Question

The velocity of a gas flowing through a duct is 300 m/s; its temperature is 127°C: Gas constant R = 0.25 kJ/kg K, the ratio of specific heat is C_p /C_y = γ is 1.6. What is the value of Mach number?
1. 0.70
2. 0.72
3. 0.75
4. 0.77

Answer 1

Correct Answer - Option 3 : 0.75

Concept:

Mach number: It is defined as the ratio of the velocity of flow to the velocity of sound in that medium.

\(M = \frac{V}{C}\)

Speed of sound is given as \(C = \sqrt {\gamma RT} \)

Calculation:

Given, V = 300 m/s, γ = 1.6, R = 0.25 kJ/kg K, T = 127°C = 400 K

\(C = \sqrt {\gamma RT} = \sqrt {1.6 \times 250 \times 400} = \;400\;m/s\)

\(M = \frac{V}{C} = \frac{{300}}{{400}} = 0.75\)