A Thermal Flowmeter for 

Measuring Velocity of 

Flow in a Well

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1544-E

I'toperty oi
A Thermal Flowmeter for 

Measuring Velocity of 

Flow in a Well

By HOWARD T. CHAPMAN and ALBERT E. ROBINSON

GENERAL GROUND-WATER TECHNIQUES

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1544-E

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1962
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington 25, D.C.
CONTENTS

Page

Abstra ct__ __-___-___--_____-_____--___---_----__--___--_-_---_., E-1

Intro duction ______________________________________________________ 1

Design of flowmeter______________________________________________ 3

Sensing unit_____-_-______-_-__________-__-____--_-_--_-------. 3

Control unit______-_-_-___-_-______-___--_____-_-----__------- 5

Operation of instrument_--_---_-_-__-_-_-------_-_-------___------- 10

Results_____________________________________________________ 11

Reference -______________-_____-._________---_-_----_----__-------_- 12

ILLUSTRATIONS

Page 

FIGURE 1. Sections of sensing unit___-_________-_-___-______________- E-4

2. Generalized wiring diagram of flowmeter__________________ 6

3. Detailed wiring diagram of flowmeter______________________ 7

4. Rating curve__-_-____-_-_-_________--_-____-----_-_--_-_ 8

5. Instrument panel._______________________________________ 9

in

GENERAL GROUND-WATER TECHNIQUES

A THERMAL FLOWMETER FOR MEASURING VELOCITY 

OF FLOW IN A WELL

By HOWARD T. CHAPMAN and ALBERT E. ROBINSON

ABSTRACT

A small flowmeter for measuring the rate of vertical flow in a well has been 

developed by the U.S. Geological Survey. The flowmeter is based on 

the principle of heating the water with an electrical heater and measuring the 

temperature difference between a point below and a point above the heater. 

The development, construction, and operation of the meter are described. The 

meter gives accurate results when measuring velocities of 1 to 20 feet per minute.

INTRODUCTION

Data on vertical flow in wells are important because they can be 

used to determine the permeability of an aquifer. Measurements of 

the rates of vertical flow at different depths in a pumped well reveal 

the location, thickness, and relative productivity of water-bearing 

zones. Similar information can be obtained if vertical flow occurs 

in a well not being pumped. Such measurements in the past have 

rarely been feasible because of the lack of a meter suitable for most 

field conditions.

The two principal requirements in constructing a satisfactory flowmeter are as follows: (1) the sensing unit must be small enough to be 

lowered into the well past the pump bowls through openings whose 

annular clearances may be less than an inch, and (2) the flowmeter 

must be capable of measuring low velocities, on the order of 20 fpm 

(feet per minute) or less. Existing mechanical flowmeters are too 

large to bypass the pump installations and are not suitable for measuring velocities as low as those normally found in an unpumped well. 

The U.S. Geological Survey has attempted to develop small 

mechanical flowmeters, but such small instruments are generally unsatisfactory in the field because they are delicate and may be disabled 

by a single grain of sand.

E-l
E-2 GENERAL GROUND-WATER TECHNIQUES

A consideration of nonmechanical flowmeters led to the idea of 

using a combination of an electrical heater as a heat source and 

thermistors to make up a sensing unit. A thermistor is an electrical 

resistor whose resistance changes at a known rate with changes in 

temperature. On March 12, 1953, the U.S. Geological Survey filed 

for a patent on such a device, called a Thermal Flowmeter. The 

patent, No. 2,728,225, is dated December 27, 1955. The pilot model 

described in the patent consists of an electric heater installed in a 

tube. When a fluid passes through the tube, it is heated and then 

flows past a thermistor. A change in the temperature of the fluid 

causes the resistance of the thermistor to change also and alter the 

amount of current flowing through it. The amount the temperature 

of the water rises depends on the rate of flow past the heater, and on 

the amount of heat being emitted by the heater. The fluctuation of 

electrical current caused by changes in resistance due to the heating 

of the water is measured by a meter at the ground surface. A 

velocity-rating curve can be produced by plotting a graph of the 

current readings for a range of known velocities. An unknown 

velocity can then be measured indirectly by utilizing this rating curve.

Because the temperature of the water in a well may vary with 

depth, or with time during pumping, it is evident that something 

must be done to compensate for the effect of such changes on the 

thermistor. This problem is solved by placing a second thermistor 

ahead of the heater. The two thermistors are wired in the form of 

two legs of a bridge circuit, and the signal received at the electronic 

meter becomes that of the electrical current owing to the unbalanced 

resistance between the two thermistors. Thus, the signal is proportional to the product of the difference in resistance between the two 

thermistors, regardless of the temperature of the surrounding water.

The range of velocities that can be measured accurately depends 

on the amount of heat generated by the heater, and on the throat 

diameter of the tube lining the inside of the heating element. The 

experimental unit was able to give consistent velocity readings with 

changes in water temperature.

The experimental sensing unit described in this report was designed 

to measure low velocities, ranging from 1 to 20 fpm. This prototype 

may not be of the best design attainable, but it is compact and reliable. Velocities of more than 100 fpm have been measured by other 

experimental thermal sensing units designed with larger liner tubes 

through the heater sections than the one described here, and containing baffles to stir and mix the heated water. Although development of a current meter to measure vertical velocities larger than 20
THERMAL FLOWMETER, MEASURING WELL-FLOW VELOCITY E-3

fpm could be useful too, the particular pilot model referred to in this 

report and most of the other experimental models used in this investigation were designed for measuring low velocities only.

DESIGN OF FLOWMETER

SENSING UNIT

The sensing unit consists of a heating element, two thermistors, 

a brass body through which the water flows, and an outside housing 

(fig. 1). The body of the sensing unit is a %6-inch ID brass tube 

3.50 inches long joined to two 1.8Y5-inch lengths of l/^-inch OD brass 

tubing. The total length of the sensing unit is Y.25 inches. The 

electric heating element is wound around the smaller brass tube. The 

outside of the heating element is coated with an insulating material to 

a diameter of half an inch. A thermistor is placed in each i/^-inch 

tube, 0.650 inch from the ends of the narrower central tube which lines 

the heating element.

The body of the sensing unit, including the thermistors and the 

heating element, is inserted into the outside housing, a %-inch OD 

brass tube. (See fig. 1.) The ends are soldered to seal the electrical 

components. To prevent water leakage where the thermistors protrude, a sealer composed of 100 parts by weight of Furane's No. 202 

epoxy resin and 10 parts by weight of Furane's No. 951 Hardener 

fills the annular opening between the i/^-inch tube and the %-inch 

housing. A flattened tube houses the wires that leave the sensing 

unit; this tube also is filled with the same epoxy compound.

The upper thermistor is a "Veco" No. 32A1D8, which is 2 inches 

long; the lower is a "Veco" No. 32A11-N8, which is l/2 incn l°ngThese are nominal lengths and are trimmed to fit in their respective 

positions. In spite of their different lengths, their electrical characteristics are identical. The nominal resistance of each thermistor 

is 2,000 (±20 percent) ohms at 25° C. The two wires from the heating element, at points a and a! on figure 1, and the two leads from the 

bottom thermistor, at point Z>, are brought to the upper end of the 

sensing unit as shown in figure 1. The wires enter the body of the 

sensing unit through two holes near its top, at points c and d. The 

upper end of the body of the sensing tube is soldered to a %6-inch 

OD brass tube that has been flattened and forms a housing for all 

wires leaving the sensing unit. The flattened tube is soldered to the 

body in such a manner that it covers the wire openings but still allows 

the water to pass. This part of the unit is shown as'section X-X' at 

the bottom of figure 1.

The maximum capacity of the heating element in the sensing unit 

is 100 watts in air. By setting the dial of a variable transformer, or
E-4 GENERAL GROUND-WATER TECHNIQUES
THERMAL FLOWMETER, MEASURING WELL-FLOW VELOCITY E-5

Variac (General Radio Corp., Type 200B), on the instrument panel, 

the output of the heating element can be positively and accurately 

controlled from 0 to 100 watts. The output amperage is read on an 

a-c ammeter in series with the output of the Variac to the heating 

element. The heating element described in this report uses 0.15 

ampere.

The two thermistors form two legs of a bridge circuit. One wire is 

common to both thermistors, and only 3 wires are needed for the 

circuitry of the 2 thermistors. In addition to the 3 wires for the 2 

thermistors, 2 wires are required for the heating element. In the 

laboratory a 5-conductor cable, Belden 8455, was used, which provided 

2 No. 18 and 3 No. 22 stranded wires. The 2 No. 18 wires are connected to the heating element and the 3 No. 22 wires are used for the 

thermistors. Belden 8455 cable comes in standard 250-foot lengths; 

longer lengths are available on special order from the manufacturer.

A manufacturer has been contacted to produce a 5-prong quick 

connector for attaching the thermal sensing unit to the 5-wire cable. 

A connector could be made that would be watertight and sufficiently 

small (%-inch diameter) to allow the sensing unit to pass through 

small openings.

Figure 2 shows a generalized diagrammatic view of the electrical 

circuit of the thermal sensing unit and its relation to the bridge 

circuit; figure 3 shows a detailed wiring diagram for the entire flowmeter and bridge unit. In the absence of heat from the heating 

element and with water passing through the unit, both thermistors 

are at the same temperature and the bridge can be balanced with 

100-ohm bridge balance potentiometer. When heat is applied the 

signal thermistor is heated, and its resistance decreases so that more 

current will flow through this leg of the bridge. It is this current 

change, caused by the unbalancing of the bridge circuit, that is the 

signal to the differential amplifier and that is measured. The current 

changes are related in the laboratory to controlled velocities of water 

flowing through the meter, and a rating curve similar to that shown 

in figure 4 is developed. The rating curve shows the relation of 

changes in electrical current to changes in water velocity. Velocities 

in wells are then determined by using the rating curve.

CONTROL UNIT

The electronic controls (Variac and amplifier) of the thermal flowmeter are mounted on an 8- by 9%-inch panel. The makeup of the 

electronic control circuit is shown in detail in figure 3, and figure 5 

shows the front of the instrument panel with the controls and their 

location. The panel is set in an S1/^- by 8- by 20-inch toolbox. The
E-6 GENERAL GROUND-WATER TECHNIQUES

Bridge balance

Signal out

 =-6v

ll' ~ N5 v

 Vanac . 'WOW

n

100 w 

AA/WW

Heater

Signal 

thermistor

Temperaturecompensating 

thermistor

FIGURE 2. Generalized wiring diagram of thermal flowmeter.
FIGURE 3. .Detailed wiring diagram of thermal flowm
E-8 GENERAL GROUND-WATER TECHNIQUES
\=0 

I 468

O O O

9

1. Line cord

2. Varlac

3. a-c ammeter

4. Varlac pilot light

5. Heat switch

6. Fuse

7. Fuse

8. Instrument pilot light

9. Power supply switch

10. Vent

11. Vent

12. 6-volt-battery Input

13. Bridge-balan

14. Mlcroamme

15. Amplifier ad

16. One branch 

driver adj

FIGUBB 5. Sketch showing components of Instrument pa
E-10 GENERAL GROUND-WATER TECHNIQUES

box is the type having a removable tray in the top. The tray is removed and the electronic panel is mounted on the brackets formerly 

used to hold the tray.

The Variac (variable autotransformer) controls the heat output of 

the heating element. The resulting amperage is read on the a-c ammeter. The difference between the electrical currents flowing through 

the two thermistors is amplified so that it may be read more accurately 

on the microammeter. The amplifier is the differential type, with 

unit voltage gain. Its main purpose is for power gain; but, if desired, 

it could also drive a recorder.

OPERATION OF INSTRUMENT

The following procedure and instructions are recommended for 

logging with the pilot model of the experimental sensing unit. Numbers in parentheses refer to numbers on figure 5. Before logging is 

begun, connect the commutator line from the reel to the instrument 

receptacle (19) and plug in the line cord (1) to a 110-volt 50-60-cycle 

line. Then lower the thermal sensing unit into the water in the well 

to be logged. Before turning on power or heat switch, follow 

procedures 1 and %.

1. Plug 6-volt battery lead into receptacle (12) and move bridgebalance and log switch (13) to the left to the word "balance."

2. Adjust microammeter (14) to zero, with bridge-balance potentiometer (18). Screwdriver-adjustment potentiometers (16) and 

(17) should be turned as far clockwise as possible unless unable 

to adjust with bridge-balance potentiometer (18).

3. Turn power-supply switch (9) on and allow 20 minutes for 

warmup.

4. Move bridge-balance and log switch (13) to the right to the 

word "log." Adjust microammeter (14) to 100 with the amplifier-adjustment potentiometer (15).

5. With Variac (2) turned to extreme counterclockwise position, turn 

on heat switch (5).

6. Adjust to desired heat with Variac (2). The a-c ammeter (3) 

registers the amount of current, which may be converted in 

terms of heat.

7. The velocity is determined on the rating curve by finding the 

value of velocity that corresponds to the microammeter (14) 

reading. Figure 4 is the rating curve for the pilot model of the 

thermal sensing unit.

8. Check instrument balance at intervals by turning heat switch off 

and allowing time for thermal sensing unit to cool. Microammeter (14) should return to a reading of 100. If not, readjust
THERMAL FLOWMETER, MEASURING WELL-FLOW VELOCITY E-ll

instrument as in procedures 1, 2, and 4. Leave power-supply 

switch (9) on during this procedure to avoid warmup delay. 

Turn heat switch (5) on and read. 

9. Turn heat switch (5) off when thermal sensing unit is out of the

water, or the unit may be damaged. 

10. Be sure to remove 6-volt battery plug when logging is finished.

RESULTS

A laboratory-constructed well, in which the vertical velocity could 

be controlled from 1 to 130 fpm, was used for testing several thermal 

sensing units. Each sensing unit required individual calibration. 

Although individual units may appear to be identical in construction, 

the velocity curves differ, probably because of differences in the 

electrical components or in the construction of the unit.

The individual calibration applies only for the laboratory conditions and setup used. Adaptation to field use requires some modifications, such as centering devices and flow-channeling devices, to cope 

with the conditions peculiar to the site. An excellent discussion of 

some of the problems involved in the field use of a thermal flowmeter, 

and the techniques employed to overcome them, is given in a paper 

by Patten and Bennett (1962).

Figure 4 shows the rating curve for one particular sensing unit 

having a %6 -inch ID bore through the heating element. Only one 

heat range, 0.15 ampere a. c., was used for this sensing unit. The 

higher temperatures produced by 0.2 or 0.25 ampere a. c. caused the 

sensing unit to become unstable at low velocities, and reliable readings 

were difficult to obtain for velocities less than 14 fpm. Sensing units 

having bore diameters greater than %6 inch through the heating element were tested in various heat ranges, and separate rating curves 

were made for each. Measurement of high velocities required more 

heat from the heater, and baffles for mixing the heated water in the 

bore of the heating element to provide uniformly heated water. The 

readings, or velocity determinations, in the velocity ranges higher 

than 20 fpm have not been completely reliable, but enough work has 

been done to indicate that satisfactory results could be obtained by 

redesigning the heating element for more thorough mixing of heated 

water.

The ability of the sensing unit described in this report to compensate for the temperature changes at different depths in the well 

bore was determined by dropping the temperature of the water l7°F 

at a known rate. The instrument responded with identical watervelocity readings time after time.
E-12 GENERAL GROUND-WATER TECHNIQUES

Direction of flow, whether up or down a well bore, also could be 

detected with a properly designed sensing unit. Detection of downward flow was tried with the sensing unit described in this paper, but 

the detectable velocity range was found to be restricted to 7.5 to 20 

fpm. The problem of measuring flow direction should be considered 

in any future experimentation and development.

The vertical flowmeter described here is potentially an important 

aid to geologists and hydrologists first, because it is capable of 

logging extremely low velocities, which heretofore have not been detectable; and second, because of its small diameter, which permits it 

to be used in wells containing pump columns. The pilot instrument 

described is reliable in the low-velocity region; it is believed that this 

reliability could be extended to higher velocities by further experimentation in design. Eventually it may be possible to incorporate all 

the features needed for low and high velocities into a single sensing 

unit.

REFERENCE

Patten, E. P. and Bennett, G.D. (1962), Methods of flow measurement in well 

bores : U.S. Geol. Survey Water-Supply Paper 1544-C, 28 p.

U.S. GOVERNMENT PRINTING OFFICE : 1962 O 644435