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Problem on Mach angle and Mach number

An Aero-plane travels in air of pressure of 1 bar at 10 degree celsuis at a speed of 1800 km/hr. Find the Mach number and Mach angle. Take k=1.4 and R=287 J/Kg K.

(8 Marks)

Subject Fluid Mechanics 2

Topic Compressible Flow

Difficulty Medium

0

Given :

Pressure = 1 bar

Temperature t = 10˚ C

T = 10 + 273 = 283 k

Speed V = 1800 km/hr

= $\frac{1800 \times 1000}{60 \times 60} = 500m/s$

K = 1.4

R = 287 J/kg K.

Now, For adiabatic process, the velocity of sound is,

$C = \sqrt{KRT} = \sqrt{1.4 \times 287 \times 283}$

C = 337.20 m/s.

$\therefore$ Mach Number = $\frac{v}{c} = \frac{500}{337.20} = 1.48$

and, Mach angle is, Sin $\alpha$ $\frac{c}{v} = \frac{1}{m}$

$\therefore \alpha = sin^{-1} (\frac{1}{1.48})$

Mach angle is $\alpha = 42.40˚$