Averaging of Periodic Pressure Pulsations by a Total-Pressure Probe Page: 3 of 31
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NACA TN 3568
For a total-pressure probe whose entrance tube is so short that it
can be considered an orifice, the mass-flow rate of incompressible flow
through the orifice is proportional to the square root of the pressure
drop across the orifice. Since this is a nonlinear function of the
applied pressure, this probe will not give the time-weighted average of
the applied pressure. If the flow is compressible, additional nonlinear
effects will result.
A third possible nonlinearity results from a difference between the
flow coefficients for the flow in and out of the probe. Because the
restricted part of the probe is essentially similar with respect to the
flow processes both in and out of the probe, this particular nonlinear-
ity is not believed to be significant for the probe geometries con-
sidered in this report.
In general, the entrance tube of the total-pressure probe will be
such that both principal nonlinear effects will be present. These ef-
fects are interdependent, and they must be considered simultaneously.
In reference 1 the averaging of some symmetrical wave shapes is
analytically treated. This report will treat the averaging of pressure
fluctuations of rectangular wave shapes (fig. 1). The averaging errors
are first estimated analytically. Then the results of experiments on
some typical probes are used to establish the probe design limits with-
in which the theory may provide an adequate estimate of these errors.
ANALYSIS
The probe shown in figure 2(a) is a tube of length L and inside
diameter D that opens into another tube of much larger diameter. The
latter tube connects the probe to a manometer, so that the pressure at
the exit of the probe is the same as the pressure at the manometer.
The pressure P at the probe entrance is a stagnation pressure that
follows the periodic pattern shown in figure 1.
The time-weighted average of the applied pressure P isP = Pmin + (P - )
a min+ max mini(1)
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Johnson, R. C. Averaging of Periodic Pressure Pulsations by a Total-Pressure Probe, report, October 1955; (https://digital.library.unt.edu/ark:/67531/metadc57829/m1/3/: accessed April 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.