 8° F. This establishes the vertical line through the temperature of 8° F, connecting with

the curve for the 4-in. vent. The significance of these vertical fines is that, as we move downward

and to the left along the curve for any given vent,

when the conditions corresponding to the intersection of the vertical fine and the curve are reached,

freezing will continue until complete closure results. The other curves for vents 6, 8, and 12 in. in diameter in figure 10 were obtained in this same

way.

Xow, considering figure 2, we note that the 8-in. stack on the Grain Exchange was found to be

completely closed on January 6, when the minimum daily temperature was —35° F. This is represented by a large circle plotted on the base

fine of figure 10. Had the agreement been perfect,

it would have coincided with the vertical fine for the 8-in. vent. Obviously the agreement is quite

good—better than might have been anticipated.

We next consider the observation of the same

vent on February 17. On this date the openingin the vent was found to be about 5.5 in. in diameter. and the daily minimum air temperature at that time was about —15° F. It can be seen from figure 10 that this point also agrees very well

with the computed curve. We consider also the observation for the 6-in. stack at the Grain Exchange on January 20, at which time the stack or vent was observed to have closed up when the daily minimum temperature was about —15° F. This point, when

plotted in figure 10, lies a little to the left of the

line plotted for the 6-in. vent. Thus the agreement is still good, if not quite as satisfactory as

for the 8-in. vent. Although these three available observations

show good agreement with the computed curves and hence will be taken as reasonably good justification for the computed temperature curves

given in this paper, too much reliance should not be placed on the exactness with which the computed curves fit the actual conditions. It should

be remembered that we do not have adequate

information in regard to the Winnipeg data. We

do not know the exact day on which the ventclosed up because the observations were made

only at infrequent intervals, and hence we are not sure of the daily minimum temperature on

the actual day of closure. We do not know tin- daily average temperatures, but only the min

mum temperatures. We do not know how the

wind velocity varied during the period in question.

Hence the comparison should be looked upon

merely7 as a rough verification.

Curves similar to those shown in figures 10. 11. 12, 13, 14, and 15 were computed, using a value

of 0.6 Btu/(br)(ft)(deg F) for ku for the ice (corresponding to completely granular ice;, and

these curves looked more reasonable for the

small-diameter vents than do those shown in the

above-mentioned figures, but they did not agree

at all with the Winnipeg data. Further experimental investigation and more detailed field data

are needed to study the matter further.

7. Test Procedure

For the purpose of studying frost closure.

])] limbing systems may be considered as comprising two broad classes. The first class will include systems having a water seal in the drain

downstream from the stack without a vent to the atmosphere on the house side of the water

seal. This condition may exist if a running house

trap without a fresh-air inlet is used (or in case the fresh-air inlet is plugged or closed off . or

it may occur if the street sewer is so full that the

outlet end of the house sewer is submerged. It i- much more likely, however, that the second das'

of installation will be found in service. In this class the house drainage system is connected

directly to the street sewer or a septic tank without

any water seal in the horizontal drain from tin- base of the stack. Here the air and sewer gases

may pass directly through the house drainage sys- tem in response to whatever forces are causing

the flow to take place. An installation having a fresli-air inlet to the house trap might also be

placed in this class, as far as the flow of air through

the stack is concerned, although air entering

through the house trap will have relatively low humidity, and hence in this respect it will tend

to promote less frosting of the roof vent than it' it were saturated. Also the air stream up through

the system will be colder, and the rate of flow w ill be less than if there were a connection between

the street sewer and the building system.

Tests were made by using the laboratory setup

shown in figure 4, with the temperature ot the ait- surrounding the top of the stack maintained at a constant value during each run. The temperature was about —30° F in most of the tests, although

a few runs were made at a lower temperature.

For those tests in which the ease of an unwonted

house trap was simulated, a trap was installed m

the house drain near the base of the stack. A arm

water was introduced through the bathtub at a.
rate of about 1.8 gal/min, and the water closet was flushed at regular intervals of time. The roof vent was observed periodically (once or twice

daily) for evidence of frosting. In most of the testing, however, no trap was

used in the house drain, and air was forced through

the system by a blower at the hase of the stack,

simulating the convective air current that would

exist in a service installation.

An important consideration in connection with

the tests was that of maintaining approximately

a constant pressure differential available for pro- ducing air flow through the system. For a given

height of stack in service and a given temperature

difference between the air inside of the stack and

the outside air, the differential can be approximated from table 1 or figure 7, or it can be computed from eq (4). In the test installation, it was possible to attain flow conditions approximating those that would be expected in service for the same stack by adjusting the blower so that a pressure reading (hm=he) was obtained on the

inclined manometer shown in figure 4, such that

ht

computed from eq (8) was equal to hu computed

from eq (4). It can be seen readily that, in order to simulate

flow conditions closely, not only must the pressure

differential for overcoming friction be maintained

in the test setup at the same value as in the service

installation simulated for the given temperature

conditions, but also that the physical dimensions,

or at least the overall flow resistance, of the setup

must be the same as in the corresponding service

installation. When these conditions are not at- tained, it may be that either more or less air flow

is actually produced in the test installation than

in any particular service installation, even though

the pressure available for producing air flow be

made the same in the two cases. In addition,

for a given pressure differential ht through the

system and for a given roof vent, the greater the

frictional resistance of the stack, building drain,

and building sewer, the less will be the relative

effect of a given degree of frosting of the roof vent on the volumetric rate of air flow through the

system.

The importance of the factors mentioned in the

above paragraph was not fully appreciated at the

time when these tests were made. Actually, many

of the tests were made using purely arbitrary set- tings for the pressure differential; hence it is unfortunate that flow conditions identical to those

that would occur during frosting in service with

the same setup were not produced.

It was necessary to make frequent calculations

and adjustments in order to make available approximately a constant pressure differential for producing air flow as each test run progressed

because the accumulation of frost and changes in room temperature would in a short time result in a differential differing from that which was desired. In making a complete cycle of computation,

temperature and pressure differential readings,

and adjustment every hour during the tests, it is believed that the effect of this tendency for the

test setup to get out of adjustment was minimized, |i although it was soon evident that highly accurate'! control over the pressure differential could not be' maintained with the test setup used.

Air and water temperatures were measured at! points shown in figure 4. The water discharging!

into the stack was maintained at a constant temperature during each run, being as high as 120° F

in a few runs, although a temperature of from 70°

to 80° F was used in most of the tests, since higher

temperatures were evidently not needed to maintain a high humidity in the air stream. The average stack temperature was computed

from readings of the air temperatures inside of the

stack, these, temperatures being measured by a

remote-recording device. The average temperature in the stack was maintained as nearly constant

as possible during each run. The temperature of

the air around the roof vent was also maintained

approximat ely constant. The thickness of the accumulation of frost inside

the vent was observed once or twice a day. Relative humidities in the stack and in the room in

which the test installation was located were obtained from wet and dry-bulb temperature readings. The rate of flow of air through the system was determined from readings of the pressure drop i

1 across the orifice through which the mixture of air and carbon dioxide escaped to the atmosphere.

The ratio of carbon dioxide to air was determined

by the special device mentioned earlier and was!1 taken into account when the rate of flow of ah* through the system was calculated.

During intervals when the apparatus was not

in use overnight or on weekends, the top of the

roof vent and the outlet to the cold chamber were

plugged, and the chamber was filled with dry ice.

[ In this way the accumulation of frost in the vent' was apparently preserved fairly well in most in- stances until the next work day, when the test was continued. However, these interruptions may

have changed the nature of the surface of the ice from a porous condition to a solid condition and

hence may have influenced the further freezing of

the vent. An effort was made to continue each

test run until the vent ceased to accumulate frost. In some instances this meant carrying the test to complete closure of the vent. The primary object of the tests was to ascertain

if roof vents 1%, 3, and 4 in. in diameter could

be frozen up completely. However, in some of

the tests the effect of varying the rate of air flow

through the vent was investigated, while in other

tests the effect of varying the temperature inside : the stack was studied. Maintenance of relatively

low humidity in the stack was found to be too

difficult to warrant an investigation of this factor; and, in any event, low humidity would tend to decrease the rate of frosting of the vent. The

humidity in the stack approached saturation at

all times during the tests, apparently because of

id#

•in

22
the continual flow of water into the stack. HowI ever, as mentioned earlier in the paper, the huinidI it y measurements made in the stack possibly ini dicat ed a greater degree of humidity than may

I actually have existed. Evidence has been found

! from observations in Canada that, when hot water

i is discharged into the stack, there is an increased

! tendency to frost closure, apparently because of the high humidity thus created.

The dimensions of the vent exposed to low temperature in the cold chamber were varied. In addition to tests on a 3-in. stack, which continued

undiminished in diameter into the cold chamber,

tests were run on the system with a 1%-in. vent

pipe mounted on top of the 3-in. stack. The 1%-in.

pipe was 38 in. long and extended 15 in. up into

the cold chamber in most of the runs, but in a few

I tests only 6 in. of its length extended up into the

chamber. A few runs were made on a 4-in. roof vent 38 in. long extending 15 in. into the cold

chamber.

8. Test Results

8.1. Tests on System With House Trap

A few tests were made in which a house trap

without a fresh-air inlet was installed in the house

drain. In these tests no attempt was made to create a forced draft through the system. The

unvented house trap eliminated the normal convective draft. The temperature of the air sur- rounding the upper 15 in. of the 3-in. -diameter

roof vent was approximately —30° F in most of these tests, and the mean temperature of the air

in the stack varied from 65° to 78° F. Runs varying in length from 3 to 24 hr were made. A constant flow of warm water was introduced to the

stack throughout the tests, and the water closet was flushed at 1-hr intervals. In no case was

there more than a slight surface coating of frost

in the roof vent at any time.

8.2. Tests on System With Air Flow up Stack

This case corresponds to a service system in

which there is free passage of air from the street sewer up through the stack and vent to the outer

air. The tests were made on a test installation in

which an upward flow of air in the stack was

maintained by means of a blower at a rate reason- ably representative of service conditions. In

these tests partial or complete closure of the vent

occurred in most instances. Four different vent

conditions were tested: (a) 1%-in. vent on a 3-in. stack, with a length of 15 in. exposed to the low

temperature, (b) the same, but with a length of 6 in. exposed to the low temperature, (c) the 3-in. stack unchanged in diameter and having a 15-in. exposure, and (d) the vent enlarged to 4 in. and

extending 15 in. up into the cold chamber. The

test data relating to temperature and flow conditions for the 1%-in. vent are given in table 11, and

Table 11. Temperatures and flow condition.' existing n>. frost-closure tests

l!4-in. -diameter vent, exposed to temperature of approximate!'. V

Length of vent exposed to low temperature 15 in., except in run ! ' ... and 17, in which the length was 6 in.

Run

Approximate head fin. of water) available

for producing flow

Approxi- mate air velocity

in roof vent at beginning

of run

Average

temperature of air entering

roof vent

A verage temperature of air At begin- in stack ning of run

Average

for entire run

fps °F °F

1 0. 013 0.015 2.3 78

2 .018 .019 4.0 76 75

3 .020 .026 4.9 69 68

4 .048 79 78

5 .060 6.0 68 68

6 .075 6.2 73 75

7 .072 .080 9.6 76 73

8 .066 .084 9.2 74 73

9 .070 .086 9.6 75 74

10 .083 . 093 8.2 72 72

11 . 100 68 68

12 .094 . 102 9.4 72 72

13 .092 . 102 10.2 72 71

14 . 103 .106 9.4 66 66

15 .018 .024 5.3 78 75

16 .046 .042 6.4 74 72

17 .057 .056 8.3 70 68

Table 12 . Temperatures and flow conditions existing in. frost-closure tests

3- and 4-in.-diameter roof vents exposed for a length of 15 in. to a temperature

of approximately —30° F.

Run

Approximate, head (in. of water) available

for producing flow

Approxi- mate air velocity

in roof vent at beginning

of run

tertmera- Average

tureofair

entering *dyck roof vent At begin- 111 stack ning of run

Average

for entire run

3-in. -diameter roof vent

fps ° F °F

IS 70 69

19 0. 065 0. 064 2.2 72 71 20 . 136 . 131 4.2 75 72

21 . 129 . 134 3.4 69 68

22 . 137 . 136 3.6 71 70

4-in. -diameter roof vent

23 0. 064 0.065 2.1 74 73

24 .066 .066 1.7 75 73 25 . 105 .096 2.6 73 71

the data for the 3-in. and 4-in. vents are given in table 12. One interesting observation applying to most ot the data obtained from tests in this investigation

is that the freezing up of the vents that is. the

increase in thickness of the ice or frost layer

apparently was approximately linear with time

There is, however, no reason to believe that this would always be the case: in fact, there is reason

to believe that, for certain temperature conditions,

and especially for large stacks, there would be a decreasing rate of frost closure with increased

thickness of the ice layer. Possibly it was moroU
a coincidence that the tests reported here yielded

results indicating that closure is linear with time,

or it may be that thisjs actually true generally in the case of small diameter roof vents. These

matters have not been investigated adequately.

The data from the tests on llj-in. vents are shown in figure 20. From this figure and the data

in table 11, it is apparent that there is no consistent. correlation of rate of freezing with stack

temperature or rate of air flow. However, in this connection a number of runs (not shown in the

above data) were made, using appreciably higher

rates of air flow than existed in the tests shown in figure 20, other conditions being similar. In

nearly all instances in which the mean air velocity

in the 1 %-in. vent at the beginning of a run ex- ceeded about 10 ft/sec, little or no frost accumulation was noted. This was possibly due in part to the air stream not being cooled sufficiently when

passing through the vent at high velocity to permit freezing in the vent to take place. Another

explanation suggested by the operator of the test apparatus is that apparently a high-velocity air flow scours the frost accumulation off the wall as

fast, as it can form. It was noted in the tests at the higher air velocities that a more or less con- tinuous spray of frost particles issued from the roof

vent, indicating confirmation of one or both of the

above suppositions.

Probably there is a gradual increase in rate of frosting with increase in rate of air flow, starting

from zero flow and continuing up to a certain

Figure 20. Experimentally determined rates of frost closure for a E/i-in.-diameter roof vent exposed to outside air temperatures of approximately —30° F.

Symbol Run Symbol Run O 1 <1 9 • 2 < 10

3 V 11 4 12 A 5 o 13

6 14 > 7 15*

8 © 16* 3 17*

*6-in. length of vent exposed. All other runs, 15 in. exposed.

intermediate range of flow rates, beyond which

there is a sharp decrease in rate of frosting to near

zero. Probably this curve is rather flat at inter- mediate flows, which may account for the fact that

only inconclusive correlation of rate of frosting

with ah- velocity was measured in tests at intermediate flows. Summarizing the results on 1%-in. vents (fig. 20), we find that in the case of the 15-in. exposure,

where all observations are given equal weight and

the temperatures are averaged (stack temperature

approximately 72° F, temperature of the air entering the roof vent, approximately 73° F, and

the temperature of the air surrounding the ex- posed portion of the roof vent, approximately —30° F), the overall average rate of frosting was

0.080 in. /hr. It. is interesting to note that if only

the 5 points that represent the runs leading to complete closure are considered, again an average

rate of frosting of 0.080 in. /hr is obtained. It will be explained here that by rate of frosting is meant

the rate of increase in thickness of the frost or ice layer adhering to the inner surface of the roof

vent, not. the decrease in diameter, which would

be double the rate specified. It is realized that, this is not. a definite dimension, but. that, the frost layer is very likely to be very irregular in thickness

and in general will probably be thickest at some

distance from the base of the roof vent, un- doubtedly near the top in the case of a relatively

short, roof vent. In the data taken in the present

investigation, an attempt, was made to record the

average thickness of the frost layer at the section

of minimum opening. It is undoubtedly true that

this method of estimating by visual inspection

gave rise to appreciable errors. The data obtained showed slightly better

correlation of rate of frosting as affected by the

temperature of the air entering the roof vent. The lowest air temperatures gave rates of frostinggreater than did the highest air temperatures,

there being a difference of about. 8 to 10 deg F in the temperatures compared (comparison of runs

3, 5, and 11 with runs 1, 2, and 4). Nevertheless,

because the results are so erratic in this respect,

especially for the intermediate stack temperatures, little else can be inferred from the result;;. Probably the erratic nature of the phenomenon of frosting of vents, the unavoidable variations in

flow and temperature conditions during the test runs, the limited range of stack temperatures and

pressure differentials covered, the fact that

partial loss of the frosted layer or changes in the

nature of the layer took place in some of the runs when it was necessary to shut down the apparatus

over night or over a holiday before continuing tb e run, and last, but not least., the very rough

method employed in observing frost accumulation,

all may have contributed to the inconclusiveness

of the data on the effects of temperature and air flow. Only limited data were obtained on the effect of roof-vent, length on rate of closure. The data

!«'

24
for the 6-in. exposure are shown in figure 20 as runs 15, 16, and 17. The data are badly scattered ; hence detailed conclusions are not warranted.

However, averaging all observations given, the

average rate of closure was 0.059 in. /hr, when

the average stack temperature was approximately

72° F. and the average temperature of the air entering the roof vent was approximately 74° F. This rate is about 26 percent less than was obtained with a 15-in. exposure under substantially

the same conditions.

The data for five tests on the 3-in. vent with a

15-in. exposure are shown in figure 21. For the

only test that was carried to complete closure, run 19, the average rate of closure was 0.069 in./hr,

which is about 14 percent less than the rate found for the 1%-in. vent having the same exposure

length. In this run the average stack temperature was approximately 71° F. and the average temperature of the air entering the roof vent was approximately 72° F. It will be noted that figure 21 does not show rim 19 going to complete closure

but shows only the first two observations.

The reason for this omission is that sometime

after the 13th hr of the run, the temperaturecontrol system failed, resulting in a partial loss of the ice layer in the vent. As the exact length

of the period during which the ice layer had

suffered reduction is unknown, we do not know

just when the ice layer was restored to its original

thickness, this having been accomplished after the apparatus was repaired. Thereafter apparent

complete closure occurred within a few hours.

The average rate of closure of 0.069 in. /hr given

above is based on the two observations shown in

figure 2 1

CO

Figure 21. Experimentally determined

rates of frost closure for a 3-in -diameter

roof vent exposed 15 in. to outside air temperatures of approximately — 30° F.

Symbol Run O 18 • 1920

21 A 22

Unfortunately none of tlx; three runs shown in figure 22 for the 4-in. vent was carried to complete

closure. Averaging all observations gives a rate

of closure of 0.063 in. /hr. The average stack

temperature was approximately 73° F and tin- average temperature of the air entering the roof

vent was approximately 74° F. The rate of closure of 0.063 in. /hr is about 21 percent h---. than was obtained in the case of the 1%-in. vent under similar conditions.

Plotting the rates of closure given above against

values of ljd (where l is the exposed length of roof

vent, and d is the full internal diameter of tin vent, both in the same units) on logarithmic

paper yields the interesting result that the data

obtained in this investigation can be represented

closely by the empirical relationship,

//\0 - 3 Rc = 0.04(|) , (34)

where Rc is the rate of closure in inches per hour.

Here Rc represents the rate of increase in thicknesof the ice layer, not the rate of decrease of diameter

of opening. Although this equation gives results that are generally in fair agreement with the

average results obtained in the investigation, it is limited in application to the conditions existing

in the tests and hence cannot be applied generally.

An attempt was made to compute rates of closure approximately, making use of the temperature curves for the ice-air surface given in the paper, but the number of unknowns was too great to permit any worthwhile attempt ot this

sort. Hence no attempt is made in the paper,

Figure 22. Experimentally deter- mined rates of frost closure for <i f-in. -diameter roof vent exposed 15

in. to outside air temperatures of approximately —30° F.

Symbol Run

/-''N 23 • 24

25
other than the computations made in connection

with figures 20, 21, and 22 to evaluate the time

factor in the process of the freezing of a vent. The results presented purport to make it possible

to predict roughly to what extent any given vent

projecting above a roof will freeze up under given

conditions, but not how fast it will freeze up.

9. Discussion of Frost Closure—Field

Reports

There are two forms of frost closure that appear

to occur in actual installations, provided the outside air temperature becomes and remains suffi- ciently low, say lower than perhaps 10° F. The

first comprises a concentric layer of frost on the

inside wall of the vent pipe that increases in thick- ness up to some particular value or to complete

closure. It is this form that has been analyzed

in this paper and that was observed in the laboratory tests. The second form comprises the

building up of a frost cap on top of the roof vent,

starting at the rim of the vent. There are several

variations of this form of closure. Field reports seem to indicate that this is the more common form of closure, but this may be

due to the fact that it is the more easily observed

of the two. One report from Canada indicates

that both forms are likely to occur simultaneously.

Presumably the form first mentioned is more

likely to occur when the exposed length of vent is relatively great. In this case the layers of air close to the cold wall of the vent commence to

chill when the warm air is still a considerable

distance from the outlet of the vent. This gives

the drops of moisture more opportunity to come

in contact with the wall of the vent and to freeze there than if the exposed length of the vent is short. In the laboratory tests made in the investigation

reported here, the exposed length of vent was 15

in. in the great majority of the cases tested. Thus

the lengtli/diameter ratios for the 1 3, and 4-in. vents were 10, 5, and 3.75, respectively, based on

the nominal diameters. In all of the tests in which frost formed, it always occurred as a layer on the inner wall of the vent, although in a few

instances it was observed that a cap also started

to form over the top of the vent. In some

instances it was noted that true ice, rather than

frost, formed on the wall of the stack. Unfortunately not enough data were obtained to clarify this point.

The manner in which the second form of frost closure comes about seems to be fairly clear. Particles of water and frost are being carried

upward out of the vent in the air stream. Some

of the water particles strike the cold rim of the

vent and freeze there. Other particles of frost and water strike the frost that has first formed on

the rim of the vent and adhere, with the result that a porous mass of frost gradually builds

upward and inward until a columnar mass roughly

cylindrical in shape with an axial opening forms.

In extreme cases this formation may possibly

j close completely at the top. Photographs of the i development of such a frost cap in the Report of Proceedings, 1913 and 1914 Conventions of the,

Canadian Institute of Sanitary Engineers [1] for the 6-in. vent on the Civic Curling Rink in Winni- 1 peg unfortunately are not clear enough to repro- duce here. The photographs in the reference [1] show that on February 3, following a period of weather with

minimum daily temperatures ranging from —5°,

to —15° F, a rim of frost had started to build up

around the upper edge of the vent, with a very

ragged contour. The daily minimum temperatures then dropped steadily, reaching a low of 1 about —40° F on February 10, then oscillated up ,

’ and down during the remainder of the month.

A photograph taken on February 10 showed that

the body of frost had built up to a height of perhaps 6 to 8 in., but the opening had scarcely ii diminished in size. On February 25 this annular Ij column of frost had grown to a height of about

18 in., but still the opening had not decreased

perceptibly.

It will be noted from figure 2 that the exposed | length of vent was very small, and it appears from

the report that a special roof jack was installed

around the vent in an attempt to retard frost

closure. Unfortunately no information is available as to the type of closure that occurred with

the other 6- and 8-in. vents shown in figure 2. The Committee on Research of the American,

| Society of Sanitary Engineering made a report [5] | on the subject of frost closure in which it presented yi facts regarding the occurrence of frost closure and . the means taken to combat it and gave information

obtained from various cities in the Uni ted States, j Excerpts that seem to be pertinent follow.

Elmira, N. Y. Considerable hoar frost. No ! knowledge of complete closure. Sioux Falls, S. D. Some trouble with vents frosting but the city has no ordinance. Trouble occurs not

| more than 3 or 4 days at a time and only in very cold weather. Milwaukee, TFts. During long stretches of very

cold weather sometimes have many complaints. All vent pipes less than 4 inches in diameter must be in- .Si creased to 4 inches and increaser must be about 18

inches below roof. Springfield, Mass. In zero weather occasionally , 9| a stack closes. Require that no soil or vent pipe shall be smaller in diameter than 4 inches where it passes through the roof.

St. Joseph, Mo. Do not increase main vent, stack d

through roof but, permit nothing less than 2 inches | internal diameter for any vent or revent pipe through , j roof. Top of vent stack rarely closes. When

weather is above zero, no frost at all is noted. Davenport, Iowa. Do not have any cases of frost

closure. Increase stacks 2 inches where they go through roof. Elizabeth, N. J. Have short cold spells when the temperature drops from 2 above to 4 below zero. Find that all pipes smaller than 4 inches were almost

closed by frost. Specify that no vent pipe shall be

smaller than 4 inches in diameter coming through

roof.

26
IfRock Island. 111. Increase all vents going through

roof 2 inches and do not allow them to extend more

than 12 inches above the roof, so as to keep the length

of the increaser below the roof. Very little trouble with frost closure and have no ordinance. Columbus, Ohio. State Plumbing Code requires that all pipes be increased to 4 inches when passing

through the roof. Obvious that in our northern

cities all soil stacks should be increased one full size at least 1 foot below the roof. Pittsburgh. Pa. Have a great deal of trouble in the Pittsburgh District from frost closure. Xo provision

in code. Allowed to run pipes outside of buildings.

Dayton. Ohio. On very cold days the vent stacks above the roof have been closed by hoar frost to such an extent that it eventually formed a solid mass of

ice, thereby closing the stack until the weather

moderated and thawed it out. Has caused siphonage

of traps in plumbing fixtures, causing sewer gas to permeate the interior of building. Law calls for all vent pipes to be increased through roof. Buffalo. X. Y. Xo complaints. Ordinance re- quires all vent pipes to be increased one size or con- nected to main vent stack before passing through the

roof.Waterloo. Iowa. Require that no pipes less than 4

inches in diameter shall pass through roof. Pipes 4

inches and larger shall be increased two sizes. Even

with this, find that, many pipes freeze up if zero weather persists for several months without thawing

spells in between. Grand Rapids, Mich. Have no trouble with frost. Allow no increaser less than 4 inches, and every stack

is increased one size at roof. Used to have trouble before fresh-air trap was abolished, but do not now,

since warm air from sewer passes through.

Waterbury, Conn. Where the house trap is used, the liability of closure is reduced. Waterbury provides against the closure by installing the house trap.

It is a matter of ordinance. Recommendations of the Committee. Naturally in

territories where climatic conditions are mild, the

question of frost closure need not be considered. In many of our northern towns there are occasional cases

of trouble from frost closure, but they do not seem to be sufficient to compel an ordinance on the subject.

We believe it would be a good idea from the data con- tained in this paper to frame an ordinance concerning

frost closure and methods of installation to prevent

it which can be generally adopted throughout the country by towns and cities requiring this protection.

There seems to be considerable agreement in the main

points of installation, and it should not be difficult to construct such an ordinance. Some attention should be given also in the discussion as to whether the house

trap should be considered a legitimate means of pre- vention or whether the remedy should in every case be found in the terminal construction of the vent line. If the vent line construction can be unanimously

adopted as being satisfactory in it provisions against

frost closure, we would suggest that a variation of the

practice could be effectively done away with by dis- pensing with the suggested house trap remedy.

The following quotations in regard to the subject of frost closure have been drawn from various

sources and are given, partly because of the factual

information included and partly because of the

suggestive ideas that some of them contain.

James Smith, Chief Plumbing Inspector, Winnipeg, Canada, [6], states:

In the Prairie Provinces of Western Canada we

claim to have overcome this trouble to a very great extent at least by simply increasing the pipe before it passes through the roof and limiting the extent to which the pipe projects above the roof to a minimum

of 1 inch and a maximum of 3 inches. This bold ex- pedient was first, suggested and experimented v, it h b a very keen student of plumbing problem- the lat< plumbing inspector of Saskatoon. Saskatchewan.

This method of treating pipe terminals has long pa--ed

the experimental stage and is now common practice i Western Canada. Frozen pipe terminals were at one

time a very common condition, and while even the method I have described is subject to frost closure it is only under very exceptional and unusually severe

conditions. In this connection it may interest you to know that wherever possible we reconnect vent pipes

to the stack before it passes through the roof arid in this way provide a circulation of air throughout the system and so prevent syphonic action. In recent years we have gone a step further and required tha" the pipe terminal shall conform to the pitch of the

roof, and for this purpose terminals are made having

a 45° and 60° pitch, as wr ell as the ordinary increaser used in a building having a flat roof. All increaser- have hubs and are finished with a lead flashing

The following opinions in regard to the use of increasers at the roof were expressed in discussion

reported m the Proceedings of the 1913 and If) 14 Conventions of the Canadian Institute of Sanitary

Engineers [1]:

(1) When the diameter of the pipe is increased below

the roof, the velocity of the outflowing air is retarded and this promotes the deposition of moisture. The les- metal in the increaser, the less is the tendency to freez-

•ing. (2) If the diameter of the pipe is increased at a considerable distance below the roof, the velocity of the outflowing air will be retarded, but, if the increaser

is made as short as possible, the stream of air does nor have an opportunity to expand fully within the in- creaser, and hence the moist air escapes without

coming in contact with the wall of the pipe and thi- tends to prevent freezing. (3) The larger in diameter

the increaser is made, the heavier the body of cold air that must be displaced by the warm air moving up the

stack. (4) Experience at Edmonton, Canada, ha- shown that when the vent pipes are cut off at the roof complete frost closure did not occur. The result - when an increaser was used, have been practically the same. (5) In St. Boniface, Canada, it was found

that, increasing the exposed length of the vent terminal

above the roof increased the trouble from frost closure. Their experience leads them to be heartily in favor of using increasers. (6) A great deal depends on the exposure of the terminal. Less trouble is experienced

with southern exposures than with other exposures. Moisture that freezes falls over on the outside of the vent in the direction of the wind and builds up there.

(7) At Winnipeg it was found that the increaser did not help matters any. The following recommendations were submit toil to the Convention referred to above and undoubtedly represent the thinking on the subject of frost closure prevalent in Canada at the time 1914

Winnipeg Recommendations. All terminals of soi waste, and ventilating pipes of 4 inches in diameter

or less shall be increased 2 inches in diameter lv' or, passing through the roof of the premises, and all ter- minals of such pipes shall project to the outer air t ot less than 1 inch and not more than 2 inches above ot the high side where passing through a pitched root and not less than 3 inches or more than 5 incite- :ibo\ c where passing through a flat roof, provided that Hie portion of all such pipe terminals above the root shall have a hub of a size in proportion to which the pipe - increased, and the same shall be made weatherprooi

by means of a lead flashing. All such lead used for

this purpose shall be in weight at least t> pounds p square foot and shall be worked over and into th
I

hub with not less than 5 inches of cover on the roof on

either side of the pipe terminal, and it shall be finished with a cast or wrought iron ring properly caulked into the hub which shall in no case project above such

terminal.

All terminals of soil, waste, and ventilating pipes

shall where passing through a pitched roof be carried to a point within 2 feet of the ridge or peak of the

roof and shall be located not less than 10 feet, from or

2 feet above any window, door, or other opening in the same or adjoining premises, provided that, in all cases a roof with a pitch of 6 inches or more in 12 inches shall be considered as a pitched roof. Saskatoon Recommendations. That all vent pipes

terminate not more than 1 inch above the pitch of roof on the high side and have a lead flashing turned

down 1 inch all around inside the top of pipe dressed

in tight and secured with a malleable iron ring. All vent pipes to be carried up to roof and to termi- nate the same size unless the vent, line is less than 4

inches in diameter, when it shall be increased to 4

inches, at least 3 feet below roof. We claim that by elimination of the roof jack and

increaser and the consequent decreased surface, we

lessen the radiation and therefore the deposition of moisture which congeals thereon.

All branch vents shall be carried back into the main

stack before passing through roofs. This will reduce

the number of roof terminals. Edmonton Recommendations. All soil, waste, and

ventilating pipes shall be located inside the premises

and all roof terminals of such pipes shall be located not

less than 10 feet distant from any opening door, win- dow, etc., in the same or any adjoining premises, nor

shall a perpendicular from any roof terminal to the grade be nearer than 10 feet to the side line of the lot; the roof terminal shall project l inch and no more

above the highest point on the roof where such roof terminal intersects the roof. All vent pipes of 4 inch diameter or less shall be

increased at least, 2 inches before passing through the

roof, and no roof terminal shall be less than 4 inches where the same passes through roof and shall terminate

with a hub and shall be flashed with sheet lead turned

down and caulked into the hub.

10. Methods of Retarding or Preventing

Closure of Roof Vents by Frost

Experience and the principles presented in this paper indicate that means of retarding the closure

of roof vents by frost include factors that affect the vent, terminal itself and factors that are independent of the vent terminal.

Of the former, we may list (1) limit the height

of exposed length of vent above the roof to the

extreme minimum that can be permitted, (2) enlarge the vent just before it passes through the

roof, (3) use a substitute material having a high

resistance to the transfer of heat in place of the

usual metallic vent pipe, (4) put thermal insulation

around the exposed length of the vent, and (5) in extreme cases provide means for heating the outer surface of the exposed length of the vent

electrically or by means of steam or hot water. In the latter category we may list the use of a house trap, either with or without a fresh-air vent.

If the discharge of hot water into the stack can be

prevented, this should help reduce the occurrence

of frost closure. The simplest, most obvious, and probably most

effective way of preventing or minimizing the

frosting up of roof vents is to reduce the length

of vent exposed to the low temperature to a minimum. In Canada it is quite customary to limit

the length of vent projecting above a sloping roof

to from 1 to 2 in. on the high side. Figure 23 shows a typical design of roof terminal

that has come into use at Saskatoon, Canada, and

has been found successful in resisting frost closure

[1], Note that the terminal is a special pipe with

the upper rim at an angle to fit approximately the

slope of the roof. This pipe is 2 ft long measured

from the rim on the lower side. There seems to be no valid reason for objecting

to a flush opening or a very short extension on a

sloping roof. Snow may occasionally block a vent

pipe, but the snow is porous and thus permits the

passage of some air and furthermore such closure,

which will occur only during heavy snow storms,

is short-lived. It would seem that any amount of

'll]!'

'

water that might, enter a vent that is flush with

the roof would be inconsequential. The situation on a flat roof, however, might be quite different,

since, if the strainers at the storm leaders should

become blocked with trash, the roof might become

flooded, and hence discharge an undue amount of

water down the roof vent. Correspondence with various persons in Canada

who have had experience with frost closure

elicited considerable interesting information, the

most pertinent of which follows:

Earle O. Turner of the University of New

Brunswick, Fredericton, states:

ii

From my own experience, the only phenomenon

of this kind in this climate is the formation of a frost cap over vents in soil pipes in buildings. This will only take place at temperatures below zero Fahrenheit

and will not, persist after the temperature rises.

*28
L. P. Cabana. Superintendent, Division of

Sanitary Inspection, City of Montreal, Canada,

| writes:

We have experienced the formation of ice at the

outlet of vents on roofs, but not to the extent of complete closure. There is always in extreme cases a oneinch opening except during a snow storm, when this opening may be blocked temporarily with snow. He states that the city does not permit house

] traps and that the vents are always 1 inch larger

] in diameter than are the stacks.

W. D. Cameron, Plumbing Inspector, Kirkland

j Lake, Canada, states:

I must say we do have difficulty to some extent, up

here with vent stacks during the extreme cold weather

which varies from zero to 55 degrees below during the

winter months. We have made some experiments

from time to time on this subject, and up to six years ago our code called for a 12-inch extension above the

roof on the highest side. This was found to be too

great an exposure, so we cut it down to 8 inches and

insulated the vent pipe from the roof to the ceiling

joists, which did help some, but in numerous cases could not be done where the stack was carried up the

corner of the building and where it was impossible to extend the stack up the roof to any other point.

We have come to the conclusion now, that by

increasing all vent stacks to 4 inches from a point

approximately 2 feet below the roof to 4 inches above

on the highest side, we have gained the most satis- faction. and where necessary, insulate the 2 feet below the roof. Although this does not entirely eliminate the ice condition, it does not completely

ice up solid under extreme conditions.

I must mention with reference to our plumbing

system here that we do not permit a main trap on

the sewer line between the main trunk sewer in the

street and the house, therefore, we have a straight vent line from the street through the roof on each

building. We do not permit anything less than 2- inch extensions through the roof; this we find is the

smallest size we can permit without completely icing

up solid. This freezing or icing which occurs here only happens

during the very lowest temperatures, perhaps from

15 to 45 degrees below zero and forms an icing on the

side of the pipe to a depth of approximately 1 inch. Then there forms a cone or light ice cap somewhat

heavier than a hoar frost and extends straight upwards

to a height of from 6 to 8 inches and remains there

until the temperature rises, which usually happens

about noon each day, or more often until the heat from the building increases sufficiently to break this

light ice cap and force an opening in the top, per- mitting the escape of the vapour. As for the wind

extending this cone or ice cap to one side of the vent, we do not have the wind here when the temperature

is at a low degree, for during such temperatures even

the smoke from the chimneys rises straight up and a heavy fog occurs. H. E. Roseborough, Building Inspector, Sudbury, Ontario, Canada, writes:

Hoar frost very seldom extends more than 6 inches from the top of the vent stack and is of very even

consistency. It generally forms in a cone shape above

the top of the stack and extends some 4 or 5 inches. The wind seems to have very little effect on the shape

of the cone of frost. During the second Great War restrictions were put on the use of 4-inch soil pipe, and at that time we

changed our by-laws to permit the use of a 3-inch stack for a two-family house. We carry our vent pipe

approximately 6 to 8 inches above the roof level, and

we do not use any interceptor trap at the entrance to our building, therefore each stack is a partial vent to our main sewer. Previous to 1938 we have had an odd case of a

4-inch stack closing with hoar frost, but since n-ing the 3-inch, only on one or two occasions, even with

the temperature at 47 degrees below zero, have we

had any trouble. During the past week our temperature ranged

from 47 below to 26 below for four days, and not one

case was reported to this office. We have had no

trouble whatever with a 6-inch stack freezing over. Gordon Park Jackson, Medical Officer of Health, Toronto, Canada, furnished the following

information:

The closure of vent stacks by frost in this City

happens infrequently. In the very few places where

this has occurred, it apparently was the result of the

excessive use of hot water. For example, when there

is a large fire in a heating furnace containing a domestic hot-water coil, the water becomes overheated

and discharges into the drain. Winter temperatures

in this City are usually below the freezing point, arid we frequently have temperatures below zero extending

over a period of three or four days. Vent stacks

less than 3 inches in diameter wffiere they extend through the roof are not permitted. V. S. Baker, Secretary-Treasurer of the Ontario

Association of Plumbing Inspectors and Affiliate- writes (referring to the City of London, Ontario.

Canada)

In the City of London the average winter temperature is around 10 to 20 degrees, with occasional temperatures of 10 to 15 degrees below zero for a day

or two. We receive a few complaints each winter from

frost closure on 4-inch vents and also on 3-inch. On

the average, the stacks that freeze are on the north

or west sides of dwellings . . . We have also noted

that the launch sink vent in the cold portion of the

attic space freezes when the building is insulated. In the western sections of the country increasers are used at the roof and very short terminals or nearly

flush. In reply to further questions Mr. Baker fur- nished the additional information that in the area

referred to, in general, stacks freeze with frost caps. Also that in the case of the lL-in. vents

in the attics of insulated homes, it was not certain

whether the pipes froze solidly or whether they were filled with a spongy ice. J. A. McDonald, City Engineer, Edmonton.

Alberta, Canada, furnished the following information in response to specific questions:

The City of Edmonton does not permit house

traps to be installed. The stack is not permitted

to extend more than 1 inch above the roof. Relatively

few cases of frost closure have been experienced there, but those that have been observed were of the type

that form on the interior wall of the pipe. Xo vent

smaller than 4 inches is permitted, and in any case, the stack is increased a minimum of 1 inch in diameter

where it passes through the roof. Edmonton fre- quently has periods of from one to three weeks when

the temperature ranges from 20 to 50 degrees below

zero continuously.

Guy S. Franks, Plumbing Inspector. Calgarv.

Alberta, Canada, states in response to specific

questions
A certain amount, of frost closure is experienced.

Every terminal of a soil, waste, or ventilating pipe

three inches, four inches, or five inches, shall be in- creased one inch in diameter, and each under three

inches shall be increased to four inches before passing

through the roof, by means of an increaser and shall project to the outer air not less than 1 inch nor more

than 3 inches above the roof and shall be made weatherproof by means of a lead flashing. All lead used for

this purpose shall be in weight at 6 pounds per square

foot and shall be worked over and into the hub of the

increaser at least 1 inch with not less than 6 inches of cover on either side of the roof terminal, and it shall be finished with cast or wrought iron ring properly caulked with lead in the hub thereof . . . We have

extreme low temperatures, lasting sometimes for days.

Maximum 10 below zero and minimum of 30 below

zero. Not the general rule. An unusual type of frost closure, caused by

moisture outside of the vent instead of moisture

inside, is reported by R. E. Andrews, Sanitary

Inspector, Niagara Falls City. He writes:

In view of the fact that Niagara Falls City is so geographically situated, we have practically no

rimeing of vent stacks even in the lJUinch size. We

do, however, have an icing condition caused by spray from the Falls being carried over the City by a South

or South-East wind. In that portion of the City and

suburbs so affected, we stress the need for a 4-inch vent stack or the existing vent to be increased immediately below the roof and carried through by 6 inches. This serves the purpose in the majority of cases, but we have exceptions where we have had the vents encircled by J4-inch copper pipe carrying hot water or steam and the whole installation lagged with hair felt and leaded over. This latter method has proved

effective and we are able to prevent blocking by ice. The following information was received from

A. E. Berry, Director, Sanitary Engineering

Division, Department of Health. Toronto, Canada:

We have been giving a good deal of consideration

to the question you have submitted. It is a problem

in this country, and unfortunately there are varying

opinions regarding it. In some municipalities they

report that closures do take place, while in others the} find no difficulty, even with a 3-inch vent. Under extreme cold weather conditions there would

probably be some closures, but even in the northern

part of this province, where the temperature quite

frequently goes down to 40 or 50 degrees below, no

particular difficulty appears to be involved. Probably it is due to the fact that these cold spells do not

last for any great length of time. We have been giving consideration to the development of a plumbing code for the Province of Ontario,

and the committee that was at work on this canvassed

the situation somewhat carefully, with the result that they did not feel any special precautions were neces- sary to prevent closures. Edward Pretious of the University of British

Columbia, Vancouver, Canada, wrote as follows:

Prior to this arrangement (see figure 24A) there was

no house trap, and the sewer cover was closed. The

w'arm sewer gases escaped through the roof vent, and freezing w'as prevalent. The present scheme

(shown in figure 24B) appears to obviate this condition. He also remarks that when the roof vent is flush with the roof, freezing does not occur.

WINNIPEG ROOF VENT

FRESH AIR VENT

-OPEN COVER 6-

///aSN\v/////\n\v///awv//a\\\y// -MANHOLE

-STREET SEWER

HOUSE TRAP

EDMONTON

rCLOSED COVER

Z

' ZHWI -MANHOLE

STACK—

VENT STOPS

FLUSH

WITH ROOF

-STREET SEWER

Figure 24. Systems used at Winnipeg and Edmonton,

Canada

11. Conclusions

1 . The roof vents of building drainage systems

may become partially or completely closed by

frost in very cold weather under certain conditions.

Among the factors that affect frost closure are:

(a) temperature of the outside air, (b) temperature

and humidity of the air passing up the stack and

vent, (c) wind velocity, (d) length of vent that is exposed to the outside atmosphere, (e) diameter

of vent, (f) thermal insulation, if any, of the ex- posed part of the vent, or the use of a vent pipe

of some material that is highly resistant to the

transmission of heat, (g) whether or not a house

trap is inserted in the building drain, either with

or without a fresh-air vent, (h) whether or not

the diameter of the vent is greater than that of the stack, and the distance to which such expansion extends below the roof, (i) the temperature

conditions in the air space below the roof, (j) the

exposure, whether northern, southern, etc., and

(k) the velocity of air flow upward through the

vent.

2. Frost closure has been observed in two general forms: (1) as a concentric layer that builds up

on the inner wall of the vent, and (2) as a cap that

builds up from the rim of the vent at its outlet. The latter form is the one that has been the more
^frequently reported, possibly because it is the

j more easily observed of the two. Sometimes the

1 two forms occur simultaneously.

3. In general, it appears that there is little like- lihood of trouble from frost closure unless the

! outside air temperature falls below about 10° F

, and remains there for at least several days.

4. Reducing the length of the exposed portion

j of the vent as much as possible appears to be the

j most certain way of reducing or preventing frost

closure.

5. Uninsulated small-diameter vents in un-

. heated attics may freeze solid unless protected by

! insulation.

6. The discharge of hot water into the stack,

1 particularly at night, when the upward convective

I air current is most pronounced, tends to increase

' the humidity of the air passing up the stack and

thus increases the tendency to frost closure.

7. The larger the diameter of the vent, the less

: likely it is to close completely because: (1) a longer

period of cold weather is required to create the

I necessary thickness of ice, and (2) because, with

j the larger diameter vents, the temperature of the

ice-air surface in the vents is generally higher for

a given thickness of ice layer than with the

smaller diameter vents. (See figs. 10 to 15).

Freezing stops when a temperature of 32° F is

j attained at the ice-air surface.

8. As the ah' from the street sewer is relatively

1 moist and warm, the use of a house trap to prevent

this moist air from passing up the stack should

reduce the tendency to frost closure. Even if a

fresh-air inlet is provided on the house side of the

trap, this provides a source of relatively cold dry

air that carries with it less moisture to condense

out and freeze in the vent.

9. Snow storms may close the vent temporarily,

i but the snow is porous, and evidence seems to be

available that this does not cause any serious

difficulty. 10. Reconnecting vent pipes to the stack before

it passes up through the roof has been found to reduce or prevent siphonage of trap seals when

the vent was completely closed by frost.

11. Increasing the diameter of the vent above

that of the stack may help in two ways: (1) It

affords the advantage of a larger diameter of vent,

so that it requires a longer time for the vent to

freeze up completely, and (2) it would seem that,

if the length of the expanded portion of the vent is relatively short, the stream of air passing up

through the vent may not expand soon enough to reach the chilled wall of the vent, and hence less moisture reaches the wall than would otherwise

be the case, so that the tendency to freeze is decreased.

12. The greater the wind velocity, the greater

the tendency to closure. In general, however, the

lower the temperature, the smaller is the wind

velocity. Less trouble seems to be experienced

when a vent has a southern exposure (in the

northern hemisphere) than when it is exposed on

the shady side of the roof.

13. The use of a material for the vent pipe that

has a higher resistance to the flow of heat than

does steel has a favorable effect. 14. As a rough estimate of the rate at which the

thickness of the ice layer in a vent may increase

in cold weather, we may take a value of 0.07

in. /hr, or roughly 1 % in. /day, assuming that the

convective current of air persists during the

greater part of the day. This value was obtained

by laboratory experiments on 3-in. vents for an outdoor air temperature of —30° F and with the

air passing up through the vent saturated with

moisture at a temperature of about 70° F. Values

of about 0.08 and 0.06 in. /hr were obtained for

1 /{-in. and 4-in. vents, respectively.

Acknowledgment is made to the Housing and

Home Finance Agency for its support of the

experimental part of this investigation. Credit is due John L. French for planning and directing the

early stages of the investigation and to James L. Johnson, Jr., for his painstaking work in developing

the experimental apparatus and in planning the

details of the tests. Particular acknowledgment

is made of the advice and assistance given by

Henry E. Robinson. He suggested to the authors

and outlined for them the method used in the

paper to compute the temperature of the ice-air surface in the vent as a substitute for the equally

accurate but more cumbersome method they used

originally. The authors also express their thanks

to Victor Brame, Jr., and Anthony L. Lembeck

for their careful experimental work and to Clarence

E. Bardsley, Otto Hintz, and Mrs. Helen Callaway

for carrying out much of the laborious computation. The paper has benefited greatly from infor- mation received from L. Glen Shields, Chief.

Department of Buildings and Safety, City of Detroit, and from numerous Canadian sources, and the authors express their appreciation of the

courtesy and patience of the individuals who

answered their numerous inquiries.

12. References

[1] Report of Proceedings of the 1913 and 1914 Conventions of the Canadian Institute of Sanitary Ei gi- neers. (Reynolds Ltd., Logan and Princess, 'Winni- peg, Canada).

[2] Recommended Minimum Requirements for Plumbum

National Bureau of Standards. Elimination of Wa>t<

Series, Report of Subcommittee on Plumbing of t Building Code Committee, U. S. Department of Commerce, BH13 (1932).

[3] William Beall Gray, Plumbing design and installation (David Williams Co., New York. N. 5 .. I'UC

[4] W. H. McAdam, Heat transmission McGraw-Hill

Book Co., Inc., New York. N. Y., 19421.

[5] Report of the Research Committee. Yearbook of t! American Society of Sanitary Engineering vol S. p. 178.

[6] Report of Proceedings, American Society of sa; r.a Engineering, vol. 14, p. 265 (192S 291.

Washington, January 2, 1954.

U S GOVERNMENT

BUILDING MATERIALS AND STRUCTURES REPORTS

[Continued from cover page n]

BMS32 Structural Properties of Two Brick-Concrete-Block Wall Constructions and a Concrete- Block Wall Construction Sponsored by the National Concrete Masonry Association. * BMS33 Plastic Calking Materials * BMS34 Performance Test of Floor Coverings for Use in Low-Cost Housing: Part 1 156 BMS35 Stability of Sheathing Papers as Determined by Accelerated Aging * BMS36 Structural Properties of Wood-Frame Wall, Partition, Floor, and Roof Constructions

With “Red Stripe” Lath Sponsored by The Weston Paper and Manufacturing Co_. 106 BMS37 Structural Properties of “Palisade Homes” Constructions for Walls, Partitions, and

Floors, Sponsored by Palisade Homes * BMS38 Structural Properties of Two “Dunstone” Wall Constructions Sponsored by the W. E. Dunn Manufacturing Co 106 BMS39 Structural Properties of a Wall Construction of “Pfeifer Units” Sponsored by the Wisconsin Units Co 10

BMS40 Structural Properties of a Wall Construction of “Knap Concrete Wall Units” Sponsored

by Knap America, Inc * BMS41 Effect of Heating and Cooling on the Permeability of Masonry Walls * BMS42 Structural Properties of Wood-Frame Wall and Partition Construction with “Celotex”

Insulating Boards Sponsored by The Celotex Corporation * BMS43 Performance Test of Floor Coverings for Use in Low-Cost Housing: Part 2 * BMS44 Surface Treatment of Steel Prior to Painting * BMS45 Air Infiltration Through Windows 206 BMS46 Structural Properties of “Scot-Bilt” Prefabricated Sheet-Steel Constructions for Walls,

Floors, and Roofs Sponsored by The Globe-Wernicke Co * BMS47 Structural Properties of Prefabricated Wood-Frame Constructions for Walls, Partitions, and Floors Sponsored by American Houses, Inc 206 BMS48 Structural Properties of “Precision-Built” Frame Wall and Partition Constructions

Sponsored by the Homasote Co * BMS49 Metallic Roofing for Low-Cost House Construction 256 BMS50 Stability of Fiber Building Boards as Determined by Accelerated Aging * BMS51 Structural Properties of “Tilecrete Type A” Floor Construction Sponsored by the

Tileerete Co * BMS52 Effect of Ceiling Insulation Upon Summer Comfort 156 BMS53 Structural Properties of a Masonry Wall Construction of “Munlock Dry Wall Brick”

Sponsored by the Munlock Engineering Co 106 BMS54 Effect of Soot on the Rating of an Oil-Fired Heating Boiler 106 BMS55 Effects of Wetting and Drying on the Permeability of Masonry Walls * BMS56 A Survey of Humidities in Residences 106 BMS57 Roofing in the United States—Results of a Questionnaire * BMS58 Strength of Soft-Soldered Joints in Copper Tubing 15(4 BMS59 Properties of Adhesives for Floor Coverings * BMS60 Strength, Absorption, and Resistance to Laboratory Freezing and Thawing of Building

Bricks Produced in the United States 30f4 BMS61 Structural Properties of Two Nonreinforced Monolithic Concrete Wall Constructions. . * BMS62 Structural Properties of a Precast Joist Concrete Floor Construction Sponsored by the Portland Cement Association 156 BMS63 Moisture Condensation in Building Walls * BMS64 Solar Heating of Various Surfaces 10(4 BMS65 Methods of Estimating Loads in Plumbing Systems .... 206 BMS66 Plumbing Manual 40)4 BMS67 Structural Properties of “Mu-Steel” Prefabricated Sheet-Steel Constructions for Walls,

Partitions, Floors, and Roofs, Sponsored by Herman A. Mugler 20(4 BMS68 Performance Test for Floor Coverings for Use in Low-Cost Housing: Part 3 25(4 BMS69 Stability of Fiber Sheathing Boards as Determined by Accelerated Aging 106 BMS70 Asphalt-Prepared Roll Roofings and Shingles 206 BMS71 Fire Tests of Wood- and Metal-Framed Partitions 306 BMS72 Structural Properties of “Precision-Built, Jr.” Prefabricated Wood-Frame Wall Construction Sponsored by the Homasote Co * BMS73 Indentation Characteristics of Floor Coverings 106 BMS74 Structural and Heat-Transfer Properties of “U. S. S. Panelbilt” Prefabricated SheetSteel Constructions for Walls, Partitions, and Roofs Sponsored by the Tennessee

Coal, Iron & Railroad Co 206 BMS75 Survey of Roofing Materials in the North Central States 156 BMS76 Effect of Outdoor Exposure on the Water Permeability of Masonry Walls * BMS77 Properties and Performance of Fiber Tile Boards ...

* BMS78 Structural, Heat-Transfer, and Water-Permeability Properties of Five Earth-Wall

Constructions 356 BMS79 Water-Distributing Systems for Buildings 206 BMS80 Performance Test of Floor Coverings for Use in Low-Cost Housing: Part 4 * BMS81 Field Inspectors’ Check List for Building Constructions (cloth cover, 5x7^ inches) — 356

•Out of print. [List continued on cover page iv]
BUILDING MATERIALS AND STRUCTURES REPORTS

[Continued from cover page hi] BMS82 Water Permeability of Walls Built of Masonry Units 250 BMS83 Strength of Sleeve Joints in Copper Tubing Made With Various Lead-Base Solders 15(5 BMS84 Survey of Roofing Materials in the South Central States * BMS85 Dimensional Changes of Floor Coverings With Changes in Relative Humidity and

Temperature * BMS86 Structural, Heat-Transfer, and Water-Permeability Properties of “Speedbrik” Wall

Construction Sponsored by the General Shale Products Corporation 15(5 BMS87 A Method for Developing Specifications for Building Construction—Report of Subcommittee on Specifications of the Central Housing Committee on Research,

Design, and Construction 200 BMS88 Recommended Building Code Requirements for New Dwelling Construction With

Special Reference to War Housing * BMS89 Structural Properties of “Precision-Built, Jr.” (Second Construction) Prefabricated Wood-Frame Wall Construction Sponsored by the Homasote Co 150 BMS90 Structural Properties of “PHC” Prefabricated Wood-Frame Constructions for Walls,

Floors, and Roofs Sponsored by the PHC Housing Corporation 150 BMS91 A Glossary of Housing Terms * BMS92 Fire-Resistance Classifications of Building Constructions 350 BMS93 Accumulation of Moisture in Walls of Frame Construction During Winter Exposure. _ * BMS94 Water Permeability and Weathering Resistance of Stucco-Faced, Gunite-Faced, and

“Knap Concrete-Unit” Walls * BMS95 Tests of Cement-Water Paints and Other Waterproofings for Unit-Masonry Walls 250 BMS96 Properties of a Porous Concrete of Cement and Uniform-Sized Gravel 100 BMS97 Experimental Dry-Wall Construction With Fiber Insulating Board * BMS98 Physical Properties of Terrazzo Aggregates * BMS99 Structural and Heat-Transfer Properties of “Multiple Box-Girder Plywood Panels” for Walls, Floors, and Roofs * BMS100 Relative Slipperiness of Floor and Deck Surfaces * BMS101 Strength and Resistance to Corrosion of Ties for Cavity Walls * BMS102 Painting Steel 150 BMS103 Measurements of Heat Losses From Slab Floors * BMS104 Structural Properties of Prefabricated Plywood Lightweight Constructions for Walls,

Partitions, Floors, and Roofs Sponsored by the Douglas Fir Plywood Association. * BMS105 Paint Manual with particular reference to Federal Specifications $1. 50 BMS106 Laboratory Observations of Condensation in Wall Specimens 100 BMS107 Building Code Requirements for New Dwelling Construction * BMS108 Temperature Distribution in a Test Bungalow With Various Heating Devices 150 BMS109 Strength of Houses: Application of Engineering Principles to Structural Design $1. 75 BMS110 Paints for Exterior Masonry Walls 200 BMSlll Performance of a Coal-Fired Boiler Converted to Oil 150 BMS112 Properties of Some Lightweight-Aggregate Concretes With and Without an Air- Entraining Admixture 150 BMS113 Fire Resistance of Structural Clay Tile Partitions 150 BMS114 Temperature in a Test Bungalow With Some Radiant and Jacketed Space Heaters 250

B MSI 15 A Study of a Baseboard Convector Heating System in a Test Bungalow 200 BMS116 Preparation and Revision of Building Codes 200 BMS117 Fire Resistance of Walls of Lightweight Aggregate Concrete Masonry Units 250 BMS118 Stack Venting of Plumbing Fixtures 250 BMS119 Wet Venting of Plumbing Fixtures 250 BMS120 Fire Resistance of Walls of Gravel-Aggregate Concrete Masonry Units.. 150 BMS121 Investigation of Failures of White-Coat Plasters 300 BMS122 Physical Properties of Some Samples of Asbestos-Cement Siding 200 BMS123 Fire Tests of Wood-Framed Walls and Partitions With Asbestos-Cement Facings 150 BMS124 Fire Tests of Steel Columns Protected With Siliceous Aggregate Concrete 150 BMS125 Stone Exposure Test Wall 300 BMS126 The Self-Siphonage of Fixture Traps 200 B MSI 27 Effect of Aging on the Soundness of Regularly Hydrated Dolomitic Lime Putties 150 BMS128 Atmospheric Exposure Tests of Nailed Sheet Metal Building Materials 200 BMS129 Fire Endurance of Shutters for Moving-Stairway Openings 100 BMS130 Methods and Equipment for Testing Printed-Enamel Felt-Base Floor Covering 150 BMS131 Fire Tests of Gunite Slabs and Partitions 150 BMS132 Capacities of Plumbing Stacks in Buildings 250 BMS133 Live Loads on Floors in Buildings 250 B MS134 Fire Resistance of Concrete Floors * BMS135 Fire Tests of Steel Columns Encased With Gypsum Lath and Plaster 150 BMS136 Properties of Cavity Walls 150 BMS137 Influence of the Wash From Bronze on the Weathering of Marble 150 BMS138 Effect of Edge Insulation Upon Temperature and Condensation on Concrete-Slab

Floors 200 BMS139 Studies of Stone-Setting Mortars 250 BMS140 Selected Bibliography on Building Construction and Maintenance 300 BMS141 Fire Endurance of Open-Web Steel Joist Floors With Concrete Slabs and Gypsum

Ceilings 200 BMS142 Frost Closure of Roof Vents in Plumbing Systems 250 BMS143 Fire Tests of Brick Walls **

•Out of print. ••In press.