David O. Davis, David J. Friedlander, and J. David Saunders

Glenn Research Center, Cleveland, Ohio

Franco C. Frate

ASRC Aerospace Corporation, Cleveland, Ohio 

Lancert E. Foster

Glenn Research Center, Cleveland, Ohio

Calibration of the NASA Glenn Research 

Center 16 in. Mass-Flow Plug

NASA/TM—2014-218128

June 2014

FEDSM2012–72266
NASA STI Program . . . in Profile

Since its founding, NASA has been dedicated to the 

advancement of aeronautics and space science. The 

NASA Scientific and Technical Information (STI) 

program plays a key part in helping NASA maintain 

this important role.

The NASA STI Program operates under the auspices 

of the Agency Chief Information Officer. It collects, 

organizes, provides for archiving, and disseminates 

NASA’s STI. The NASA STI program provides access 

to the NASA Aeronautics and Space Database and 

its public interface, the NASA Technical Reports 

Server, thus providing one of the largest collections 

of aeronautical and space science STI in the world. 

Results are published in both non-NASA channels 

and by NASA in the NASA STI Report Series, which 

includes the following report types:

• TECHNICAL PUBLICATION. Reports of 

completed research or a major significant phase 

of research that present the results of NASA 

programs and include extensive data or theoretical 

analysis. Includes compilations of significant 

scientific and technical data and information 

deemed to be of continuing reference value. 

NASA counterpart of peer-reviewed formal 

professional papers but has less stringent 

limitations on manuscript length and extent of 

graphic presentations.

• TECHNICAL MEMORANDUM. Scientific 

and technical findings that are preliminary or 

of specialized interest, e.g., quick release 

reports, working papers, and bibliographies that 

contain minimal annotation. Does not contain 

extensive analysis.

• CONTRACTOR REPORT. Scientific and 

technical findings by NASA-sponsored 

contractors and grantees.

• CONFERENCE PUBLICATION. Collected 

papers from scientific and technical 

conferences, symposia, seminars, or other 

meetings sponsored or cosponsored by NASA.

• SPECIAL PUBLICATION. Scientific, 

technical, or historical information from 

NASA programs, projects, and missions, often 

concerned with subjects having substantial 

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientific and 

technical material pertinent to NASA’s mission.

Specialized services also include creating custom 

thesauri, building customized databases, organizing 

and publishing research results.

For more information about the NASA STI 

program, see the following:

• Access the NASA STI program home page at 

http://www.sti.nasa.gov

• E-mail your question to help@sti.nasa.gov

• Fax your question to the NASA STI 

Information Desk at 443–757–5803

• Phone the NASA STI Information Desk at

443–757–5802

• Write to:

 STI Information Desk

 NASA Center for AeroSpace Information

 7115 Standard Drive

 Hanover, MD 21076–1320
David O. Davis, David J. Friedlander, and J. David Saunders

Glenn Research Center, Cleveland, Ohio

Franco C. Frate

ASRC Aerospace Corporation, Cleveland, Ohio 

Lancert E. Foster

Glenn Research Center, Cleveland, Ohio

Calibration of the NASA Glenn Research 

Center 16 in. Mass-Flow Plug

NASA/TM—2014-218128

June 2014

FEDSM2012–72266

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

2012 Fluids Engineering Division Summer Meeting

sponsored by the American Society of Mechanical Engineers (ASME)

July 8-12, 2012, Rio Grande, Puerto Rico
Acknowledgments

Funding from the Supersonics Project of the NASA Fundamental Aeronautics Program is gratefully acknowledged. The 

authors would also like to thank Hyun Dae Kim of NASA GRC for acquiring the 16 in. MFP data.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://www.sti.nasa.gov

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 

This report is a formal draft or working 

paper, intended to solicit comments and 

ideas from a technical peer group.

This report contains preliminary findings, 

subject to revision as analysis proceeds.
NASA/TM—2014-218128 1

Calibration of the NASA Glenn Research Center 16 in. Mass-Flow Plug

David O. Davis, David J. Friedlander, and J. David Saunders

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Franco C. Frate

ASRC Aerospace Corporation

Cleveland, Ohio 44135

Lancert E. Foster

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

The results of an experimental calibration of the NASA 

Glenn Research Center 16 in. Mass-Flow Plug (MFP) are 

presented and compared to a previously obtained calibration 

of a 15 in. Mass-Flow Plug. An ASME low-beta, long-radius 

nozzle was used as the calibration reference. The discharge 

coefficient for the ASME nozzle was obtained by numerically 

simulating the flow through the nozzle from the WIND-US 

code. The results showed agreement between the 15 and 16 in.

MFPs for area ratios (MFP to pipe area ratio) greater than 0.6 

but deviate at area ratios below this value for reasons that are 

not fully understood. A general uncertainty analysis was also 

performed and indicates that large uncertainties in the 

calibration are present for low MFP area ratios.

Introduction

Large-scale model supersonic aircraft inlets are routinely 

tested in NASA Glenn Research Center’s (GRC) larger wind 

tunnels such as the 8- by 6-ft and 10- by 10-ft Supersonic 

Wind Tunnels (SWT). Two key objectives of such tests are to 

ensure that the air supplied by an inlet matches the mass-flow 

demand of an engine and that the inlet operates in a stable 

condition over a wide range of mass-flows. Thus, accurate 

measurement of inlet mass-flow is of primary importance. Due 

to its relatively simple mechanical design, the mass flow 

through an inlet is often controlled and measured by a 

calibrated conical mass-flow plug (MFP). For larger models, 

GRC uses a 16 in. diameter MFP which was fabricated by 

modifying a pre-existing 15 in. MFP. Calibration of the 16 in.

MFP plug was performed in-house using an ASME low-beta, 

long-radius nozzle as the reference measurement. The 

procedure and resulting calibration, as well as a comparison to 

the calibration of the previous 15 in. MFP are reported herein.

Nomenclature

A Area (in2)

AR MFP area to cold-pipe area ratio (Eq. (20))

CD Discharge coefficient

D Diameter (in)

L1 ASME nozzle throat length (in, Figure 3)

M Mach number

MFP Mass Flow Plug

R Radius (in)

R1 ASME nozzle ellipse major radius (in, Figure 3)

R2 ASME nozzle ellipse minor radius (in, Figure 3)

Rair Gas constant for air (53.3525 ft·lbf/(lb·R)

Red ASME nozzle Reynolds number

Red,s Scaled ASME nozzle Reynolds number

Red,s = Red ×10×10–6

T Temperature (R) or throat tap location (in, Figure 3)

U Velocity (ft/sec)

d ASME nozzle diameter (in)

gc Proportionality constant (32.17405 lb·ft/(lbf·s

2

)

p Pressure (psi)

s Slant height of the frustum of a cone (in, Figure 5)

w mass flow rate (lb/s)

x,r,θ Cylindrical coordinates

x,y,z Cartesian coordinates

xplug Measured position of MFP (in)

x′plug Effective position of MFP (in, Figure 5 and Eq. (23))

β Ratio of ASME nozzle-to-approach pipe diameter

δXi Uncertainty of measure and Xi

φ MFP cone half-angle (deg, Figure 5)

γ Ratio of specific heats

ρ Density (lb/ft3

)
NASA/TM—2014-218128 2

Subscripts

a Pertaining to the average component

amb Pertaining to ambient conditions

i Pertaining to ideal conditions

n Pertaining to the normal component

noz Pertaining to the ASME nozzle

pipe Pertaining to the cold-pipe

plug Pertaining to the MFP

pot Pertaining to potential flow conditions

t Pertaining to total conditions

v Pertaining to the vertical component

δ* Pertaining to boundary-layer blockage (displacement 

thickness)

Superscripts

* Pertaining to choked flow conditions

Figure 1.—Schematic of 16 in. MFP Setup in 10- by 10-ft SWT.

Calibration Procedure

The calibration of both the caged 15 and 16 in. mass-flow 

plugs were carried out with the experimental setup shown in 

Figure 1. The four primary components of the calibration rig 

are the American Society of Mechanical Engineers (ASME) 

inlet flow nozzle assembly, an adapter spool piece, the coldpipe assembly, and the mass-flow plug assembly. The entire 

calibration assembly was mounted vertically on the floor of 

GRC’s 10- by 10-ft Supersonic Wind Tunnel and protruded 

through a sealed opening in the ceiling. The ASME nozzle 

was fed by atmospheric ambient pressure and temperature air 

while the wind tunnel exhausters were used as a vacuum 

source to establish a flow through the assembly. A photo of 

the ASME nozzle on the top of the 10- by 10-ft. SWT is 

shown in Figure 2 and a schematic of the geometry is shown 

in Figure 3. A photo of the 16 in. MFP attached to the coldpipe is shown in Figure 4 and a schematic of the plug is shown 

in Figure 5.

The spool piece is an adapter to match the ASME nozzle 

exit diameter to the cold-pipe diameter under test. The coldpipe is simply a 96 in. long constant-area pipe whose primary 

purpose is to allow for a flow-settling length between the inlet 

exit and the mass-flow plug. Near the forward end is a 

spherical-nosed centerbody supported by three equally spaced 

struts. The centerbody nose is intended to simulate the fan 

spinner on a turbojet engine. Attached to the forward end of 

the cold-pipe is a spool piece that houses eight compressor 

face rakes. The rakes lie in the plane of the tip of the 

centerbody nose. The inside edge at the exit plane of the coldpipe is sharp to fix the position of the mass-flow plug choke 

point.

Figure 2.—ASME nozzle assembly.
NASA/TM—2014-218128 3

Figure 3.—ASME nozzle schematic.

A picture of the 16-in. mass-flow plug attached to the coldpipe is shown in Figure 4. The cone is actuated by a hydraulic 

cylinder and concentricity of the cone with the cold-pipe is 

maintained by wedge bearings on three of the six knife-edged 

support struts (cage). A position transducer (potentiometer) 

can be seen on the top of the assembly in Figure 4.

The ultimate goal of the calibration is to determine the 

discharge coefficient for the 16 in. MFP over an operating 

range typical of the supersonic inlet testing. The discharge 

coefficient for the mass-flow plug is defined as:

*

plug,

,plug

i

noz D

w

w C = (1)

where wnoz is the actual mass flow through the cold-pipe and 

* wplug,i is the ideal inviscid choked flow through the massflow plug. For the purpose of calibrating the mass-flow plug, 

the actual mass flow was measured with an ASME LongRadius Flow Nozzle. A description of this nozzle is as 

follows.

ASME Nozzle

Geometry: An ASME Long-Radius Flow Nozzle with 

throat taps was used to provide a reference mass-flow measure 

for calibrating both the 15 and 16 in. mass-flow plugs. The 

geometry of the nozzle is shown in Figure 3. This design 

conforms to the Low-β Nozzle with Throat Taps illustrated in 

Fig. II-III-14 of Reference 2 with the following two 

exceptions. First, no approach pipe exists before the nozzle

(D=∞), hence β=d/D=0. And second, the nozzle exit flow does 

not exhaust into a sudden expansion but rather into a shallow 

angle conical diffuser. The nozzle throat-to-conical diffuser 

and conical diffuser-to-constant area end section are both 

transitioned by 27.96 in. radii.1

Figure 4.—Caged 16 in. Mass-Flow Plug.

 1 Note that this diffuser geometry differs from the description given by Iek 

(Ref. 1) where the diffuser is described as being a “cubic contour.”
NASA/TM—2014-218128 4

Figure 5.—Schematic for MFP sonic (choked) area.

Citing the desire to maintain fully turbulent flow in the 

nozzle, the calibration tests were performed both with and 

without a boundary-layer trip in the inlet region of the nozzle. 

Details of the trip were not supplied by Iek (Ref. 1) but 

inspection of the ASME nozzle indicated the trip location and 

width are as shown in Figure 3. Most of the tests were 

performed with an 80 grit trip, but limited testing was also 

performed with a 36 grit trip with essentially the same results.

Flow Equations: The flow through the ASME nozzle is 

calculated by the following equation:

wnoz CD,noz wnoz,i = ⋅ (2)

where

wnoz i noz Unoz Anoz = ρ ⋅ ⋅ , (3)

and where ρnoz and Unoz are evaluated at the throat of the 

ASME nozzle. Substitution of the ideal gas law, Mach number 

definition, and isentropic and adiabatic relations for pressure 

and temperature, respectively:

air noz

noz noz R T

p

⋅

⋅ ρ = 144 (4)

Unoz Mnoz gc R Tnoz = ⋅ γ ⋅ ⋅ ⋅ air (5)

1 2

,

2

1 1 γ−

γ





 



 ⋅ γ − +

=

noz

t noz noz

M

p

p (6)





 



 ⋅ γ − +

=

2

,

2

1 1 noz

t noz noz

M

T

T (7)

into the expression for w0 and rearranging yields:

2 ( 1)

( 1)

2

,

,

air

,

2

1 1 ⋅ γ−

− γ+





 



 ⋅ γ − ⋅ + ⋅ ⋅ ⋅ γ ⋅

=

noz

t noz

c t noz noz noz

noz i

M

T

p M A

R

g

w

(8)

Substituting the values for γ, gc and Rair and replacing pt,noz and 

Tt,noz with pamb and Tamb, respectively, gives the final form:

( ) 3 2 , 0.91884 1 0.2 − ⋅ + ⋅ ⋅ ⋅ = ⋅ noz

amb

amb noz noz noz i M

T

p M A

w (9)

where Mnoz is the Mach number of the flow at the throat of the 

nozzle and is given by the isentropic relation:

























− 













 = ⋅





 





5 1

3.5

1

noz

amb noz p

p M (10)

and pnoz is the static pressure measured at the throat of the 

nozzle. All of the variables in Equations (9) and (10) are 

directly measured or calculated from directly measured 

quantities. The only remaining parameter required to calculate 

the nozzle flow rate is the nozzle discharge coefficient (CD,noz).
NASA/TM—2014-218128 5

ASME Nozzle Discharge Coefficient

Historical Correlation: The discharge coefficient for a 

nozzle with throat taps is a function of the potential flow nonuniformity and the boundary-layer displacement thickness 

resulting from viscous effects. As discussed by Rivas and 

Shapiro (Ref. 3), if the length of the cylindrical sections before 

and after the throat taps are on the order of or greater than 1⁄4 

throat diameter, then the effects of potential flow nonuniformity are negligibly small.

In the absence of a calibration, ASME recommends reading 

the discharge coefficient for a low-β long-radius nozzle with 

throat taps from Fig. II-III-19 of Reference 2. The source of 

this curve is not referenced but it appears to be the “Calculated 

Curve” in Fig. 22 of Cotton and Westcott (Ref. 4). No 

uncertainty is given for using this curve but based on similar 

analysis, it is likely to be on the order of ±1.5 to 2.0 percent. 

Much of the data used to generate this curve was based on

incompressible flow data. In 1973, Smith and Matz (Ref. 5)

investigated an 8-in. low-β, long-radius nozzle under 

incompressible and compressible conditions and reported a 

Mach number dependence.

Two-Code Computational Approach: For the March 1996 

calibration of the 15 in. caged mass-flow plug (Ref. 1), due to 

the uncertain effect of the β parameter and the nozzle exit 

diffuser on the discharge coefficient, the ASME correlation 

was not used. Instead, the theoretical method first performed 

by Smith and Matz (Ref. 5) and later by Lahti and Hamed 

(Ref. 6) was used to establish a discharge coefficient. With 

this method, the discharge coefficient is assumed to depend on 

two components, an inviscid part (CD,pot) that accounts for the 

radial pressure variation in the throat, and a viscous part 

(CD,δ*) that accounts for the effective boundary-layer 

blockage. Computer programs were used to calculate each 

component and the discharge coefficient of the nozzle was 

determined from the product of the components:

, ,2 , ,δ* CD noz C = CD pot ⋅CD (11)

This approach will hereafter be referred to as the “TwoCode” (2C) nozzle calibration. In Lahti and Hamed’s (Ref. 6)

study, the potential solution was obtained with the Stream 

Tube Curvature (STC) computer code (Ref. 7), chosen 

because of their many years of experience with it and because 

it is driven by global mass conservation as part of its solution 

procedure making it a natural choice for mass-flow calibration 

studies. The boundary-layer correction was obtained using

Harris and Blanchard’s code (Refs. 8 and 9). This code was 

chosen based on its wide use and thorough documentation. 

Lahti and Hamed (Ref. 6) report that comparisons with 

experimentally determined discharge coefficients indicate that 

an accuracy of ±0.25 percent can be achieved with their 

method.

For the calibration of the GRC ASME nozzle, Iek (Ref. 1)

followed a similar approach but used different computer 

codes. For the potential solution, Stockman and Farrell’s code 

(Ref. 10) was used and for the viscous solution, Herring’s PL2 

code (Ref. 11) was used. With these codes, the theoretical 

discharge coefficient for the ASME nozzle was determined at 

six discrete throat Reynolds numbers.

TABLE 1.—DISCHARGE COEFFICIENT 

VERSUS REYNOLDS NUMBER

Red,s=Red×10-6 CD,noz

1.6828 0.98553

3.0386 0.98667

3.7659 0.98728

4.0302 0.98728

4.3062 0.98755

4.6056 0.98796

For data reduction during the mass-flow plug calibrations, 

the data in Table 1 were interpolated with a third-order 

polynomial function:2

3

, 2,

, ,2 ,

0.0004063900Re 0.00004062582Re

0.982982 0.002081573Re

d s d s

CD noz C d s

+

= + − (12)

and extrapolated by setting points outside the calibration range 

to the end points of the calibration.

RANS Computational Approach: More recently, a different 

computational approach was taken for obtaining the discharge 

coefficient of the ASME nozzle as well as the 16 in. MFP. 

Rather than use a potential code coupled with a boundarylayer calculation, WIND-US, which is a general purpose 3-D 

Reynolds-averaged Navier-Stokes (RANS) code, was used for 

the numerical studies (Ref. 12). Versions 3 Alpha and 2 of 

WIND-US calculated the CFD derived discharge coefficients.

WIND-US is a mature, multi-zone, structured-grid, 

compressible flow solver offering a variety of turbulence 

models. All simulations were run steady-state using the 

Menter Shear Stress Transport (SST) turbulence model 

(Ref. 13). The SST turbulence model was chosen for all of the 

simulations because previous studies (Refs. 14 and 15) have 

shown that this particular model performs well for jet flows.

An axisymmetric structured grid, composed of roughly 

119,000 grid points and divided into 17 zones, was used to 

model the test rig assembly shown in Figure 1. Grids were 

created for 19 different plug positions, ranging from xplug = 2.4 

to 16.4 in. with xplug defined as shown in Figure 5. Zones 

upstream of the experimental boundary-layer trip location (see 

Figure 3) assumed laminar flow while zones downstream of the 

 2 Reference 1 indicates a fourth-order polynomial was used but the actual data 

reduction program uses the third-order fit shown.
NASA/TM—2014-218128 6

trip location assumed turbulent flow. An example grid is shown 

in Figure 6 while Figure 7 illustrates the solid computer model.

The simulations used a constant Courant-Friedrichs-Lewy 

(CFL) number of 0.5 rather than a constant time step. To 

reduce computational costs and convergence time, parallel 

processing along with three levels of grid sequencing were 

used to obtain converged solutions. First, a coarse grid 

sequence included only every fourth point in each direction. 

Second, a medium grid sequence was used that utilized every 

other point in each direction. Third, a fine sequence used 

every grid point. Solution convergence was achieved when the 

computational equation residuals were reduced by several 

orders of magnitude and the mass flow rates in the bellmouth 

entrance and near the cold pipe exit each varied by less than 

0.09 percent per iteration. Convergence was typically obtained 

in a little over 3 hr.

Figure 6.—Sample primary grid layout, laminar zones are in blue, turbulent zones are in red.

Figure 7.—The 90° sector of the axisymmetric solid model.
NASA/TM—2014-218128 7

Initially, the WIND-US code was run with the as-tested 

ambient inlet conditions (pamb=14.3 psia), but then to better 

resolve Reynolds number effects, additional cases were run at 

inlet pressures of 5.0 and 50.0 psia. For all pressures, the 

ambient total temperature was set to 520.0 °R with an initial 

inflow Mach number set to 0.001. Whereas for the 5.0 psia 

case, the back-pressure at the MFP exit was set at 1.0 psia, for 

the two higher pressure cases, the back-pressure was set at the 

as-tested pressure of 2.0 psia.

After the CFD analyses were completed, the data was postprocessed to acquire the discharge coefficients for the 

bellmouth nozzle. First, the mass flow rate through the cold 

pipe was calculated from the average mass flow rate between 

the downstream tangential edge of the radial nose of the 

conical plug to the cold pipe exit:

N

w

w

N

i

∑ x i

= = 1

pipe, ,

pipe (13)

where

∫∫

φ

= ρ⋅ ⋅ ⋅ ⋅ θ

r

wpipe,x Ux r dr d (14)

This was compared to the average mass flow rate at the 

throat of the bellmouth to check for continuity. The solution 

was converged when the average mass flow rates in the 

bellmouth throat and just upstream of the cold pipe exit varied 

by less than 0.09 percent of each other. The discharge 

coefficient could then be calculated from:

noz i

D noz w

w C ,

pipe

, = (15)

where wnoz,i is given by Equation (9).

The data from the WIND-US computations are plotted in 

Figure 8. For reference, the ASME curve, the data from Smith 

and Matz, and the numerical data from Iek are also shown. For 

the WIND-US data, only points where the throat Mach 

number was between 0.2 and 0.8 are plotted. Due to the use of 

a boundary-layer trip on the nozzle, the distribution does not 

display the transitional behavior of Smith and Matz (Ref. 5)

data and indeed seems to agree well with the turbulent portion 

of their “Critical” curve (Red,noz > 2.0×106

). Another 

observation of the current data is the saw-tooth nature of the 

combined distributions indicating a small Mach number 

dependence. To illustrate this dependence more clearly, data at 

constant Mach numbers of 0.3, 0.5 and 0.7 were extracted and 

are plotted in Figure 9. Although the dependence on Mach 

number is small for the current data, the trend is opposite that 

of Smith and Matz (Ref. 5), but since their low Mach number 

data was in the transition region, nothing firm can be drawn 

from this. Comparing the present WIND-US data to the 

previous distribution established for the same nozzle 

configuration by Iek (Ref. 1) shows that the present data 

trends about 0.2 percent higher than Iek’s.

Figure 8.—ASME nozzle discharge coefficient.

0.975

0.980

0.985

0.990

0.995

1.000

1.005

0.1 1.0 10.0

CD,noz

Red (X10-6)

ASME (Ref. 2) Iek (Ref. 1)

S&M, M~0.4 (Ref.5) WIND, 5.0 psia

S&M, M~0.7 (Ref.5) WIND, 14.3 psia

S&M, Critical (Ref.5) WIND, 50.0 psia
NASA/TM—2014-218128 8

Figure 9.—ASME nozzle discharge coefficient, constant Mach number.

In order to apply easily the present data to the 16 in. MFP 

calibration, a correlation was developed that fits the data and 

accounts for the small Mach number dependence. This was 

accomplished by first curve fitting the M=0.5 data which 

resulted in the following expression:

d

CD M

Re

6.73896 , =0.5 = 0.993003− (16)

An empirical correction to this nominal discharge 

coefficient was established such that the Mach number 

dependant discharge coefficient is defined by:

C WU CD M f (M ) D noz = = ⋅ , , , 0.5 (17)

where

( ) ( ) 0.00863415 2 0.999514 1 0.2 − M = ⋅ − Mnoz f (18)

Since it is unlikely that the current ASME nozzle would ever 

be operated at anything but ambient pressure conditions, the 

coefficients in Equation (18) were determined from the 

14.3 psia data only. A comparison of Equation (17) and 

Equation (16) with the numerical data is shown in Figure 

10(a) and Figure 10(b), respectively.

16 in. Mass-Flow Plug

Geometry: With reference to Figure 5, the plug itself is a 

φ = 16.5° half-angle cone with a 2.18 in. nose radius. The 

downstream end of the cone is Rplug=15.800 in. in diameter 

followed by a 0.610 in. wide cylindrical shoulder.

Flow Equations: The discharge coefficient for the massflow plug is assumed to be a function only of the plug position 

and defined as the ratio of the actual mass-flow to the ideal 

theoretical mass-flow (see Eq. (1)). The ideal mass-flow is 

calculated from the following equation:

plug 1 pipe pipe * wplug,i = ρ ⋅U ⋅ AR− ⋅ A (19)

where

pipe

plug

A

A

AR = (20)

and where Aplug is the choked-flow area between the cold-pipe 

exit plane edge and the conical plug. With reference to Figure 5, 

the definition of the choked area (Aplug) of the MFP is based on 

the area of the frustum of a right circular cone where the slant 

height (sa) is defined as the average of the vertical distance from 

the cold-pipe edge to the MFP and the slant height of a cone 

whose slant height is normal to the MFP surface.

Aplug = π⋅sa ⋅(Rpipe + Ra ) (21)

where (see Figure 5)

( )

( ( )) a a n a

a n v

v

n

R R s s s

s s s

s x

s x

cos arccos

2.0

tan( )

sin( )

pipe

plug

plug

= − ⋅ φ −

= +

= ′ ⋅ φ

= ′ ⋅ φ

(22)

0.975

0.980

0.985

0.990

0.995

1.000

1.005

0.1 1.0 10.0

CD,noz

Red (X10-6)

ASME (Ref. 2) Iek (Ref. 1)

S&M, M~0.4 (Ref.5) WIND, M=0.30

S&M, M~0.7 (Ref.5) WIND, M=0.50

S&M, Critical (Ref.5) WIND, M=0.70
NASA/TM—2014-218128 9

(a) Fit of constant Mach number data.

(b) Fit of all data.

Figure 10.—Comparison of ASME discharge coefficient correlation with numerical data.

and

( ) tan( ) xplug ′ = xplug + Rpipe − Rplug φ (23)

where x′plug is the distance from the end of the cold-pipe to the 

theoretical intersection line of the plug conical surface and the 

cylinder of the cold-pipe internal diameter (see Figure 5). The 

choice of sa to approximate the sonic line (curved line in 

Figure 5) is arbitrary but must be used consistently for the 

calibration to be valid.

The area ratio can be expressed in terms of the Mach 

number in the pipe by the following isentropic relation:

( ) 2( 1)

( 1)

2 pipe pipe

2 1

1

pipe

plug

2

1 1

2

1 γ−

− γ+

γ−

γ+





 



 ⋅ γ −  ⋅ ⋅ +  



 γ + = M M

A

A

(24)

0.982

0.983

0.984

0.985

0.986

0.987

0.988

0.989

0.99

0.991

0.992

0.1 1.0 10.0

CD,noz,WU

Red (X10-6)

M= 0.30

M= 0.50

M= 0.70

Eq. 17

0.982

0.983

0.984

0.985

0.986

0.987

0.988

0.989

0.99

0.991

0.992

0.1 1.0 10.0

CD,noz,WU/f(M)

Red (X10-6)

5.0 psia

14.3 psia

50.0 psia

M=0.5 Points

Eq. 16
NASA/TM—2014-218128 10

Substituting Equation (24) and Equations (4) to (7) (with the 

subscript “noz” replaced with “pipe”) into Equation (19)

yields:

2( 1)

( 1)

plug

,pipe

air

*

,plug 2

1 γ−

− γ+





 



 γ + ⋅ ⋅ 















⋅ γ ⋅ = A

T

p

R

g w

amb

c t

i (25)

The total pressure in the cold-pipe (pt,pipe) is calculated from 

Equation (6) (with the subscript “noz” replaced with “pipe”). 

The static pressure in the cold-pipe (ppipe) is directly measured 

with static pressure taps and the Mach number in the cold-pipe

(Mpipe) is calculated from Equation (24) which assumes that 

the flow at the mass-flow plug exit is choked. 

Instrumentation: With reference to Figure 1, the test setup 

was instrumented as follows. The ambient air pressure and 

temperature were each recorded with four transducers which 

were then averaged to obtain pamb and Tamb. There were a total 

of six throat taps on the ASME nozzle and eight static taps at 

the mid-point of the cold pipe. These were also averaged to 

obtain pnoz and ppipe. The temperatures were measured with 

Type-E thermocouples and the pressures were measured with 

ESP 8400R 0 to 15 psia modules. The data was recorded on 

the GRC ESCORT data acquisition system.

Calibration Runs: For the caged 16 in. mass-flow plug 

calibration runs, there were six sweeps of the mass flow plug. 

The first three were performed with the boundary-layer trip 

installed on the ASME nozzle and the last three were 

performed with the trip removed. 

Uncertainty Considerations

A general uncertainty analysis was performed for both the 

15 and 16 in. MFP calibrations. The uncertainty in the MFP 

discharge coefficients was estimated by:

2

1

,plug ,plug ∑

=















 ⋅δ

∂

∂

δ =

J

i

i

i

D

D X

X

C

C (26)

where Xi are the measurands which are summarized with their 

assumed uncertainty in Table 2.

The measurands Pamb, Pnoz and Ppipe are actually calculated 

averages of four, six and eight individual pressure 

measurements, respectively, and the uncertainties in Table 2

reflect the measurement redundancy. In addition, different 

pressure uncertainty levels were used for the 15 and 16 in. 

MFP calibrations to reflect an upgraded pressure measurement 

system for the 16 in. MFP. The measurement uncertainty for 

the individual modules was 0.012 and 0.009 psi for the 15 in. 

and 16 in. MFP, respectively (Ref. 16). The uncertainty in the 

nozzle discharge coefficient is comprised of two components. 

The first is related to the grid and solution convergence and is 

generally small (<0.003 percent). The second is related to how 

well the CFD models the flow physics. In particular, since the 

nozzle discharge coefficient is primarily a function of the 

boundary-layer growth, the turbulence model will have an 

influence on the result. Further, the difference between how 

the boundary layer transitions on the nozzle will also affect the 

discharge coefficient. In the CFD, the flow is assumed laminar 

until the leading edge of the boundary-layer trip and fully 

turbulent downstream. In the experiment, there is a finite 

width of grit material. These effects are not easily quantifiable, 

thus the uncertainty specified for the nozzle discharge 

coefficient is to be considered a “best guess” by the authors. 

Finally, although the ambient temperature is measured and 

used in the calculations, it does not contribute to the MFP 

discharge coefficient uncertainty.

TABLE 2.—MEASURAND UNCERTAINTY

i Xi δXi

(15-/16-in. MFP)

Units

1 xplug 0.015 in.

2 Tamb 2.5 °R

3 pamb 0.0060/0.0045 psi

4 pnoz 0.0049/0.0037 psi

5 ppipe 0.0042/0.0032 psi

6 d 0.0025 in.

7 Dpipe 0.0075 in.

8 Dplug 0.0050 in.

9 φ 0.05 deg

10 CD,noz 0.001 N/A

Results and Discussion

Caged 15 in. MFP Calibration

The 15 in. MFP was calibrated over a range from 

xplug = 0.25 to 17.0 in. with and without distortion screens 

installed in the cold-pipe. A correlation was established based 

on the data without distortion screens. The discharge 

coefficient was assumed to be only a function of the choked 

flow area ratio (Eq. (20)) and is expressed as a segmented 

third-order polynomial function where the coefficient values 

are given in Table 3:

3 3 2 CD,plug,2C = c0 + c1 ⋅ AR + c2 ⋅ AR + c ⋅ AR (27)

TABLE 3.—COEFFICIENT VALUES FOR 

CAGED 15 in. MASS-FLOW PLUG

AR < 0.203943 0.203943 ≤ AR < 0.811515 0.811515 ≤ AR

c0 1.0340732 0.96163863 1.1845804

c1 –0.58958996 0.0047836495 –0.60737883

c2 1.1527497 –0.030427921 0.42665471

c3 0 0.050854378 0
NASA/TM—2014-218128 11

This original calibration (Eq. (27)) was based on the twocode ASME nozzle calibration. To update the calibration to 

use the more recent WIND-US based nozzle calibration, two 

approaches are possible. First, the data calibration data points 

could be recalculated with the WIND-US based nozzle 

calculation and a new fit established, or second, an adjustment 

could be applied to Equation (27) by multiplying by the ratio 

of nozzle discharge coefficients:

CD,plug,WU = CD,plug,2C ⋅(CD,noz,WU CD,noz,2C ) (28)

The nozzle discharge coefficients based on both methods 

are plotted in Figure 11 as a function of the 15 in. MFP area 

ratio. Also plotted is the ratio of the coefficients which can be 

approximated by the following empirical relation:

7 3 4

5 2 3

2

, ,2

, ,

4 4263225 10 AR 0 018204318 AR

2 3567944 10 AR 0 049185331 AR

0 00069852959 AR 0 046818586 AR

10014446 0 017657109 AR

− × − ⋅

+ × + ⋅

− − ⋅

= + ⋅

−

−

. .

. .

. .

. . C

C

D noz C

D noz WU

(29)

The original and adjusted 15 in. MFP calibrations along 

with the data they were derived from are shown in Figure 12. 

The nozzle Mach number and Reynolds number are also 

plotted for reference. With regard to the original calibration, 

there are a couple of things to note about this distribution. At 

area ratios below approximately 0.2, the curve has a large 

negative slope and at the lowest area ratio, the discharge 

coefficient exceeds unity with large data scatter. At the largest 

area ratio, the slope and scatter also increases. During the test, 

the ratio of the cold-pipe base pressure to pipe total pressure is 

monitored to ensure the plug is operating under choked 

conditions. The two highest area ratio positions are 

approaching flow conditions that challenge the assumption of 

a well-defined choked flow.

The adjusted 15 in. MFP discharge coefficient curve fit is 

re-plotted in Figure 13 with the uncertainty bounds from the 

general uncertainty analysis. Also plotted is the percent 

uncertainty based on the assumed measurand uncertainties 

(Table 2).

These results indicate that the measurement uncertainty 

exceeds 0.5 percent for MFP area ratios below 0.5. Based on 

this calibration, the inlet should be sized to operate within the 

area ratio range 0.2<AR<0.8 (1.85 in.<xplug<10.4 in.).

The relative contribution from the individual measurands is 

plotted in Figure 14. Also plotted for reference is the absolute 

uncertainty. The large uncertainty at low area ratios is 

primarily due to the low Mach number in the nozzle (see 

Figure 12) which is calculated from Equation (10).

Figure 11.—ASME Nozzle discharge coefficient as a function of 15 in. MFP area ratio.

0.990

0.992

0.994

0.996

0.998

1.000

1.002

1.004

0.978

0.980

0.982

0.984

0.986

0.988

0.990

0.992

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

CD,noz,WU/CD,noz,2C

CD,noz

Aplug/Apipe

Two-Code (2C) Nozzle Correlation (Eq. 12)

WIND-US (WU) Nozzle Correlation (Eq. 17)

Discharge Coefficient Ratio (WU/2C)

Discharge Coefficient Ratio Fit (Eq. 29)
NASA/TM—2014-218128 12

Figure 12.—Original and adjusted 15 in. MFP discharge coefficient

Figure 13.—The 15 in. MFP discharge coefficient uncertainty.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.950

0.960

0.970

0.980

0.990

1.000

1.010

1.020

1.030

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Nozzle Mach or Re (x1.0E-07) Number

CD,plug

Aplug/Apipe

Original Calibration Data

Original Fit (Eq. 27)

Adjusted Calibration Data

Adjusted Fit (Eq. 28)

Nozzle Mach Number

Nozzle Re Number

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1.00

1.01

1.02

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

% Uncertainty

CD,plug

Aplug/Apipe

Adjusted Fit (Eq. 28)

Uncertainty Bounds (Eq. 26)

% Uncertainty
NASA/TM—2014-218128 13

Figure 14.—Measurand contribution to overall 15 in. MFP discharge coefficient uncertainty.

Caged 16 in. MFP Calibration

The results of the calibration of the 16 in. MFP for both 

tripped and un-tripped nozzle boundary layer are shown 

Figure 15. The nozzle Mach number and Reynolds number are 

also plotted for reference. At a given area ratio, due to its 

larger size, the 16 in. MFP has a larger flow rate than the 15

in. MFP. At large area ratios, this results in choking of the 

nozzle for the 16 in. MFP. Thus data beyond an area ratio of 

0.7 will be excluded from further analysis as the MFP would 

be operating unchoked.

Comparing the 16 in. MFP data with and without the 

boundary-layer trip shows agreement above an area ratio of 

about 0.5, but deviates significantly below this value. At an 

area ratio of 0.5, the nozzle Reynolds number is about 

3.0×106

. From Figure 9, a Reynolds number of 3.0×106 is 

consistent with the end-of-transition implied by the data of 

Smith and Matz (Ref. 5) and the ASME curve (Ref. 2). Smith 

and Matz data show a large increase in discharge coefficient 

below this transition value. Since a fully turbulent nozzle 

discharge coefficient was used in the 16 in. MFP calibration, 

which was artificially low for the case with sweeps with no 

boundary-layer trip, the resulting MFP calibration is under 

predicted. In fact, what the transitional nozzle discharge 

coefficient would have been could be estimated by correcting 

the no-trip data to agree with the tripped data.

A comparison between the adjusted 15 in. MFP and the 

tripped 16 in. MFP calibration data is shown in Figure 16. The 

16 in. MFP calibration data above an area ratio of 0.7 has been 

removed (ASME nozzle choked) and the remainder of the data 

was fit with a second order polynomial:

2 CD,plug = 0.943044 + 0.026915⋅ AR + 0.017376 ⋅ AR (30)

Also included in this plot are the uncertainty bounds from 

the general uncertainty analysis. The experimentally 

determined discharge coefficients for the 15 and 16 in. MFP 

tend to agree well above an area ratio of 0.6, but deviate below 

this ratio. In particular, the 16 in. MFP curve does not exhibit 

the abrupt increase in flow coefficient below an area ratio of 

0.2. Inasmuch as the calibration curves lay at the edges of the 

others uncertainty bounds, this suggests that the differences in 

calibration are not fully attributable to measurement 

uncertainties. For both MFPs, the method of calibration 

produces large uncertainties at low area ratios. This is 

primarily due to the low Mach number in the ASME nozzle. 

The use of a delta pressure transducer at low Mach numbers 

would mitigate the large uncertainties significantly.

As previously mentioned, the numerical study with WINDUS included a numerically based determination of the 16 in.

MFP discharge coefficient (see Figure 6 and Figure 7). This 

study is still in progress and will be reported in a future 

publication, but the preliminary results indicate a trend very 

similar to the experimental 16 in. MFP results but shifted up 

about 0.25 percent. However, results for area ratios below 0.2 

have not yet been obtained so no comment can be made 

regarding the tail-up behavior of the 15 in. MFP.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

% Uncertainty

Uncertainty Contribution (δX/i δCD,plug)2

Aplug/Apipe

Xplug

Pamb

Pnoz

Ppipe

d

Dpipe

Dplug

φ

CD,noz

% Uncertainty
NASA/TM—2014-218128 14

Figure 15.—The 16 in. MFP discharge coefficient data.

Figure 16.—Comparison of 15 and 16 in. MFP calibrations.

Concluding Remarks

The results of a calibration procedure for the GRC 16 in.

MFP have been presented and compared to a previous 

calibration of a 15 in. MFP. The 16 in. MFP was fabricated

from the 15 in. MFP so all future testing will be with the 16 in.

MFP. For the 16 in. MFP, a calibration has been established, but 

a difference in character between the 15 in. MFP and the 16 in.

MFP for area ratios below 0.6 is observed. Unfortunately, this 

region of disagreement coincides with large uncertainty levels. 

The recommended path forward is to first complete the 

numerical calibration of the 16 in. MFP; in particular obtaining 

calibration data below an area ratio of 0.2. And second, the 

experimental calibration of the 16 in. MFP should be repeated 

with a focus on minimizing measurement uncertainties.

References

1. Iek, C., “Calibration of the 15” Mass-Flow Plug in 

NASA LeRC’s 10’x 10’ Supersonic Wind Tunnel,” Case 

Western Reserve University EMAE 657 Report, March 

19, 1996.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.930

0.940

0.950

0.960

0.970

0.980

0.990

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Nozzle Mach or Re (x1.0E-07) Number

CD,plug

Aplug/Apipe

SWP 1, w/ BL Trip

SWP 2, w/ BL Trip

SWP 3, w/ BL Trip

SWP 4, w/o BL Trip

SWP 5, w/o BL Trip

SWP 6, w/o BL Trip

Nozzle Mach Number

Nozzle Re Number

0.930

0.940

0.950

0.960

0.970

0.980

0.990

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

CD,plug

Aplug/Apipe

16" MFP, w/ BL Trip

16" MFP Fit (Eq. 30)

Uncertainty Bounds (Eq. 26)

15" MFP Adj. Fit (Eq. 28)

Uncertainty Bounds (Eq. 26)
NASA/TM—2014-218128 15

2. Bean, H. S. (ed), 1971, Fluid Meters: Their Theory and 

Application, 6th Ed., American Society of Mechanical 

Engineers, New York.

3. Rivas, R.A., Jr. and Shapiro, A.H., “On the Theory of 

Discharge Coefficients for Rounded-Entrance 

Flowmeters and Venturis,” Trans. ASME, Vol. 78, No.

3, 1956, pp. 489-497.

4. Cotton, K. C., and Westcott, J. C., “Throat Tap Nozzles 

Used for Accurate Flow Measurements,” Journal of 

Engineering for Power, Transactions of the ASME, 

October 1960, pp. 247-263.

5. Smith, R. E., and Matz, R. J., “A Theoretical Method of 

Determining Discharge Coefficients for Venturis 

Operating at Critical Flow Conditions,” Journal of Basic 

Engineering, Transactions of the ASME, December 

1962, pp. 434-446.

6. Lahti, D.J. and Hamed, A., “Verification of the 

Theoretical Discharge Coefficient of a Subcritical 

Airflow Meter,” Journal of Propulsion and Power, Vol.9, 

No.4, July-August, 1993, pp.615-621.

7. Keith, J.S., Ferguson, D.R., Merkle, C.L., Peck, C.H., 

and Lahti, D.J., “Analytical Method for Predicting the 

Pressure Distribution about a Nacelle at Transonic 

Speeds,” NASA CR-2217, July, 1973.

8. Harris, J.E., “Numerical Solution of the Laminar, 

Transitional, and Turbulent Boundary-Layer Equations 

and Comparison with Experimental Data,” NASA TR R368, August, 1971.

9. Harris, J.E., and Blanchard, D.K., “Computer Program 

for Solving Laminar, Transitional, or Turbulent 

Compressible Boundary-Layer Equations for TwoDimensional and Axisymmetric Flow,” NASA TM 

83207, 1982.

10. Stockman, N.O. and Farrell, C.A., “Improved Computer 

Programs for Calculating Potential Flow in Propulsion 

System Inlets,” NASA Technical Memorandum TM73728, July, 1977.

11. Herring, H.J., “PL2 – A Calculation Method for TwoDimensional Boundary Layers with Cross-flow and Heat 

Transfer,” Dynalysis of Princeton Report Number 65, 

June 1981.

12. Towne, C., “Wind-US User’s Guide, Version 2.0,” Glenn 

Research Center, NASA/TM—2009-215804, Oct. 2009.

13. Menter, F.R., “Two-Equation Eddy Viscosity Turbulence 

Models for Engineering Applications,” AIAA Journal, 

Vol. 32, No. 8, 1994, pp. 1598-1605.

14. Georgiadis, N., and Papamoschou, D., “Computational 

Investigations of High-Speed Dual-Stream Jets,” AIAA 

Paper 2003-3311, May 2003.

15. Georgiadis, N.J., Rumsey, C.L., Yoder, D.A., and Zaman, 

K.B.M.Q., “Turbulence Model Effects on Calculation of 

Lobed Nozzle Flowfields,” Journal of Propulsion and 

Power, Vol. 22, No. 3, 2006, pp.567-575.

16. Blumenthal, P.Z., 1995, “A PC Program for Estimating 

Measurement Uncertainty for Aeronautics Test 

Instrumentation,” AIAA Paper 1995-3072, 31st AIAA 

Joint Propulsion Conference and Exhibit, San Diego, CA.
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and

maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including

suggestions for reducing this burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite

1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it

does not display a currently valid OMB control number.

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE (DD-MM-YYYY)

01-06-2014

2. REPORT TYPE

Technical Memorandum

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Calibration of the NASA Glenn Research Center 16 in. Mass-Flow Plug

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Davis, David, O.; Friedlander, David, J.; Saunders, J., David; Frate, Franco, C.; Foster,

Lancert, E.

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

WBS 475122.02.03.03.01

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

John H. Glenn Research Center at Lewis Field

Cleveland, Ohio 44135-3191

8. PERFORMING ORGANIZATION

 REPORT NUMBER

E-18891

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

10. SPONSORING/MONITOR'S

 ACRONYM(S)

NASA

11. SPONSORING/MONITORING

 REPORT NUMBER

NASA/TM-2014-218128

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited

Subject Category: 02

Available electronically at http://www.sti.nasa.gov

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

The results of an experimental calibration of the NASA Glenn Research Center 16 in. Mass-Flow Plug (MFP) are presented and compared

to a previously obtained calibration of a 15 in. Mass-Flow Plug. An ASME low-beta, long-radius nozzle was used as the calibration

reference. The discharge coefficient for the ASME nozzle was obtained by numerically simulating the flow through the nozzle from the

WIND-US code. The results showed agreement between the 15 and 16 in. MFPs for area ratios (MFP to pipe area ratio) greater than 0.6 but

deviate at area ratios below this value for reasons that are not fully understood. A general uncertainty analysis was also performed and

indicates that large uncertainties in the calibration are present for low MFP area ratios.

15. SUBJECT TERMS

Nozzle coefficients; Nozzle flow; Compressible flow; Flow measurement; Flow regulators; Discharge coefficient; Supersonic inlets

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

 ABSTRACT

UU

18. NUMBER

 OF

 PAGES

22

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email:help@sti.nasa.gov) a. REPORT

U

b. ABSTRACT

U

c. THIS PAGE

U 19b. TELEPHONE NUMBER (include area code)

443-757-5802

Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39-18