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Chapter 3: Some Fundamental Aspects of Compressible Flow


Problem 3.6:

An airplane is flying at km/h at an altitude where the temperature is oC. Find the Mach number at which the airplane is flying.

Solution:

Given:
\( V = \) 2000 km/h = 2000/3.6 m/s,
\( T = \)-50oC = 223 K.

To calculate: \( M=? \)

The problem description is schematically shown in Fig. 1.
Fig. 1: Schematic of the problem description

The Mach number can be calculated using the equation,

\[ M=\frac{V}{a}=\frac{V}{\sqrt{\gamma\,R\,T}}=\frac{2000/3.6}{\sqrt{1.4\times287\times223}} \]
\[ \boxed{M=1.86}\ . \]


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