The effect of compressibility on the pressure reading of a Prandtl pitot tube at subsonic flow velocity Page: 3 of 14
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N.A.C.A. Technical Memorandum No. 917
Every stationary compressible or incompressible par-
allel flow may be visualized as being the creation of loss-
free discharge from a tank in which the medium is at rest
under a higher pressure, The speed can be predicted ac-
cording to Bernoulli if the static pressure of the flow
and the tank pressure are known.
The introduction of a body in such a flow produces
in the stagnation point the same state as in the tank so
long as there is no energy loss on the streatlines toward
the stagnation point. In incompressible fluid, the flow
toward the stagnation point is free from loss, and like-
wise in compressible flow so long as the speed remains be-
low the velocity of sound. But in supersonic flow a com-
pression shock forms before the obstacle w kh divides the
zones with supersonic speed upstream from the subsonic
speed downstream toward the stagnation point. Energy is
lost in this compression shock, hence the pressure in the
stagnation point becomes lower than the tank pressure.
Thus a Prandtl pitot tube with its forward orifice in
the stagnation point indicates the tank pressure of the
flow if the medium is incompressible, or, when in compres-
sible fluid the speed remains subsonic.
The field of disturbance which is impressed upon the
undisturbed flow in the circulation about the Prandtl
pitot head disappears again downstream. Now, the normal
Prandtl pitot is so designed that the static orifice is at
the place where in inconpressible fluid the undisturbed
state is re-established. Then the speed can be predicted
on the basis of the pressure readings of the Prandtl tube.
In compressible fluid the curvature of the stream-
lines around the head of the tube is amplified because of
the change of density with the pressure. So long as the
local velocity of sound is not exceeded at any point (the
velocity of sound changes with the temperature along a
stream filament) the field of disturbance is merely dis-
torted while qualitatively remaining similar to that in
incompressible flow. But its character changes as soon
as the flow velocity becomes high enough to create a zone
with supersonic speed during the circulation about the
Prandtl tube, which downstream must again change to sub-
sonic flow with a compression shock. This causes a nore
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Walchner, O. The effect of compressibility on the pressure reading of a Prandtl pitot tube at subsonic flow velocity, report, November 1939; (digital.library.unt.edu/ark:/67531/metadc63232/m1/3/: accessed July 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.