An aircraft flies at true airspeed through air at

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

Fluid Dynamics, Ch Euler's equation in Lamb's form and the four Bernoulli theorems

Problem

An aircraft flies at true airspeed U=200 m s−1U = 200\,\mathrm{m\,s^{-1}} through air at 20∘C20^\circ\mathrm{C}, treated as an ideal gas with γ=1.4\gamma = 1.4, R=287 J kg−1 K−1R = 287\,\mathrm{J\,kg^{-1}\,K^{-1}} and ρ=1.20 kg m−3\rho = 1.20\,\mathrm{kg\,m^{-3}}. A Pitot tube measures the stagnation pressure excess p0−pp_0 - p, and its indicator converts this to a speed using the incompressible formula Uind=2(p0−p)/ρU_{\rm ind} = \sqrt{2(p_0-p)/\rho}. ((a)) Find the Mach number of the flight. ((b)) Using the compressible Bernoulli result p0−p=12ρU2(1+14Ma2)p_0 - p = \tfrac12\rho U^2\left(1 + \tfrac14 Ma^2\right), find the percentage by which UindU_{\rm ind} overestimates the true airspeed UU.

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