A car model is tested in a wind tunnel whose working section runs at m s

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Fluids & Continuum Physics · Waves, acoustics and compressible flow

Fluids and Continuum Physics, Ch Acoustics: sound propagation, radiation and attenuation

Problem

A car model is tested in a wind tunnel whose working section runs at

U = 95

m s

^{-1}

. The air in the tunnel is at

15

°C and an absolute pressure of

1.013\times10^{5}

Pa, and is treated as an ideal gas with ratio of specific heats

\kappa = 1.40

, molar mass

M = 0.0289

kg mol

^{-1}

and

R = 8.314

J K

^{-1}

mol

^{-1}

. On the nose of the model there is a stagnation point; for the streamline that reaches it take the flow to be steady, inviscid, incompressible and evaluate Bernoulli's theorem along that streamline, with the streamline horizontal so gravity drops out, and convert the pressure rise to a density change with

p' = c^{2}\rho'

. ((a)) Find the speed of sound in the tunnel air. ((b)) Find the Mach number of the working section. ((c)) Estimate the percentage rise in density at the stagnation point. ((d)) The laboratory's rule is that a test may be analysed as constant-density flow only if the density changes by no more than

2.0

per cent anywhere. What is the highest working-section speed that satisfies that rule, and does the

95

m s

^{-1}

test satisfy it?

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