Question 12.9: 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. 12–32 from the figure alone. Compare with the known value of Mach number provided in the figure caption.
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: 𝜇 ≅ 19°. The Mach number is obtained from Eq. 12–47,
\mu=\sin ^{-1}\left(1 / Ma _1\right) (12.47)
\mu=\sin ^{-1}\left(\frac{1}{ Ma _1}\right) \rightarrow Ma _1=\frac{1}{\sin 19^{\circ}} \rightarrow Ma _1= 3 . 0 7
Our estimated Mach number agrees with the experimental value of 3.0 ± 0.1.
Discussion The result is independent of the fluid properties.