A Pitot-static probe on an airliner in cruise reads a static pressure and a Pitot excess

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow · Waves, acoustics and compressible flow

Signal Speeds in Fluids, Ch Steady compressible flow: energy, stagnation and the Mach number

Problem

A Pitot-static probe on an airliner in cruise reads a static pressure

p=50.0\,\mathrm{kPa}

and a Pitot excess

p_0-p=20.0\,\mathrm{kPa}

. The static air temperature is

T=250\,\mathrm K

. Take air as an ideal gas with

\gamma=1.4

and

R=287.05\,\mathrm{J\,kg^{-1}\,K^{-1}}

, and the deceleration to rest in the probe as isentropic. ((a)) Find the flight Mach number from the stagnation-pressure ratio, and hence the true airspeed. ((b)) Find the airspeed the incompressible formula

p_0-p=\tfrac12\rho u^2

would report from the same two readings, with

\rho

from the static state, and by how many per cent it overestimates. ((c)) Compare the exact ratio

(p_0-p)/(\tfrac12\rho u^2)

at this Mach number with

1+\tfrac14M^2

, the first correction of the series, and say what the difference shows.

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