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Question 17.10: Estimation of the Mach Number from Mach Lines Estimate the M...

Estimation of the Mach Number from Mach Lines Estimate the Mach number of the free-stream flow upstream of the space shuttle in Fig. 17–36 from the figure alone. Compare with the known value of Mach number provided in the figure caption.

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We are to estimate the Mach number from a figure and compare it to the known value.
Analysis Using a protractor, we measure the angle of the Mach lines in the free-stream flow: \mu \cong 19^{\circ} . The Mach number is obtained from Eq. 17–47,

Mach angle:      \mu=\sin ^{-1}\left(1 / Ma _{1}\right)

 

\mu=\sin ^{-1}\left(\frac{1}{ Ma _{1}}\right) \quad \rightarrow \quad Ma _{1}=\frac{1}{\sin 19^{\circ}} \quad \rightarrow \quad Ma _{1}=3.07

Our estimated Mach number agrees with the experimental value of 3.0 ± 0.1. Discussion The result is independent of the fluid properties.

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