‘lHWINIHIWI

 

”THS

11 METHOD OF MEASURéNG MiGfiRTES
OF A FLUID

flash for firs {hares of M. S.
MICHIGAN STATE COLLEGE
Edward Amhie Daiy'
195231

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A METHOD OF MEASURING PROPERTIES
OF A FLUID

_ BY
Edward Archie Duly

A THESIS

Submitted to en. School of Graduate Studio. of Htohignn
State College of Agriculture and Applied Solenoo
in partial fulfillment of the requirement.
for the degree of

Master of Science

Department of Mechanical Engineering
1951

A O K N O W L E D G H I l f

I would like to erpreee Iy appreciation to Mr.
R. n. Dotty of the Mechanical Engineering Departnent tre-
vhcl I received advice and euggeeticne; Profeeeor Oharlel
Peeterfield of the Mechanical Engineering Depart-ent, my
Major Prefeeeor; Dr. R. J. Jettriee of the Electrical
Engineering‘Departnent from when I obtained an exteneive
bibliography on thie eubject: and the Mechanical Engineer-'
ing, Electrical Engineering and Phyeice Departmente from
which I borrowed the equipment for the experimental portion
of thie theeie.

TABLE OF CONTENTS

PAGE

Hiltcry and Development of The Hot-Wire Anemometer. . . 1
Xing'e Equation . . . . . . . . . . . . . . . . . . . .
.Byeteme of several Hirer. . . . . . . . . . . . . . . . l3
Oonetruction of Instrument and Data Taking. . . . . . . 21
Diecueeion of Experimental Resulte. . . . . . . . . . e E5
Diecueeion of Points of Poeeible Error. . . . . . . . . 31
General Conclusion! . . . . . . e . . . . . . . . . . e 33
Appendix a - Rotatione. . . . . . . . . . . . . . . . . 35
Appendix B airiguree

Figure 1.. Wiring Diagram. . . . . . . . . . . . .

Figure 2 - Section Drawing of wind Tube. . . . . .

Figure 3 ~‘Drawinge cf‘flire Mountinge. . . . . . .

8333

lppendianDntaandGraphI...o.........o
Appendix D . Referenoee

Specific Referencee. . . . . . . . . . . . . . . .

‘a’i'

General Reference. . . . . . . . . . . . . . . . .

HISTORY AND DEVELOPMENT or war
acumen marches-ea ’

The Hot-wire Anemometer in its simplest form is s.de~
vice for leasuring the velocity of a moving fluid.by measur-
in the heat loss of a small, electrically heated, wire
placed in the fluid path. This is at present handled in
either of two ways. First, by maintaining a constant wire
resistance and, therefore, a constant wire temperature;
second, by maintaining a constant current flow through the
wire.

A small metallic wire ~ nickel, platinun or tungsten is
generally used ~ in suspended in the moving fluid. This
wire is then heated, by an electric current, to some telper-
ature above the ambient temperature of the fluid. The re-
sulting heat loss can then be measured by measuring the power
dissipated. how, since the fluid is moving, that around the
wire will constantly be being replaced. The rate at which
this fluid around the wire is replaced is the sass flow of
the fluid. Therefore, the heat loss is a function of the
mass flow of the fluid as well as the existing telperature
difference. There are other factors and cosplications in-
volved. some of Which will be discussed later on.

The first article I could find on, or pertaining to.this
subject was published by three Americans, A. E. Kennelly.

O. A. Iright and J. 8. Van Bylevelt (1). These sen cone
ducted experiments and worked out some theory on the heat
loss fros snail copper wires. In 1912. two Englishmen. use
Gregorond and horris (2). constructed a.hot-wirs ans-ouster
and determined an equation relation of the heat loss and
velocity fro. experiments with this instrument. About this
same tine an Italian. U. Bordoni (3). carried out some work
along this line; I did not obtain translations of his
article. and, therefore. as not sure if he did his work an-
perimentally or theoretically. Bordeni's work was sentionsd
in several articles, but chiefly in an article by Carlo
Ferrari (M. H .
The most detailed and ispcrtant theoretical work. and
the one on which most all of the present development is based.

was done by an Englishman, L.‘V. King (5), and the equation

1. Kennslly, a. n., wright, c. A. and Van Bylavelt. J.a.

“The Convection of Heat from Email Copper Wires' ,InnE
, " Amer" nag mag-1mg; .QLEW ‘ s
ol. 9, Part 1, 1910. pp. 3 3-397.

2. Mac Gregorond and Morris, J. T.. “The Electrical
measurement of Wind Velocity',.fing1nge;ing, Vol. 9“. No. 25.
UGO. 27' 1912. PD. 892“89u'e

73o Bordoni. Us. mm. vOle 70. HOVe 22. 1912.
De 2 e
h. Ferrari, Carlo. "Electrical Equipment for The EXpori-

mentagogtudy of The Dynamics of Fluids',.E.A.Q‘A._Igflh_flgln.
HO. 1 ' 19kg.

5. King, L. V., 'On The Convection of’fieat Fro- Small
Cylinders in a Streal of Fluid: Determination of The Convec-
tion Constants Of Small Platinum Wires with Application To
Hot-Wire Anemoneter' a , See.
A, Vol. 21“, Nov. 19in. pp. 373- 32.

 
  

relating the properties of a roving fluid and the heat less
of s.heatee wire bears his case. King carried out an exten-
sive theoretical development free which he developed tee
equations;

for ssall velocities

n a are. / [lain/a3] (l)
for large velocities

3.3%.afifinpuig m)
where

a i: the heat loss per unit tine per unit length of the
I :00

h is the thermal conductivity of the fluid.

9b i: the temperature difference between the fluid and the
' to. z

s is the specific heat of the fluid.

d is the diameter of the wire.

f is the density of the fluid.

v is the velocity of the fluid.

Only the second equation is of much general interest and of
any interest in this report. ,

King developed this equation on a number of rather lis-
iting assumptions and the equation. in this fore. is only of
passing interest.

Since Ting developed his equation there has been exten-
sive develop-ant of this type of instrument. Among the other

important articles are reports by R. L. Dryden and Xuethe
(6) in 1929; three reports by J. a. snake (7. 8 and 9) in
19%} and l9h9; and one by Stanley Oorrsin (10) in 19h9.

The article by Dryden and Kuethe is the bases of such
of the work using the constant current smthod of’neasuring
velocity fluctuations. They did their work on the assumption
that the equation depended only on the instantaneous values
of its terms and not on their rate of change; that is. that
the equation would held under varying conditions provided the
instrument was capable of reacting to these changes. The re-
sults they and others have obtained has shown this assump-
tion to be valid.

J. 8. Weeks did some work on extendingrthe useful range
of the instrument in to the subsonic range of velocities.
He also experimented with the effects of different wire Is~
terials and dimensions.

Oorrsin's work was chiefly theoretical. be advanced
theory on the extended use of this type of instrument in the

 

3. Dryden H. L. and Kuethe, A. ii... 'The neasurement of
fluctuations of Air Bpeed by the Hot-wire Ans-caster“
w Rep. so. 320. 1929.

7. Weeks, J. R. 'Hethod of Measurement of High sir
Velocities by The Hot-Wire Isthod', w. to.
880. 19“}.

8. Desks J. R., "A Hot~lire Circuit lith Very Snell
me has“. W. No. 881. 19113.

9. Weeks. J. 8., "fleasurement of Arithmetic Mean Velocity
of Pulsating Flow of High Velocities 19{grin-Wire nethcd',
We 30. 990. Aprils,-

lO. Oorrsin ‘Stanlsy‘r "Extended Applications Of The Hot-

wire Aneucneter‘, W, No.1 1865, April 1949.

- h.-

study of turbulent flow and the mixing of gases.

Many other articles have been written on the directional
characteristics of the Hot—wire Aneacmeter and on instruneno
taticn for its many varied uses. A list of some of these
articles can be found in "Appendix 0' under “General Refer.

encee'.

KING‘S‘EQUATIOH

Since this report sill only be concerned with an in-
strument for measuring constant. or relatively constant,
values, the discussion here will be of that type of inetrnp
rent.

The assunpticns that ring (5) lads in developing his
equation are briefly these; that
l. The temperature difference between the wire and the fluid
remain constant.

2. The properties of the fluid - thermal conductivity. spec
cifie heat and density - remain constant.

3. There he leniner flow over the wire.

#. The wire be normal to the direction of fluid flow.

5. The wire temperature be unifors over the length of the
wire,

6. The leases of radiation from the wire and viscosity of the
fluid are negligible.

Hany of these conditions either can not be set or it is il-
practical to satisfy then in practices. Also, the equations

-5-

given are only approximate forms of the more detailed equa-
tion he deve10ped. The approximate forms were necessary to
simplify the equation for this type of application.

The first. second and third assumptions can be satis-
fied in practice, but it is impractical to do so as this
would lilit the usefulness of the instrument. And, within
limits, it is not necessary to satisfy these essuepticns if
a system that is not sensitive to snail fluctuations is need.
This can be accomplished by using a galvancnster with a
period necessary to damp out small fluctuations cr‘by using
a wire with a.heat inertia that will prevent it free react-
ing to snall changes. Since e.very snail wire is desirable.
the first sethod would seen to be preferable.

The fourth assumption can be satisfied within reesonlble
limits by adjusting the wire in the fluid stress to the po-
sition of greatest heat loss (ll). While there will he sees
snail variations under even good conditions, these will be
taken up by the inertia.uoed to approximate the first three
assumptions. For conditions which hare variations of any
magnitude. it is necessary to use the directional character-
istics of the Hot-dire. This is covered in some of the ref.

erences listed under “General References“.

 

fill. Siemens, L. F. G. and Bailey A.. “An instrument for
leasuring Speed and Dggecticn of Air §low',.£h11‘_gggh,
v01. 3. 1927. PD. 81- o

The fifth and sixth assumptions are probably the lost
difficult tomeet in practice. Since the wire must be sup-
ported, there will be and losses and the wire temperature
will. therefore. not be uniform over its length. Also the
wire must be very small. the order of thousands of an inch.
and its characteristics will be difficult to deter-ins with
any degree of accuracy. Even if these characteristics could
be accurately determined. it is more convenient to handle it
in another way.

The seventh assumption may, or may not, be approached
in practice. I did not find any convincing proof either way
in the ssny articles on this type of instrusent. since ibis.
loss will be very lllll. lost of those who worked with this
type instrument have assumed that they will be sorely addi-
tive. There are several noteworthy cases of disagreement
with this assumption (lo and 12), but results here justified
it to s large extent. This idea is further brought out by
others (12) who have compared orperimental results with the
expected results from King‘s more exact fore of his equation.
Here it was found that the curve of orperinental date and the
theoretical curve were nearly parallel over a rather large
range.

It can be seen. from the fact that some of these sssunp-

tions cannot be completely set in practices, that there sust

A.

12. chdans. I. H.. .flgg1_z;§nmniggign, new and
London: Hearse - Hill Book Co. 1933.

- 7 -

he sees aethod used to compensate for those conditions that
here not been considered in the developeent.

In developing the equation relating the properties of a
loving fluid and the heat lees of a heated wire suspended in
it, King used only a unit length of a wire of infinite
length. He did not consider the losses by radiation or those
resulting free the viscosity of the fluid. Further, in using
a unit length.‘he neglected any losses to the supports‘hy as-
suring a constant wire teapereturs ever the length used.
these. therefore. are the conditions whidh sale it necessary
to use a soaewhat different fora of this equation.

In constructing a practical inetrusmnt alonsrthe lines
of his theory. tins changed his equation (5) fro. the theo-
retieel fora
n e [x e riff-T gov)” (r - a"). ' (2)
where 65 has been replaced by the difference between the wire
temperature (2) and the fluid teepereture (3‘) at were dis-
tanee free the wire,
to a fora siailar to this
tan a s e 347 (f - 9.). (3)
In this fora.the constant
A e aunt/J)

[- is the length of the wire.
3 is a conversion factor between watt-houre and 310's.
a is a eonstant whieh corrects for errors caused by losses

not taken into account in the theoretical development.

H

or.

and

B - (EL/J) W7“).

where

b is a constant sisilar to a.

King went ahead and showed that, within the lisits of his
work this equation could be used with cone degree of accur-
I”.

a number of those who have worked on this type of in.
strunent have taken the density tern (f) out of the 'ccnstant'
and made their instruaents acaeure sass-flow. this is a
logical (inclement as the density tern would not be constant
over any large range of velocities. pressures or teeperaturss.
this rewritten fore of King's equation,

:2: e [i . a goat] (r - 1-,). - (n)
has been used with a high degree of success in wort with
these inetruacnts.

The and losses are one of the cost troublesoae factors
in calibration of the Hot-wire Aneeoaetsr. The wire aust be
counted in such a cancer that the counts will interfere as
little as possible with the flow of the fluid ever the wire
and therefore met be nan. Keeping these mounts shall as-
cessitates using a material which will conduct electricity
and such material will also conduct heat. Although the
mounts can be of such else that the current passing through
then will not heat then such, there is the probability that
it any conduct heat free the wire and disperse it as a

-9...

function of the temperature difference between it and the
fluid stress. This would then cause the calibration scan
stunts to be a function of the tenpsrature difference exist-
ing.

This possibility does not sees to have received such
written consideration. The only article that I found rhioh
discussed this possibility or says of overcoaing it'sas
erittsn by Alfred H. Daria (13). Davis was doing:scne work
on heat transfer‘by free and forced convection and using a
Hotctire inescaeter to study the convection currents. He has
calibrated his instrument for a certain tesperature differ.
ence. then. using the instrument as a resistance thermometer.
he detersines the temperature of the fluid steel. to be
studied and sets the sire temperature the set amount shove
the ambient temperature. This offers somewhat of a refine-
sent. but would require that the fluid temperature rennin very
nearly constant over the period the fluid'eas being studied.

In this report the calibration constants hare been
changed some from those generally used. The terns cf thersal
conductivity and specific heat hare been removed in a hope of
getting these constants more exact. The rsrissd fore used
here will be
133 abet e515? 9")“ (T - 1'.) (5)

13. Daria, Alfred 3.. 'An instrument tor Use in Heasur-
in Convected Host”, ,
033. 1920 G 21.. Pp. 2-1 30

-10..

where

fl - (L/Jh .

and ~

8 e (at/Jh’nTI’h)

The proposed instrument based on this will be somewhat more
complicated to calibrate, but it is hoped that this and
other refinements will make frequent calibration less neces—
sary than with the present instruments.

the advantage expected to be gained.by this change is
not too evident with the equation as it stands. though it
can be seen that with any large change in the fluid tempersn
ture, the value given to k will hare some effect.

In the usual method of calibration. the temperature
termc, 2 and 2‘ are replaced by their values of resistance
from the equation (1n)

a . no [i .«(r . 10).] (5)
In doing this, it must be assumed that the ambient fluid
temperature will remain very nearly constant. If a great
enough difference can be maintained between the ambient

fluid temperature and the wire temperature, small variations
of the fluid temperature will here little or negligible ef-
fect. Since these instruments are used mostly in experiments
with forced fluid flow. it is questionable if any large range

A

in. mm.) L. 9. (Edited by), z r o
‘flgg§§6gsw'lork and London, Mcoraw o Hil Book 00.. 19 l.
D. e

of velocities could be accurately investigated. This follows
because a change in velocities would necessitate a chance is

the energy input to the moving fluid and a resultinglehange a
in fluid temperature. This was one of the complications men-
tioned in one of the articles by J. R. Weeks (7).

Since it is impractical to have laminar flow in prac-
tical problems, the type of instrument being discussed here
must necessarily have some limit in the variations to which
it will respond. This limit is best set by the response of
the galvancmeter. The galvanometer used in obtaining data
for this report had a period of from 2 to h seconds and this
was found to work out quite well. The result here is that an
average value of the heat loss is obtained. That is. that
very small changes in velocity. temperature or density did
not effect the amperage reading. thus giving only the average
effect of these. ‘

There are instruments which will react to very small
changes and many good articles can be found on the many
phases of instrumentation and calibration of these velocity
fluctuation measuring devices.

While the method of handling the calibration and use of
these instruments which is now used has served well and is
in wide use. it seems that it has many shortcoomings that
might be corrected. It is recognised that many of these prac-
tices which seem to introduce inaccuracies are used to sim-

plify the instrument and the simplifications hare added more

- 12 -

in making the instrument useful than they have done to make
it inaccurate. With a growing need for greater accuracy and
the use of the instruments in new fields, it would seem some
improvements could be made. Although this is not the primary
purpose of this thesis, it is hopedthat some progress along

these lines will he a hy—product of it.

SYSTEES OF SEVERAL WIRES

since the time King'developed his mathematical analysis
of the Hot-lire and demonstrated its possibilities, there
has been much work and thought put into making it a.velccity
measuring device. The Bot-Wire instrument has founds its
greatest field in measuring‘velocity fluctuations. From time
to time attempts have been made to make use of its other pos-
sibilities such as its directional characteristics and its
ability to measure other statistical data needed in turbulent
and boundary layer research.

Examination of the equation in the form used in this
report.
123 «Lek .542? (/37)&] (r - 1.). (5)
shows that the equation has two independent variables. These
are the velocity and ambient temperature of the fluid. Be-
sides these. it also has three other variables - the thermal
conductivity, the specific heat and the density of the fluid -
which are. for all practical purposes, independent of the

velocity, but are dependent on the ambient temperature and
the fluid being studied.

Since the heat loss is dependent on two independent
variables, the determination of one will depend on the accur-
acy with which the other in known. Since the Hot-Wire in—
strument has been chiefly used to measure velocity, an abil—
ity to make an accurate measurement of the anbient tempera-
ture is very necessary if the resulting velocity measurements
are to be accurate. At low velocities the normal temperature
measuring devices will serve quite well, but as the velocity
increases it has been found that the temperature measurements
become more and more inaccurate (7). This brings up the
question of whether or not the dependence on temperature
could be eliminated or minimized.

In locking'cver the terms of King's equation, it is
seen that it depends on the temperature difference between
the fluid and the properties of the wire. The diameter en-
ters in only the second term of the ecuation and, therefore,
if a different diameter were used, a different equation would
result. The lengflh enters in each term of the equation and,
therefore, changing it would probably only give a constant
times the same equation. Also the temperature enters the

equation in each term, but aince it is the temperature

7: Weeks, J. 3.. “A Method of Measurement of High Air

Velocities by The Rotatirc Method", n,g,g,a, Tenn figgg.
lo. 880, 1943.

difference. changing the wire temperature would egaMn reeult
in a conetant tinee the right hand eide of the equationg‘hnt
due to the complex relaticnehip between eire teepereture end
eire reeietance. changing the wire temperature eight eake a
further difference in the equation that can he need.

theee ooneideretione ehce that it will he poeeible to
nee a eyeten of tee and three equatione to evaluate the rar-
iehlee.

taking up the thernal conductivity firet, proper eenip-
ulation of three equatione, obtained in the eanner'deeerthed.
‘eill give an equation for thereel conductivity ee aunt a
function of the power dieeipeted through the hot-eire and
the ccnetante of the hetaeire. Thie eould he in the fore of
a quadratic equation and.eould take a couplicated‘eleetrenie
circuit to eolre it. but could he a very neetul device in -
eoehuetion reeeeroh ehere there eae reeecnably conetant flee.

the ambient fluid temperature ie the eecond quantity
that could he detereined with thie type of inetrueent. Again
it could take three equations to eliminate all the other
variablee. but. as with the thermal conductivity. they can
ell he eliminated and the ambient teeperature obtained an a
function or the power dieeipated and the equation ccnetante.

The velocity ie the third quantity that thie type c!
inetruaent night he need to neaeure. Although thie ie the
only one that the hctueire inetruaente ere preeentlr need to

neaeure, it ie the one that. theoretically, thie arrangement

of the inetrunent would he leaet capable of neaeurinc. Le
can.he aeen by examining the equation, the velocity. unlike
the other two, cannot be found an a function of juet the
power dieeipated and the eonetante of the inatruaent with

any number of einultaneoue equaticne. By using two equatione
the aahient teeperature can he elieinated. but the thereel
conductivity and epecific heat will etill rennin. The one
consolation ie that these quantitiee do not wary Inch over a
fairly large temperature range.

One trouble with the aethod Juet deecrihed ie that the
equaticne become wary long and complicated." But it elee~
trical circuite can he made to handle then, they ehould be
quite ueeful in nany typee of reeearoh.

fhie nethod depende on the eeeunption that the tern-,6
end.6 of the equatione will rennin reaaonahly constant over
a large range of relocitiee and teaperature differencee.
thie ie aeeuming that the loss of radiation to and riecoeity
of the fluid will he email and nearly conetent. Another
factor that could affect the waluee of fiend 6‘ ie the pee-
eible end lceeee. In an article by Weeke (7) it ie eug-
geeted.that if the ratio of the length of the wire to ite
diameter ie kept over 250 that the end lceeee will he negli-
gible.

A report through the Bureau of Standarde by Gt B.
Schubauer (15) hae ehown that changoa of’humidity have little

  

15. Schuhauer, G. 8., 'Effeote of Humidity In Hot-lire
Aneuoncter', 8 a . a , ..a a ,

(a: 850) p. '~57 78

effect on there ccnetante over a normal range of huniditiee.
Earlier two other non. A. E. Kennelly and H. B. Sanhorn (16),
investigated thie and found a 2 percent change in heat icee
per degree rise in temperature for a change in relative
humidity free 25 to 70 percent for temperaturee around 25
degrees centigrade. For~noet typce of work this would have
little effect.

‘ The limitations of this instrument would he velocity
liritatione and the came an those of the etandard inetrn-
mente. First. it is assumed that the product of velocity and
diameter of the wire is over 0.0187 (the velocity in ce./eec.
and the diameter in ca.) (5). Essentially. this requiree
that the velocity be large enough to overcome the effects of
any induced convection and to make the effect of any heat
file which might form over the wire negligible.

Since the thermal conductivity and the specific heat of
a fluid very very little over a rather large temperature
range and are generally known functicne of temperature. theee
terme can be retained in the equation without seriously col-
plicating it. Thin will make it poeeihle to use a conhina-
tion of two eiree to obtain'eeparate equations for ears-flow

Spv) and ambient fluid temperature (7‘) an functione of the

1:. Kennelly, A. I. and Sanhorn. H. 8.. "The Influence
Of Atmospheric Pressure Upon the Forced Thermal Convection

from Small Electrically Heated Vireo“,.zggg‘_§g‘_£h11‘_§gg.,
Vol. 52. 1911;. p. 55-

- 17 -

‘0

wire conetante, thermal conductivity and specific heat.
Theee equations are obtained in this manner:

Setting up two equations. one for each of the two wiree
to he need, and aeeuling that they are both evaluating the

same fluid propertiee under the same conditione,

ignl - [5: t 511/17 (pm (21 - r.) m
1532 III/921: 4» 821/757 90v)” "2 - I.) (8)
and putting in

r-[n.(°<r.-1HnJ/ («3.) (6')

for the value of i' in each equation, using the proper lub—
ecripte, and eclving the two reeulting equeticne simultan-
ecuely, first for (fv) and then for i“, theee equations are

Obtained;

{fv}egfv)'}0e330 (9)
01'

g") ' [Fag m, ’332e ‘9',
where

o - (21:73) . (-1 «in [ugnaa . aim/(n; . age] (as)
n - (ck/I) . w.) Bsgazq - firm/(n; - 333)] . (91»)
end .
rfier‘rer-o (10)
I!

2‘ a (-3 t W)”, (10')
IhOI'O

e e (elk) (ignae . ifnl) '- :(nl - Rae) - 2p (10a)

-18-

r .- (np/k)(1§n1 - 151134) e (Rlfiajh/k) (ig- - 13s .
Dim; - Re" 9 rfilfig o 1)2 (1%)

This gives two equations. the data for which can be
taken fro- the same instrument. Equation 9 gives the product
of gpv) with only slight dependence on a knowledge of the
fluid temperature. Since the value of thermal conductivity
varies very little over temperatures of 15 to 20 degrees.thie
would be roughly the accuracy necessary to obtain reasonably
good results. Equation 10 gives a method of obtaining the
temperature (2.) of a moving fluid that,'thecretically at
least, gives promise of being accurate at very high velocities.
The email wire used would not present the friction problem nor
would it distort the fluid flow in obtaining its measurements.

These equations are long and complicated and their so-
lution would be troublesome in this form. There are several
ways in Which this night be overcome. One would be to always
operate each wire at a set resistance. thus making every ter-
constant, except I. e and lé ‘ 1. A eecond method would be
to operate each wire at the name resistance. The first
method would cut down the number of operations needed in so-
lution, while the only improvement of the second over the
first is that it would simplify the needed operations.
neither of these simplifications. changes the original condi-
tions assumed in setting up the two-wire equations as the
wiree are still of different diametere and operated at diff-

erent temperatures.

There is a third possible simplification which involves
Operating both wires at the same temperature difference and
relying on Just the difference in diameters to produce the
two separate equations. This would be to out two wirescf
different diameters into lengths having equal zero relie-
tanoes. Now, it can be seen from the temperature-resistance
equation
a . no [1 .au .. 20)] (6)
that, if the two wires are of the same material and.hare
equal sero resistances. these two wires operated at equal re-
sistances will be at equal temperatures. The two equations

9 and 10 then become

(fut :- wa/a' [(1:41 - 1§m1§ - 134)] (9")
and I
a" e a [3 - (u/kHigd - 1%)] . p. (10")

Any notation that has not been explained can be found in
Appendix A.

Both forms of equations 9 and 10 would depend on the
accuracy with which the oonstantefi and 5 could be deternined
as ratios of each of these terms for the two wires appear in
the equations. Also there could be no variation of these

terms over the range of operation.

-20-

CONSTRUCTION OF THE INSTRUMENT
AND DATA TAKIRG

The Hot-Wire Instrument used for obtaining data for
”this orperiment was of the constant resistance type used for
Isasuring constant velocities. It consisted of a uhsatstone
Bridge for measuring the resistance of the wire, an smmeter
in the wire are for measuring the amperage flow in the wire.
a voltage divider for varying the voltage on the wire and
two small wires so mounted that they could be placed in I
moving air stream. '

The resistances of the Wheatstone Bridge, a wiring dia-
gram of which is shown in Figure 1 of Appendix B, were can»
mercisl. wire-wound resistances of 10 percent accuracies and
rated to be used at ten watts or less. The accuracy of the
resistances had no bearing on the accuracy of the bridge as
the bridge was calibrated after construction. This was nec-
essary because the resistance of the lead wires and soldered
Joints could not be balanced or controlled.

One arm on the bridge contained a variable resistance of
three chss. marked a, on the diagram, which was used to db-
tain s'bslancs when different values of current were used.

The calibration of the bridge was accosplished.by celi-
brating a three ohm variable resistance of approximately lin-
ear taper, and then placing this in the instrument bridge in
place of the hot-wire and using this to calibrate the variable

- 21 -

resistance of the bridge. A current of about 0.3 ms was
used to assure approximately the ease gaivsnoaeter sensi-
tivity as when the bridge was in use.

The variable resistance used for calibrating the‘bridge
was calibrated from standard resistances in this leaner:

First a one on. standard resistance was placed in the
are of a commercial Uheatstcne Bridge and balance eas ob-
tained using a sensitive wall-galvanoaster. Then the steam
dard was replaced by the variable resistance and this was
varied until the balance was again obtained. This point was
marked on the face of the variable resistance.

this was repeated with s one-tenth obs standard. tee
oneutenth oha standards. the one obs standard and a.one-
tenth she standard and the one ohn standard with hot! one-
tenth obs standards.

Oars was taken to use the seas leads to connect in the
variable resistance as were used to: the standard or contine-
tion of standards. The resistance of the leads. which were
soldered to tile variable resistance was included as part of
the resistance'cf this rhecstst.

The five calibration marks which were obtained.in this -
aanner showed no deviation fro- a linear taper. Direct in-
terpolation between these points was used to establish a
complete set of graduations.

lines it was necessary to have points beyond the 1.3 obs

mart found in this manner, a.box variable-resistance was

- 22 -

adjusted to one-tenth and two-tenths ohms by adjusting it ts
balance the bridge set for‘balanoe at these points. then
this was used in combination with the standards to obtain
other combinations on the variable resistance.

Platinum was selected as the wire waterial because of
its high resistance, its high temperature coefficient of re-
sistance and its ease of handling. The wire dimensions and
characteristics were:

Length (approximately) a - - - -w. - - - - - - 0.5 inches

Diameters -»- a»o - - - - - - - - - - - ~ - - 0.003 inches
- . . . . - s o s a o - c 0 - a - - 0.0015 inches
feaperature Coefficient of Resistance v o - . 0.00!On/°f
The Bigmund Oohn Corporation supplied the wire and gave its
properties as being approximately 99.999 percent pure plati~
one with a coefficient of resistance of 0.00398/°G
(0 - 10090). The wire was supplied unannealed end was en-
nealed by passing a current through it, which caused a vis-
ibls glow; and keeping it heated for approximately one hour.

Since it is not necessary to know the exact length of
the wire, no great care was taken in adjusting the length ex-
cept to be sure that the wires were long enough so the ratie
of the lengnh to the diameter was over 250.

A drawing of the sountinge of the wires is shown in
Figure 3 of Appendix B. the wires were mounted on Fuaber 7
needles which were in turn supported by carved, hard'wcod
bases. The wire end was placed in the eye of the needle and

- a} -

the eye filled with a soft solder. Lead wires going‘bach to
the instrument were soldered to the lower end of the needles
and supported by the wood mountings. The wood aountings were
held in the air stream by copper tubes which were attached to
a plate that could be revolved in a horisontal plane about
its vertical axis. the plate was supported on a 3/“ in. di-
saster pipe. the plate could be rotated about the horiscntal
axis of the pipe. 80 arranged. the wires could be adjusted
in any direction to bring it into a position serial to the
air stress.

A tube in inches in disaster. fed froa a squirrel-cage
fan. was used for calibration tests on the inatruaent. Boas
approximation of lssiner flow was obtained by running the
tests at a point some 30 ft. down the tube from the fun. new
tween this point and the fan. the tube contained a set of
'straighteners' which tended to brake up the turbulent flow
from the fan.

A static-pitct tube was used to measure the velocity in
the wind tube. The wire mounts and the pitot tube were ac
counted as to take three positions approximately equal dis-
tance apart and approximately equal distance from the center
of the tube. This was done to have each measuring as near
equal velocities as possible.

There was a gate arrangement on the wind tube, near the
fan. which was used to vary the velocities in the tube.

The reference resistance of the wire was found first.

..2t»-

To do this, the resistance of each wire was measured at were
eral air temperatures and the reference resistance (3.) cos»
puted from equation 5.

The measurable properties of the air were obtained by
placing a thermometer in the wind tube, near the test section,
to obtain the adhient air temperature, two nanometers con-
nected to the pitot tube, one to read static head and the
other to read the difference in static and total head. and
the baroaetric pressure was taken from a‘barometer in the
recs.

Since it is necessary to find the variation in the con-
stants with variation of both velocity and tenperature dif-
ference. it was necessary to take two sets of data for each
wire. One set of data was taken with constant velocity and
varying temperature differences. the other with constant
teapcrature difference with varying velocity. In the first
set, the velocity was held constant. near the sari-ms for
this experiment. and the temperature difference was varied
by varying the voltage impressed on the instrument'bridge.
In the second set. the velocity was varied by closing the
control gate by degrees and the temperature difference was
held constant by varying the voltage impressed on the bridge
to keep the bridge in balance at a set resistance. The ten-
perature difference was not kept constant as the air temper»
ature varied a little.

Since the-variation of the constants with varying

-25-

tssperature difference was considered likely to be the nest

ilportant, two sets of data were taken on this for each

wire.

DISCUSSION OF EXPERIEEHTAL RESULTS

Although it would seem legioal to compute the constants
for each point since the variation in the constants was to
be checked, for several reasons this was not done. First,
computing these would be a very long and tedious Job; second.
if this were done. it would involve only average values bee
tween sets of adjacent points: third. it would involve ratios
of the differences in numbers which are very nearly equal and
thus increasing the error many times; fourth. the instrument
used in obtaining this data was not sufficiently accurate to
warrant attempting this method; and last, there is a simpler

and more direct way.
If equation 5 is rearranged in the following manner,

,6 . fies/mm] - 5 1/71? govfi (5')
and it is aeeused that and are constants. this eqaaticn
sen be compared to the equation of a straight line.

,6 I y a. S: (53)
where

y - tan/(mm

I «5717 gm"

If, as assessed. fiend 5 are constants. it can be seen that for

a set value of 3 there is a set value of y. Further, if the

,~
.I.

values of r and y are known, these can be plotted and the
curve of equation 5' will result. this can be done with no
knowledge of the values of either flcr 5 . Now. if the as-
suapticn made here is not correct. a curved line and not a
straight line will result when r is plotted against 7. This
does not assume that any of the variables of the equation
have been held constant.

This curve will then serve tee purposes. It can serve
as a check on the extent to which these "constants” are con-
stant and also as a calibration curve for the wire. The
equation here is the slope~intsrcept equation of a straight
line where/6 is the intercept and 5 is the slope.

The first set of values. the tabulation and graphs of
which can be found in Appendix 0, were taken with a constant
wire temperature and varying velocity. the hope. in holding
the wire temperature constant, was to get a curve at con.
stant tenperature difference. but variation in the ambient
air temperature prevented this. The velocity was varied fros
approximately 5 to 27 ft. per sec. The temperature differ-
ence shows a variation of around 6°F. Straight lines could
be drawn through nest of the points for both wires. This had
not been expected and it is quite possible that, if a greater
range of velocities were used and greater accuracies were ob-
tained, the curves would show some variation from a straight
line. Some of the points on these curves are out of line and

these can probably be attributed to errors in making the test

-27-

readings. This is shown by the fact that in some of the
cases a second reading under the same condition has fallen
on the line.

The second two sets of values taken for each wire are
at constant velocity and variable temperature differences.
This presents a slightly different problen as now the ter.

1 in equation 5' is a constant, or reasonably so. If 1,19
and 8 are all constants then 7 also sust be constant and the
curve here would be a single point. This would not serve to
show the extent of any variation in the constants.

This has been overcome by observing that if y is a con-
stant. then if (r)(A!) is plotted against 133, this should
give a straight line. Any deviation from a straight line
could indicate that the constants varied with the tesperature
difference. This, of course, would not give an indication of
which constant varied or. if both varied. the extent of var-
iation of each. But. if a variation were found here. con-
stant tesperature difference curves could be run for a nua-
ber of different temperature differences and the place and
extent of the variation evaluated.

The tabulation of data and plotted curves for this are
shown in Appendix 0. A straight line could be draan through
most of the points except those from zero to 60 degrees teen
perature differences. The data taken was not accurate
enough to give this portion of the curve any meaning. Again

a few of the points are out of line of the curve, beyond

- 28 o

those in this erratic portion of the curve. These points
can probably be attributed to errors in data taking as there
is little uniformity with the way they deviate fro: the line.
The temperature differences used ranged from sero to around
100°F, this end point differed with each set of date.

The results from this show that. within the accuracy of
the work and the limit of temperature differences used. the
constants did not vary any appreciable amount.

The problem of determining the value of a reference.
wire resistance is a very important one. because upon how
well this is determined will depend the accuracy of the
aeasurements of the fluid properties with the instrument.
This is a probles because of the sire of the wire. Since the
resistance is very small. a current of the value used in cost
standard resistance aessuring devices will tend to heat the
wire and the value determined will be too large.

Three ways of determining this will be listed here. The
first two were used in obtaining the data for this thesis.
the first as a check on the second. This instrument was not
considered accurate enough to use the third method.

1. A piece of the wire about u inches long was connected
in series with a larger known resistance and an anneter. the
wire was placed in oil and heated to “00°F. The circuit had
been tested beforedhand under a certain impressed voltage and
the current recorded. The wire was then included and the same

iapressed voltage used. The current was kept well below that

-29-

which would beat the wire at these temperatures. All the
leads used were included in both tests so they would not add
to the resistance. The resistance of this piece of wire was
computed from the difference in amperage reading before and
after adding in the heated wire. Then, from the measured di-
mensions of the wire and this resistance and temperature. the
characteristics of the material were computed.

This method was not considered much of a success as the
resistance of the wire was not large enough to make such
change in the current flow.

2. The wire was placed in the calibrated bridge of the
instrument and a small voltage impressed on the bridge. The
bridge wae‘balenced and the resistance read from it. This
was repeated at a number of air temperatures as a.manner of
check. The reference resistance was then cceputed from equa-
tion 6.

The drawback with this method is that a very small volt-
age must be used to keep from heating the wire. The galvanc-
actors that are used in this type of instrument cannot be the
:jype that will seasure as eesll a voltage variation as would
be required here.

The reference resistances obtained by this method are
given on the data sheets in Appendix 0.

3. This method requires a very accurately calibrated
instrument bridge and an ammster that can be read to as many

places as are required in the resistance accuracy.

is was stated in the discussion of the terms of equation

5' for constant velocitydvarying temperature difference. if

‘19. x and 8 are constant then all the terms of the equation
are constant for each point. Therefore, the y terms of any
two points can be set equal.

71 O 72

or

fire/(uteri) s igaa/(anrz)

Cancelling the k from each side of the equation and substi-
tuting in
A! . (RA-<3.) [no - 1/«0 «- 2.]

for cached and solving for Ro this equation is obtained,

R. - [3132“? - 1%)] IBM, - a) - 1] (15a, - ifal) (n)
This gives an equation for no that eliminates the troubles
found in the other two methods. Also. if the instruments are
constructed for use of the two-wire equations developed in
this thesis. this method will not require any more accuracy

than is needed for working with these equations.

DISOU3?ION OF POINTS OF POSSIBLE ERROR

The method of calibrating the instrument left roan for
some error. Since only one and one-tenth chm standards were
used, it was necessary to assume a linear taper between
these points to mark the variable resistance off in one-

hundredth ohm division. A further error may have been

-31-

introduced by calibrating a commercial variable resistance
and then using it to calibrate the bridge. This was asses.
sary as the bridge was changed a number of times and a
method of speedy calibration was needed. The resistance
readings used are given to the third place beyond the deci-
mal point, but they are probably not accurate to more than
t 3 in m. place.

The readings of the ammeter are given to the third
place. These are not accurate to more than t 2 in this third
place.

The ambient air temperature is another place of possible
error. The temperature here was continually changing while
the tests were being made. In general, it was climbing, but
at times it would drop as much as 2 degrees in a period of a
few minutes. It is possible that the mercury thermometer
used did not always react to these changes as fast as they
occurred. The temperature readings are given to the third
place with a probable reading accuracy of 2 2 in this third
place.

The velocity and static pressure were measured with a
staticupitct tube and it was assumed that the readings of
this tube were correct over the complete range. The statie
headland difference in static and total head readingm did
not show the fluctuations that the temperature did. It is
hard to believe that the velocity did not fluctuate while the

temperature did and it is possible that the nanometers were

- 32 -

too slow to record these fluctuations. The static head read.
ings were taken to three places and were accurate to this
place. The difference in heads was read to the third place
with an accuracy of 2 2 in this place.

There is also a possibility of error due to turbulent
flow which would affect the Hot-lire, but not the pitet tubs
readings.

In general, control was not considered good enough to
attempt to obtain any experimental evidence on the use of the
tweawire equations.

GEKIRAL CONCLUSION.

- The graphs of the data taken for each of the two wires,
operated first at constant temperature difference and vari-
able velocity and second at constant velocity and variable -
temperature difference, has been plotted in such a.sanner as
to show a variation of the constants if the experimental data
does not fall on a straight line. This experimental data, in
each case, has formed a straight line within the lisits of
this orperiment and over the range for which the data was
taken. The experiment was only accurate enough to give an
indication and not within close enough limits to give proof.

Since the theory of the two-wire equations presented re-
quires that these ‘constants' be constant over a rather large

range, the data presented gives a definite indication that

\

-33-

theee two-wire inctrumente are feaeible; although, it would
take a much more accurate and.hetter controlled experiment
to prove or dieprove thie. The indication given here ie
that the variation of the conetante over the range inweeti-
gated ie only very alight, if at all, and that there would
he a fairly good range where a etraight line would approxi-
mate the curve very cloeely.

The advantagce theee Tucawire Inetrunente eeem to offer
are: the eliminating of the need to know the ambient fluid
temperature ec accurately in neaeuring welcoitiee. I method
of finding the ambient fluid temperature at high velocitiee

and more accurate information on the thermal conductivity of

fluids.

S

as a velocity neaeuring device. ite dieadventagee ae
compared to the mum lnetrumente would be: the ccnetruc-
tion of a direct reading instrument would be Inch acre coetly
and complicated and the lie. of the inetru-ent heed.wculd be
I02. than doubled.

In general. if the inetrunent ie feaeible. it would only
be profitable to uee it there ccneiderable. accurate infor-

nation on both telperature and velocity were needed.

-3n-

APPEEDIX A

NOTATIOHB

Fluid and Wire Rotations

If

éb’ d 1;! \b 3

"IF“
O

'8! 33 ea

U'QOU-Ix

ie the thermal conductivity of the fluid.

ie the epecific heat of the fluid.

ie the deneity of the fluid.

to the ambient temperature of the fluid.

in the velocity of the fluid.

or A? ie the temperature difference between the wire and
the fluid at come dietance from tlie wire. ‘

ie the diameter of the wire.

in the length of the wire,

1 , fl and r

I 2
ie the alperage flow through the wire.

are wire temperaturee.

ie the reeietance of the wire at some temperature 2.

ie the reeietance of tlie wire at the reference tenpera-
tux. 10.

ie the temperature coefficient of recietance for the wire.
ie the reeietanoe reference temperature for the wire.

ie a convereion factor between watt-lee and BTU'I.

ie a ccnetant correcting the firet tern of Kins'e equation.

ie a conetant correcting the eecond tern of King'e

equation.

-35-

APPENDIX 5(continued)

Oonetante of The Two-lire Equatione

.8 - (Ia/J):
6 - (EL/J) M113)
4 351/52

f 3 W61) .. (52/63)
8 'fl. ,6’2/8. 83

h - 52“}93 $1 “26152)
J ' "(“301)
"*%fli

:1 II 9139; flfl/(fifiz)
v '- (I'o - 1/“)

Q " 231/252

1' ' ”(‘zaol‘lw’

n e 1/292“ - cl]
'2' flg/Sgi  

" " Roll “on

-36...

 

APPEHDIK B

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10/0 023m:
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Circuit

Fig ure .1.

 

 

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““._\ / Tube 553/, /

Secl‘z'on Drawing of Wind fade at 71:57-

Jcci'z'on Sore/91"?"

Figure B

-33..

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AFPESDIX C

1. Data for oonetant velocity curve for Wire 1 (Set 1)

Diameter 0.0015 inch
Length (approximately) 0.5 inch

°< 0.002011/01'
R .1.l9l chm

O

Baronetrio Preeeure 29.17 in. of Hg.

 

Velocity 27.2 ft. per eec.

i a 39 123 g. 131' 1211/11:
.5321 .flhIfl ..ua— ._!fliifi. F .._§_. -t*
0.150. 1.355 88.2 3.09:10'9 99.6 11.n 2.71:10‘3
0.179 1.385 ‘ 87.u t.nt 112.3 2h.9 1.70
0.180 1.386 87.6 h.h9 112.3 2n.7 1.82
0.203 1.n01 87.0 5.77 115.5 31.5 1.82
0.232 1.h17 86.0 7.63 125.1 39.1 1.95
0.236 1.h32 87.5 7.98 131.3 R3.8 1.82
0.251 1.nn7 87.0 9.1% 137.5 50.5 1.81
‘0.261 1.u63 87.0 9.97 inn.1 56.7 1.77

.0.278 1.h78 86.5 1.1ux10‘1 150.2 63.7 1.79
0.291 1.u93 85.5 1.26 155,n, 70.9 1.73
0.300 1.509 85.5 1.36 163.0 77.5 1.75
0.318 1.52h 06.5 1.5% 169.2 82.7 1.86
0.320 1.539 87.0 1.58 175.u 88.4 1.79
0.337 1.555 87.6 1.77 182.0 9u.u 1.37

Q\\

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hwefik .0...th not \NcQ c...
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-41..

12288011 0(oontinued)

B. Data for conetant velocity curve for Wire 1 (Set 2)

Barometric Preeeure 29.27 in. of Hg.

Velocity 25.9 ft. per 800.

.1... .1... .8. .8“... .2. .11. -1121
0.030 1.326 86.6 1.19:10'3 87.6 1.0 1.19:10-3
0.122 1.383 86.5 2.00:10'2 98.6 8.1 2.87210-3
0.150 1.358 86.5 3.06 100.8 18.3 2.18
0.168 1.378 86.2 3.88 107.8 21.2 1.83
0.170 1.378 86.0 3.97 107.8 21.8 1.86
0.181 1.398 86.6 8.58 117.3 30.7 1.89
0.191 1.808 86.7 5.12 - 119.8 33.1 1.55
0.219 1.820 86.6 6.78 126.3 39.7 1.71
0.228 “1.835 86.6 '7.86 132.5 85.9 . 1.62
0.285 1.850 86.6 8.70 138.7 52.1 1.62
0.258 1.866 86.8 9.81 185.3 58.9 1.67
0.261 71.881 86.2 1.01:10'1 151.5 65.3 1.53
0.282 1.896 86.5 1.19 157.7 71.2 1.66
0.291 1.512 86.5 1.28 168.2 77.7 1.65
0.301 1.527 86.8 1.38 170.8 83.6 1.65
0.311 1.582 86.8 1.88 176.6 89.8 1.65
0.320 1.558 86.8 1.60 183.2 96.8 1.66
0.338 1.573 86.2 1.80 189.8 103.2 1.78

- 82 -

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9. .

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APPENDIX 0 (continued)

0. Data for constant wire temperature for Wire 1

Barometric Preesure 29.17 in. of Hg.

Wire Temperature 188.1 °F

Hire Reeietance 1.57 0h:
0.353 2.01110”1 85.5 3.8921108“ 27.8 1.80
0.352 1.98 85.2 3.890 25.3 1.35
0.388 1.90 ' 85.8 3.891 23.7 1.30
0.333 1.88 ‘ 86.2 3.896 ‘ 23.1 1.28
0.332 1.73 87.8 3.906 20.5 1.21
0.330 1.71 87.0 3.901 20.6 1.21
0.310 1.51 87.5 3.905 15.8 1.08
0.281 1.28 90.5 3.922 10.3 0.85
0.288 8.18310'2 91.0 3.925 8.9 0.58

t
Valuee of therlal conductivity and specific heat are taken.

reference 18, p 395 and 1909.

12288011 0 (continued)

1505?
251.5
251.6
251.6
251.5
251.2
251.3
251.3
251.1
250.9

mm

lentil!!!” at 5311*"

508
885
475
868
882
“33
388
328
215

352
380
327

322
304
308
261

213
186

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APPENDIX 0 (continued)

0. Data for constant velocity curve for wire 2 (Set 1)

1 a r
.JnuuL. .Jflflll. .ldt.

0.030
0.110

0.116
0.172
0.233
0.262
0.326
0.358
0.360
0.822
0.831
0.860

Diameter 0.002 inch

Length (approximately) 0.5 inch

o< o.00208/°r

Ra 0.850 ch:
Baronetric Pressure 29.07 in. of Hg.
Velocity 27.5 ft. per eec.

0.988
0.955
0.956
0.971
0.987
1.002
1.018
1.033
1.033
1.068
1.079
1.098

82.8
82.8
82.6
82.8
82.6
81.6
82.8
82.8
82.8
82.6
82.6
63.2

132
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8.50:10'“
1.16:10"2
1.29
8.07
5-75
6.68
1.08210"1
1.32
1.38
1.90
2.00

2.32

- 87 -

.31.
86.2
93.2
93-2
101.8
111.1

119.7

‘128.9

137.6
137.5
155.5
168.1
172.8

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8.0
10.8
10.6
19.0
28.2
37.1
87.1
55.2
55.2
72-7
81.3
89.6

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2.122102“
1.07:10'3
1.21
1.51
2.08
1.85
2.30
2.80
8.82
8:61
8.87
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12282011 0 (continued)

B. Data for conctant velocity curve for Wire 2 (Bot 2)

Barometric Preeeurc 29.27 in. of Hg.

Velocity 26.9 ft. per eec.
..n;21. ._.§... .111.. ..J§SZLL.. _§¥é_ .figi. 12278: +
0.100 0.950 86.2 9.5011073 89.6 3.8 2.80:10'3
0.122 0.955 86.1 1.82210‘2 92.8 6.3 2.26
0.150 0.971 85.2 2.18 101.6 16.8 1.33
0.162 0.971 88.2 2.55 101.6 17.8 1.86
0.168 0.971 88.0 2.78 101.6 17.6 1.56
0.220 0.987 85.6 8.78 110.8 25.2 1.90
0.270 1.002 85.0 7.30 119.8 38.0 2.15
0.272 1.002 85.6 7.81 119.8 33.8 2.19
0.310 1.018 88.2 9.78 128.6 88.8 2.20
0.310 1.018 85.0 9.78 128.6 83.6 2.28
0.318 1.018 85.0 1.00210"1 128.6 83.6 2.30
0.389 1.033 88.5 1.26 137.2 52.7 2.39
0.353 1.082 85.0 1.30 182.8 57.8 2.26
0.362 1.088 86.2 1.37 185.8 59.6 2.30
0.371 1.088 85.0 1.88 185.8 60.8 2.37
0.372 1.088 85.0 1.85 185.8 60.8 2.38
0.825 1.079 86.1 ' 1.95 163.7 77.6 2.51
0.830 1.079 86.0 . 2.00 163.7 77.7 2.57
0.867 1.110 86.0 2.83 181.5 95.5 2.53
0.869 1.110 86.0 2.88 181.5 95.5 2.56
0.500 1.139 85.8 2.85 198.2 112.8 2.52

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APPENDIX 0 (continued)

I. Data for constant tire temperature curve for Hire 2

Barometric Preasure 29.1? in. Of Hg.

wire Temperature 363.? °F

81:0 Resistance 1.079 oh.
.J:LNL.. .JJSZEL.. ..3§E_.IUHUE£EUUUQMHI.JHJLMNL..IJ§2;g§=lllulé.
0.366 1.85:10‘1 85.5 3.892110‘6 27.8 1.80
0.358 1.38 85.5 3.892 25.3 1.38
0.351 1.33 86.5 3.897 23.8 1.30
0.388 1.30 ' 85.9 3.898 23.3 1.29
0.338 1.23 87.5 3.905 20.5 1.21
0.318 1.09 _87.0 3.901 15.8 1.08
0.288 8.98210-2 89.5 3.916 10.3 0.85
0.282 8.58 90.0 3.919 10.3 0.88
0.236 6.11 91.5 3.928 8.8 0.58

13"»
AP.8.DIX 0 (continued)

308

297
215

303

213
211
186

 

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APPEHDIX D

REFERENCES

lpccltlo References

1.

7.

8.

9.

10.

Kennelly, A. 8., Wright, 0. A. and Van J. 8..
“The Convection of Heat From 80211 Copper Wtree',.zng
..:! -3 .1. 3_ W- ‘gm _9 t - 2 916 t 8
m '93.. .v01. 3. Par‘ . 1:10. pp. '3‘} e

828028302028 and Harri-8 J. 7., "The Electrical Ree-ure-

1311'; of Hind vuoouy , 333mm, v81. 98. 088. 27.

Ferrari. 08:10, “Electrical Equipment Ior The Experimcno
tel 88087 of Fluids", ‘ oe. ADV,~U . .'.£ . -

   
 

Kins. L. V., "On The convection of fleet Iron Small 0311a-
dere In 8 Stream of Fluid: Determination of The Convec-
tion Constants of Small Platinum Wires wzth Application
To H0t~81re Anenomctcr'. 3!. -.--. ~- 9:1. .8
U!» '0 3 J'q- ' t?!539 . 890. A0. V01; 2 ‘ NOV.

1 8 PD. 37 '32-

Dryden, E. L. and Kuetho, A. 8.. “The Measurement of
Iluotugtlone of Air Speed By The 30888120 Anemometer',
' - .1 _ 7 _ . I A. . - ',_ . _‘ . ROD. 320:

 

80880, J. 3.. "Method of Heaeurement of High A12 Veloci-

ties By The Hot-Wire Method', .H£31235§—£91%fi§11_gnlail'
W211” Tech- Note 80- 0. 1 .

Weekc‘ J. R., '8 got-Wire Circuit With Very Dwell Tin.

 

80880. J. R. 'Heaeuroment of Arithmetic Mean V01001ty 0!
Huang how of High 1701801118. 2y 808.812. MOthOd'
- c a . , t. ‘-. Tech. HO‘.

  
 

 

Corr-1n. afienley. “Extended Application! 0! The Hot—lire
Anemometer', Eat A v on t F A
Tech. Note 30. 1 , April. 19 9.

-58..

Specific Reference. (continued)

11. simmonl. L. I. 0. and Bailey, A.. “An Instrument for
Measuring apeed and Direction of Air Flow“, M

We V0)" 3| 1927. P90 81.96:
12. MaoAdame, I.H.,,‘flg33"1z§n{gig§1gn, new York and London:
Heart! . Hill Book 00., 933. .

13. Davie. Alfred 3.. “An Instrument For Use In Measuring
Convectod Heat” . ' , a ; ,_‘ -»

m. Vol. 33a

in. Berke. L. a. (sauce b y). . '
.figg§§sgev‘rork and London: MoGraw — Hiii Book 05.. 19u1,

 

15. Schubauer G. 8., ”Effects of Hunidity In Hot-Wire
Anemometer' » f i. . __ a .

WM

16. Kennelly. A. E. and Banborn. H. 6.. 'The Influenoe 0t
Atnolpherio Ireesure Upon The Forced Thermal Convec—
tion From Email Electrically Heated Vireo”. ..€z¥g2§gg

. , ... L .... L ..._._ é . . O O .

 

 

APPENDIX D (continued)

General References

1. Davis, A. H., “The Heat Lose By Convection From Vireo
In a Stream of Air and Its Relation To The Mechanical

     

Resistance“.
.5 “35‘ .1-
pe ‘99.

2. Iing. L. V. "Precision Measurements 0! Air Velocity by
Means of *he Linear Hot.eire Anemomeger',

We V010 18’ 191

3. Hagnan, A., "Nethods of Recording Rapid Wind Changes".
A . A . Tech 0
Memo. No. 92. NOV. 19 20

n. Martinells, R. 0., and Randall, R. D.. ”Behavior of Hot-
Wire Anemometer Subject To Periodic Velocity',

War 8 WW - Tran-o. V01-
. Jun. 19 0 pp. 75‘79'

5. Hook. I. 0. and Dryden, H. L., "Improved Apparatus For
e Moanurement of Air Speed In Turbulent Flow'.
5. -'_ ' - «911.9. ‘3 . A .13 ‘ . Rep. 80.

5- on! 1!- WM. London: Chapman
an nail. 933.

7. Runyon. R. A. and Jeffries, R. J.. “Empirical Method For
equency Compensation of The Hot-Wire Anemometer',
er- 4 A .r ‘ . . ' -qgi - , Tech. '0‘.

   
 

  
 
  

      
   

j

  
 
  
 

O

 
      
 
 

   

8. Townsend; A. A., 'Heasurement Of Double and Triple
1

Derive was In Isotropic Turbulence“, W
W' "01- “3. Oct. .

pp. 7 e

 

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