Report 953
NAVY DEPARTMENT
THE DAVID W. TAYLOR MODEL
WASHINGTON 7, D.C.
SUMMARY REPORT ON THE DEVELOPMENT OF A HOT-WIRE
TURBULENCE-SENSING ELEMENT FOR USE IN WATER
by
R.G. Stevens, A. Borden, and P.E. Strausser
RESEARCH AND DEVELOPMENT REPORT
December 1956 Report 953
SUMMARY REPORT ON THE DEVELOPMENT OF A HOT-WIRE
TURBULENCE-SENSING ELEMENT FOR USE IN WATER
by
R.G. Stevens, A. Borden,and P.E. Strausser
December 1956 Report 953
NS 715-102
TABLE OF CONTENTS
Page
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ABSTRACT
A summary is given of the work done since 1946 at the Taylor Model Basin
to develop a hot-wire turbulence-sensing element for use in water and of some of
the uses to which the wire has been put. Recent efforts to determine the causes
of wire instability and to eliminate them are described. As a result it was deter-
mined that these wires should be heated with an alternating carrier current and
that the exposure of dissimilar metals in the probe assembly should be eliminated.
With these precautions the wire could be stabilized in well-filtered water. In or-
dinary water, instability from the accumulation of dirt and surface film on the
wire could not be controlled except by removing the wire frequently for cleaning.
It appears that the only satisfactory solution to this problem lies in the develop-
ment of a dynamic calibration technique. Theoretical expressions for the sensi-
tivity and frequency response of a coated hot wire are included.
INTRODUCTION
Since 1946 experimenters at the David Taylor Model Basin and elsewhere have attempt-
ed to apply the principles of hot-wire anemometry to turbulence measurements in water. Al-
though many hydrodynamic problems can be simulated in wind tunnels and studied with con-
ventional hot-wire methods, there are a few important problems, particularly where surface
effects are important, which are not amenable to this procedure. Although the techniques for
the use of a hot-wire turbulence-sensing element in air are now well developed and widely
used, some very serious difficulties arise when efforts are made to adapt this instrument for
use in water.
It is the purpose of this report to review the efforts of various investigators at the Mod-
el Basin who have contributed to the development of a hot-wire element for use in water, to
discuss the problems and difficulties involved and to report on current investigations. M.S.
Macovsky and W.L. Stracke developed the first element and made a few quantitative turbulence
measurements with it. The wire has been used by Macovsky and J.P. Breslin in qualitative
experiments in turbulence detection. Mr. Stracke worked out a method for a dynamic calibra-
tion of the element and made preliminary experiments for developing the technique. Recent
experimental investigations to develop a more stable wire have been carried out by R.G. Stev-
ens and P.E. Strausser. Dr. Borden has made theoretical studies of the sensitivity and fre-
quency response of hot wires on which a surface film has formed.
EARLY DEVELOPMENT OF THE HOT WIRE FOR
USE IN WATER AND ITS APPLICATION
Beginning in 1946 Macovsky and Stracke developed a constant-current, hot-wire, turbu-
lence-sensing element for use in water.!’2 The element was heated with a direct current and
was used in a conventional constant-current hot-wire circuit which had been developed at the
National Bureau of Standards.? Most of the effort at the Taylor Model Basin was expended in
selecting wire material and in developing methods of fabricating the probe and a technique for
making turbulence measurements. In addition, the hot-wire element, as originally developed,
has been used with varying degrees of success in quantitative turbulence measurements and
has been used very successfully for qualitative measurements and for turbulence detection.
The choice of a wire material depends not only on favorable electrical properties but
’ also on its ability to withstand the corrosive action of water and the relatively large hydro-
dynamic forces. The most suitable material was determined to be tungsten. Probes fabricated
from 0.3-mil tungsten wire, about 4 in. long, had a resistance of from 5 to 10 ohms and could
be given a temperature elevation of 15F with a heating current of about 120 milliamperes.
Such wires did not corrode and were able to withstand water speeds up to 20 knots without
failing.
In fabricating the probe the wires were carefully copper plated, leaving a gap of the
desired length for the sensitive portion. Then the plated portions were soldered across the
tips of the metal supports. Finally, the supports were painted with insulating material to re-
duce electrolysis. Details of the fabrication technique are reported in References 1 and 2.
The major obstacle in obtaining accurate turbulence measurements with a hot wire is
the instability of the wire resistance caused by the accumulation of gas bubbles, dirt, and a
surface film on the wire. This contamination starts as soon as the wire comes into contact
with the water. If the resistance fluctuations arising from changes in the convective cooling
of the flow are to be measured quantitatively, all measurements must be made with a freshly
cleaned wire a few seconds after it has been placed in the flow. The measuring technique
developed by Macovsky and Stracke consisted of removing the wire before each measurement,
cleaning it with a camel’s hair brush which had been dipped in acid, positioning the probe
again, and quickly taking a reading. The heating current in the wire was automatically turned
on and off by means of a microswitch as the probe was swung into and out of the water. To
check a reading it was necessary to repeat the whole process. Thus the reliability of the
turbulence measurements depended a great deal on the patience and dexterity of the investi-
gator. With care, measurements could be repeated.
The foregoing technique was used in the 1/22-scale model of the Taylor Model Basin
circulating water channel! to repeat some of the classic wind-tunnel experiments of free-stream
turbulence behind grids and cylinders. In the first experiment the hot-wire sensing element
was mounted at various distances downstream from a grid and quantitative measurements of
Ieferences are listed on page 14.
in percent
frie
Uo
Turbulence Intensity
Rod Diameters, Y/D
Figure 1 - Distribution of Intensity of Turbulence 91
Diameters Downstream from 3/32-inch Rod
The solid line is due to Townsend (R, = 850); the points are TMB hot-wire data (R, = 1050)
turbulence intensity and correlation were made. Although the wake intensities are very sensi-
tive to the magnitude of the background turbulence, the intensity measurements made in the
TMB model circulating water channel are of the same magnitude as those obtained in the wind
tunnel at the National Bureau of Standards. 2+ The validity of the correlation data obtained
in the TMB facility is uncertain owing to experimental difficulties.
In the second experiment the sensing element was mounted downstream from a rod
mounted horizontally across the water channel. As seen in Figure 1, the data obtained from
wake traverses behind the cylinder are in good agreement with Townsend’s data,° if allowance
is made for the rather high level of background turbulence in the water channel (about 1 per-
cent).
Preliminary measurements were also made of the decay of turbulence in the TMB towing
basin after the passage of a full-form ship model.! Although it was difficult to make quantita-
tive measurements under such conditions, it was estimated that after a waiting period of 10
minutes between runs the turbulence level in the basin had decayed to such an extent that it
would not affect the resistance measurements.
Although quantitative turbulence measurements in water were difficult and sometimes
of doubtful accuracy, the hot wire has been used with great success for qualitative measure-
ments. After the wire has been submerged in water for a few minutes it accumulates a film
at a slower rate and it becomes a useful instrument for detecting turbulence where a calibra-
tion is not required.
A useful qualitative application of the hot wire was made in an experimental study of
various methods of artificially stimulating turbulence in the boundary layer of a tanl_er mod-
el.4© For the purpose of mapping out regions of laminar, transitional, and turbulent flows,
2, =8.4% 10°
||
i
R= 14.1105
R= 17.6 105
|
R= 22.9 x 105
W
TIMING LINES
Laminar Flow
Transitional Flow
Transitional Flow
Transitional Flow
Ly
i
i
aul
Transitional Flow
Turbulent Flow
"0.10
sec.
n
i
aN
Ps
U=1.2 knots
|r
U=1.6 knots
U=1.8 knots
|
U=2.0 knots
U=3.25 knots
Figure 2 - Oscillogram Records from a Hot-wire Sensing Element
Showing Turbulence in a Boundary Layer
These records show how the hot-wire sensing element gives qualitative detection of turbulence.
4
removable turbulence-sensing elements were mounted at various positions within the boundary
layer on the forebody of the model. Although no information was obtained as to the intensity
or scale of turbulence, the oscillogram records clearly delineated the regions of laminar, trans-
itional, and turbulent flow. Typical oscillogram records are shown in Figure 2.
The same qualitative technique has also been used to determine the spanwise phase
configuration of vortex shedding behind a cylinder towed horizontally through the water. Fol-
lowing a procedure used by Roshko’” one element was placed at a fixed point behind the cylin-
der while a second one traversed the wake along the same horizontal line parallel to the cylin-
der.
RECENT EXPERIMENTAL INVESTIGATIONS TO IMPROVE WIRE STABILITY
The inherent instabilities of the hot wire as it was developed by Macovsky and Stracke
precluded its extensive use for quantitative turbulence measurements in water. Early in 1954,
however, interest in obtaining a practical instrument for quantitative turbulence measurements
was revived and work on the hot wire was resumed at TMB and also at the Iowa Institute of
Hydraulic Research.® Efforts at both laboratories were directed toward obtaining a hot-wire
instrument which would be as easy to operate in water as in air.
It was discovered independently at both laboratories that much of the wire instability
could be eliminated by the use of an alternating heating current. The bubbles which formed
on the wire when it was heated with a direct current were largely a result of electrolytic dis-
sociation of the water. As the bubbles formed and broke away erratic changes were produced
in the rate at which the wire was cooled by the flow. With an alternating heating current of
several thousand cycles per second, however, the bubble formation and the resulting resis-
tance instability were eliminated. Even in highly aerated water bubble formation was no prob-
lem.
Even with the elimination of bubble formation enough instability remained to make cali-
brations uncertain. In order to track down these other instabilities the hot wire was mounted
in an a-c bridge circuit and resistance changes could be observed as the bridge became un-
balanced. A diagram of the circuit is shown in Figure 3. The heating current was supplied
by a power oscillator and the bridge unbalance was observed on an oscillograph. It was nec-
essary to use isolation transformers on the input and output of the bridge to avoid ground loops.
In the preliminary experiments the sensing element was fabricated of 0.3-mil tungsten
wire using the same techniques previously developed by Macovsky and Stracke. After all
ground loops and electrical pickup had been eliminated an instability persisted which was
finally attributed to a galvanic action between the dissimilar metals used in the probe sup-
ports, solder, and plating on the wires. Consequently, the old technique of soldering copper-
plated tungsten wires to the probe tips was abandoned and unplated tungsten wires were weld-
ed directly to the probe holders. The joints and probe holders were painted with a good
Power
Amplifier
Oscillograph
Figure 3 - Bridge Circuit Used to Study the Stability
of a Hot Wire in Water
quality insulating material* to cover all dissimilar metals. It was almost impossible to effec-
tively coat the plated portions of the wires if the old technique of mounting the wire was used.
Ideally the same metal should be used throughout and the wires should be welded in place. At
present, however, the technique for welding tungsten wire to tungsten has not been developed.
It may prove worthwhile to reconsider other wire materials which would be easier to weld. For
example, platinum or certain nickel alloys might be suitable.
If all the above mentioned precautions are taken it is possible to obtain a wire which
is stable for a reasonably long time in well-filtered water. In ordinary water found in test fac-
ilities, however, an instability develops as the wire accumulates dirt and hair-like fibers from
the water. Dr. Hubbard has found that the film formation is slower in highly turbulent water
and is retarded by shaping the wires in a V.® In slowly moving streams as in the TMB channel
the angle of the wire did not seem to delay the dirt accumulation. Part of the dirt could be
swept away by a small stream of water from a syringe,but none of these methods were adequate
to maintain a wire calibration which could be relied upon for a practical length of time. It was
still necessary to remove the wire at frequent intervals for a thorough cleaning. There had
been, however, a large gain in stability over the direct-current wire used in the early work.
DYNAMIC CALIBRATION TECHNIQUES
As it is usually not practical to remove the wire for cleaning very often, it may be nec-
essary to develop a dynamic method of calibration. For example, it may be feasible to super-
impose on the flow a known turbulence field immediately before or after each reading. Itis
important, however, that the imposed turbulence be uncorrelated with the field of turbulence
*The only satisfactory insulating material on hand at TMB for this purpose was liquid Neoprene which requires
several hours to dry. Faster drying materials, such as Glyptol or Tygon, were not sufficiently waterproof.
under investigation.* In this instance, if ie is the mean square of the response to the original
turbulence, rea 7 the response with the addition of the superimposed field, the signal from the
superimposed field alone is
alp 4, -T? [1]
Now since the turbulence corresponding to 17 is known, the turbulence of the stream may be
readily obtained without knowing the wire resistance or any of the constants of the amplifier
or metering circuits. More important, the accumulation of dirt and surface film on the wire
would be unimportant provided the time response of the wire were not seriously impaired.
Mr. Stracke worked for some time on a dynamic calibration technique in which the wire
is given a known vibratory motion. The probe was mounted on a specially designed arm which
could be mechanically vibrated. The wire moved in a small arc which was essentially parallel
to the flow. There are a number of inherent difficulties in this vibration method which were
never completely ironed out. First, it is necessary that the vibrator be well designed to elim-
inate spurious motions so that the displacements and amplitudes can be accurately measured.
Corrections must be made for a possible sag in the wire as it moves. As strains in the wire
would become excessive if the vibration frequency were too high, itis necessary to limit the
frequency to about 10 cycles per second. It is also necessary for the wire, the amplifier, and
associated circuits to have a flat frequency response over the turbulence range down to the
vibration frequency of the mechanical oscillator. Some of these difficulties may be overcome
by comparing the vibration response to the wire response in a known turbulence field, such as
that behind a grid or rod. Details of the technique must still be worked out.
Another method of dynamic calibration which has been suggested is to insert a grid or
cylinder a known distance ahead of the wire. Since the turbulence of the wake of these objects
is already known a calibration could be obtained as before, provided the two turbulence fields
are not correlated. The grid or cylinder could be swung in and out of position without disturb-
ing the wire. The principle objection to this method of calibration is that it would be difficult
to use in a confined space.
INSTRUMENTATION
Very little work has been done in developing instrumentation for use with the hot wire at
the Taylor Model Basin since the early constant-current instruments were procured by Macov-
sky and Stracke.? Although the recent studies were made with a constant-current a-c bridge
it would be highly desirable to use a constant-temperature circuit for turbulence measurements.
The constant-temperature wire has advantages even though the frequencies of the turbulence
fluctuations expected to exist in water are low enough that compensation would not be a ser-
ious problem. In flows where the velocity remains constant for only short intervals it would
*An investigation of how two such turbulent fields are correlated will be made in the TMB Low-Turbulence
Wind Tunnel.
be inconvenient to have to set the temperature elevation and time compensation of the wire
each time. Thus a constant-temperature instrument would be convenient for surveying wakes
in the large towing basin or for making measurements in a boundary layer. There would also
be no danger of burning out the wire as it is moved into regions of low-velocity flows.
Dr. Hubbard at the Iowa Institute of Hydraulic Research has developed a suitable con-
stant-temperature instrument in which the wire element is heated with a carrier current of sev-
eral thousand cycles.® For this reason no further effort will be expended at TMB in this dir-
ection.
SENSITIVITY AND FREQUENCY RESPONSE
OF A COATED HOT-WIRE ELEMENT IN WATER
Since a hot-wire element acquires a surface film when it is used in water a theoretical
study was made to determine how the sensitivity and frequency response of the wire are af-
fected by the film.? As an aid in determining the magnitudes of the quantities under consider-
ation Tables 1 and 2 were prepared which list the physical properties of several flow mediums
and wire materials. Since the physical constants depend upon the precise composition of the
particular sample, the reference is given in each case. In these tables the constants stand
for the following quantities:
a Radius of film on wire
b Radius of wire
Cy Specific heat at constant pressure
a Sensitivity of wire at temperature Ne
fk, Total resistance of wire at temperature ie
T, Reference temperature
a Temperature coefficient of resistance
kK Thermal conductivity
p Density
o Tensile strength of wire
When subscripts are used with these parameters, 1 refers to the wire, 2 to the coating, and 3
to the flow medium. In addition to physical constants the tables include useful combinations
of these constants, some of which will be defined later. As many of these quantities include
the wire diameter, the numerical values refer to a 1 mil wire and d is the wire diameter in mils.
If a hot wire is placed in a stream of fluid which is moving with a constant velocity,
the relation between the rate of convective cooling and the electric power supplied to the wire
is given by King’s law.!5 When the wire has a film or coating King’s law may be written as
TABLE 1
Useful Constants of the Flow Medium
Fresh Water Sea Water Air
Units 20°C 20°C 0°c
Ref 10 Ref 10 Ref 11
5 fe (cm sec C)~! 1.43x 1073 | 1.341073 | 0.533 x 10-4
3 On
joule(cmsec C)* | 5.98 x1073| 5.60 x 1073 | 2.23 x 1074
Cp, cal (em ic lms 1.00 0.993
p, gmem~S 1.00 1.025 1.293 x 10-3
U, cm/sec 0.08962 0.0825 2 10.76 2
TABLE 2
Useful Constants of Wire Materials
tite Platinum Pt-Ir
Ref 12 Ref 13 Ref a Ref oe
o 1000 Ib in.~? BG
a (°C)7! 0.0035 ante
7, 107° ohm-cm 11.4 32.9 6.84
ee 20
K, cal(cmsec%)—? | 0.165 0.042 0.48 0.22
Room en? 205 t?
*
0.644 d2
0.00913 d*
0.759 d2
0.0108 d#} 0.0149 d*| 0.0173 d+
Kyl /e Ry (amp)?
m
(amp)2 sec *
*Numerical values given here for Kyl/aR y and m are based on a flow medium
of fresh water.
PR, = Kyl (T, - ro( oR 7 1) [2]
where
K
= cWewes | [3]
0
27a pc
P3 Ps
In these equations and in the derivations to follow
I is the heating current,
R is the average wire resistance,
l is the wire length,
T is the temperature at film surface,
T, is the temperature at wire surface,
is the ambient temperature of fluid,
» iS the average temperature of wire, and
U is the flow velocity.
The wire resistance is related to the average temperature of the wire T,, by the equation
i, = Bella Gl = Ho) [4]
It will be convenient to represent the temperature elevation of the wire by an overheating
ratio a, defined as
RR -K _ ak (7, =)
ts, R R
e e
[5]
where Ff, is the wire resistance at the temperature T,. Even though the temperature elevation
of the wire may be large, the temperature elevation at the surface of the film may be much
lower. Therefore it will be convenient to define an effective overheating ratio as
i ak (7, = i)
a, R
e
10
Then King’s equation may be written in terms of a, anda,
1l+a,, ak, og.
From Reference 9 it can be shown that the steady-state temperatures at the inner and outer
surfaces of the coating are related by the equation
K
oe era (VE + )ios-.|
2 fy
is very much larger than Ky the temperature is nearly
If the thermal conductivity of the wire x,
uniform within the wire. and 7, may be substituted for 7,. For this approximation
a
ms Ww
a=
a3 U a
1+ ‘Y +1) log —
27k, ( Uy b
It is clear that a film on a wire will impair its sensitivity, particularly at high veloci-
ties. If PaRy/Kgl is plotted against ~U/U, for the same value of a, but for different film
thicknesses, the family of curves shown in Figure 4 is obtained. Only the curve for no film
is linear. As the velocity becomes infinite the different curves approach the asymptotic
values
ak a 27 Ky
k,) 144, kz log a/b
The larger the coating ratio a/b and the lower its thermal conductivity, the more quickly the
curves flatten off and the less sensitive the wire becomes. All the curves would be linear if
it were possible to keep the ratio a@,/ (1 + a) constant instead of a,.
The sensitivity of the wire in responding to a change in velocity U or a change in am-
bient temperature 7, is obtained by differentiating King’s equation with respect to U and T,.
Then the response of a constant-current wire becomes
AR Ot ING oie
—— =.
ey, | EURO BO nari,
11
SSC
a
Sree
JENN
a
sone
ake
om
an
rel
oe
on
ee
oe
Ze
AAS
Figure 4 - Effect of a Surface Film on the Sensitivity of a Hot Wire
\\
:
The response of a constant-temperature wire becomes
Al 4 SS NG OAM
Da. A 7. U i+aAP,
If a, is small in these equations the wire may be just as sensitive to temperature fluctuations
as to velocity fluctuations. In the towing tanks at TMB there is sometimes a temperature dif-
ference of about 10 F over a 20-ft depth, and some thermal microstructure may be expected
when the water is disturbed. A hot wire must be used with caution in such facilities.
The response of a bare constant-current hot wire to a step-like change in convective
cooling is given to a very good approximation by a simple exponential function
es —t/M
Avie = AE) liye ]
12
where A 7* is the final temperature change produced by initiating disturbance. The time con-
stant has been derived by Dryden and Keuthe and may be written in the form!
2
a 70 Ura a
[2 ak, [2
Values of m which depend only on constants of the wire materials are listed in Table 2.
The response of a bare constant-current hot wire to a step-like change in current input
is also given by a simple exponential function. To the approximation used here, the time con-
stant for a change in current input is the same as the time constant for a change in convective
cooling.”
The frequency response of a system is defined as the frequency for which the response
is attenuated 70.7 per cent. Furthermore, if the response of a system to a step function is
given by a simple exponential function with time constant M, the frequency response is
1/27M. If a hot wire for use in water has a diameter less than one mil, it will have a frequency
response of several hundred cycles. If a higher frequency response is desired, a suitable com-
pensation circuit may be used. As the frequency response of a bare wire to a change in cur-
rent is the same as that for a change in convective cooling the elements of the compensation
circuit may be adjusted by applying a time-varying current input of the desired frequency to
the wire.
If the wire has a coating or acquires a film the response of a constant-current wire is
no longer a simple exponential function but is given by an infinite sum of exponential terms.?
If the coating is not too thick the sum converges rapidly and an equivalent time constant may
be found as the time in which the exponential portion decays to e ~! of its initial value. In
this case the time constant for a step-like change in convective cooling is greater than the
time constant for a change in current input. Therefore it would not be possible to fully cor-
rect for the time lag by adjusting the elements of the compensation circuit to obtain a good
frequency response to a time-varying current input.
Even a constant-temperature wire has a time lag in responding to a change in convec-
tive cooling if the wire is coated or acquires a film.? If the film thickness is less than half
the wire diameter the time constant under probable operating conditions is no greater than the
time constant of a bare constant-current wire of the same diameter. Therefore, a thinly-coated
constant-temperature hot. wire should have a reasonably good frequency response when it is
used in water. The simple method of setting the elements in a compensation circuit for a con-
stant-current hot wire can not be used here, as a constant-temperature wire responds with no
time lag to a change in current input.
13
SUMMARY AND CONCLUSIONS
As a result of research done at the Taylor Model Basin and the Iowa Institute of Hydrau-
lic Research over the years, a hot-wire instrument for making turbulence measurements in
water under controlled conditions has been developed. It is essential that the wire be heated
with an alternating current to prevent electrolytic action and that only the wire metal be ex-
posed to the water. Unless the wire supports and joints are of the same metal as the wire
these must be covered with a good waterproof insulation to prevent galvanic action. With these
precautions the wire is stable enough for quantitative turbulence measurements in well-filtered
dust-free water.
_ Although the wire is stable in clean water it acquires a surface film when it is used in
ordinary water such as that found in most test facilities. The rate at which the film forms de-
pends upon the degree of contamination of the water. The usefulness of the hot-wire element
for practical purposes appears to depend upon the development of a satisfactory method of
dynamic calibration. Although film formation will decrease the wire sensitivity and frequency
response, a coated wire may still be useful for turbulence measurements. If the wire is used
in a constant-temperature circuit the decrease in frequency response should not be serious
until the film thickness exceeds half the wire diameter.
REFERENCES
1. ‘‘Progress Report on Research in Frictional Resistance,’’ David Taylor Model Basin Re-
port 726 (Sep 1950).
2. Macovsky, M.S., ‘*The Measurement of Turbulence in Water,’’ David Taylor Model Basin
Report 670 (Oct 1948).
3. Schubauer, G.B. and Klebanoff, P.S., ‘‘Theory and Application of Hot-Wire Instruments
in the Investigation of Turbulent Boundary Layers,’’ ARC No. 5K27 (Mar 1946).
4. Dryden, H.L. et al, ‘‘Measurements of Intensity and Scale of Wind-Tunnel Turbulence
and Their Relation to the Critical Reynolds Number of Spheres,’’ National Advisory Commit-
tee for Aeronautics Report 581 (1937).
5. Townsend, A.A., ‘‘Measurements in the Turbulent Wake of a Cylinder,’’ Roy. Soc. Lon-
don, Proc. A., Vol. 190, (Sep 1947).
6. Breslin, J.P. and Macovsky, M.S., ‘‘Effects of Turbulence Stimulation on the Boundary
Layer and Resistance of a Ship Model as Detected by Hot Wires,’’ David Taylor Model Basin
Report 724 (Aug 1950).
7. Roshko, Anatol, ‘‘On the Development of Turbulent Wakes from Vortex Streets,’’ Na-
tional Advisory Committee for Aeronautics TN 2913 (Mar 1953).
14
8. Hubbard, P.G., ‘‘Constant Temperature Hot-Wire Anemometry with Application to Mea-
surements in Water,’’ PhD Thesis, University of Iowa, (Jun 1954).
9. Borden, A., ‘‘Time Coastants and Frequency Response of Coated Hot Wires Used as
Turbulence-Sensing Elements,’’ David Taylor Model Basin Report 952 (to be published).
10. ‘‘Handbook of Chemistry and Physics,’’ 26th Edition, Chemical Rubber Publishing Co.,
Cleveland, Ohio (1942).
11. ‘International Critical Tables of Numerical Data, Physics, Chemistry and Technology,”’
McGraw-Hill Book Company, Inc. New York (1926).
12. ‘‘Metals Handbook’’ 1948 Edition, The American Society for Metals, Cleveland, Ohio.
13. Lowell, Herman H., ‘‘Design and Applications of Hot-Wire Anemometers for Steady-
State Measurements at Transonic and Supersonic Airspeeds,’’ Nationa! Advisory Committee
for Aeronautics TN 2117 (Jul 1950).
14. King, L.B., ‘‘On the Convection of Heat from Small Cylinders in a Stream of Fluid,’’
Phil. Trans. Roy. Soc., Vol. 214 A (1914).
15. Dryden, H.L. and Keuthe, A.M., ‘‘The Measurement of Air Speed by the Hot-Wire Ane-
mometer,’’ National Advisory Committee for Aeronautics Report 320 (1929).
15
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Chief, BuShips, Library (Code 312)
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Mr. M.A. Hall, Univ of Minnesota, Minneapolis, Minn.
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Dr. A. Kantrowitz, Cornell Univ, ithaca, N.Y.
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Dr. C.C. Lin, Dept of Math, MIT, Cambridge, Mass.
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Dr. C.R. Soderberg, Dept of Mech Engin,
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Hopkins Univ, Baltimore, Md.
Or. C.A. Truesdell, Dept of Math, Univ of
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Mr. G.R. Hamilton, Navy Sofar Station,
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Dr. E.G. Richardson, King's College
Newcastle Upon Tyne, England,
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Dr. H.W. Lerbs, Dir, Hamburg Model Basin,
Hamburg 33, Germany
Dr. A. Anderoni, Head of Naval Station, Instituto
de Pesquisas Tecnologicus, Sao Pulo, Brasil
Dr. J.F. Allan, Supt, Ship Div, Natl Phys Lab,
Teddington, Middlesex, England
Dr. J. Ackeret, Inst fur Aerodynamik der
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de Experienceas Hidrodinamicas, El
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Inst of Science, Bangalore 3, India
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Construction Navale, 1 Blvd Haussmann,
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des Sci, Dir de |’Ecole Natl Superieure,
D’Electrotechnique et d’Hydraulique, 4 Blvd
Requit, Toulouse, France
Prof. K. Howarth, Dept of Math, Univ of Bristol,
Bristol, England
Mr. W.P. Jones, Natl Phys Lab, Aero Div,
London, England
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Universite de Lille, Lille (Nord), France
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Trondheim, Norway
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Recherches Aeronautiqu, 25 Ave de la
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18
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Toronto, Toronto 5, Canada
Gen. Ing. U Pugliese, Pres, Inst Nazionale per
Studi ed Esperienze di Architettura Navale,
via della Vasca Navale 89, Rome, Italy
Prof. L. Rosenhead, Univ of Liverpool, Liverpool,
England
Dr. J.H. Preston, Univ Engin Lab, Cambridge
Univ, Cambridge, England
Prof. J.L. Synge, Sch of Theo Physics, Natl
Univ of Ireland, Dublin, Ireland
Prof. Dr. H. Schlichting, Inst fur Stromungs,
Technische Hochschule, Braunschweig,
Germany
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suotsseidxe [eojeioeyy, “enbruyse} uoryeaqijeo orweuAp e jo yuauidozeAop ey) ul sel] welqoid suotsseidxe [eojoiooy], “anbiuyoo, uorjvaqiyeo o1weudp v jo queudojoaep oy ul sat] we,qoad
SIqj 07 uoTyNTOs AlojoBJsyes ATUO oy} yey} Sivedde yy “Sutuveyo 10; ATquenbesy e1tm ay} FutAouwol SITY} 07 UOTNTOS AsojORJSIVeS ATUO eYY yey Savedde yy “Sutuveyzo 310j ATyUonbed o11M Oy} FuTAOWI
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suotsseidxe [worjo100y], “onbruyoe, uo1yeaqrvo o1meuAp & jo yueuidojeaop oy} ut ser] weyqosd suotsseidxe [eoeiooyy, ‘anbiuyoe; uorviqiyeo o1weudp & Jo yueudoyeAep ey) ut sat] we,qoid
STy} 07 UOTyNTOS AlojOVJsyyes ATUO oY} yeyy Suvedde yy “Furuveyo 10} ATUONboey oI oy) FutAowes SITY} 07 UOTyNTOS AsoyOeJStVeS A[UO ey} yey} Savedde y “Sutuveyzo 10j ATyUenbey o11M ayy FutAouiol
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