Question 2.4: Mach Number of Air Entering a Diffuser Air enters a diffuser...

Air enters a diffuser at high speed. The speed of sound and the Mach number are to be determined at the diffuser inlet.
Assumption   Air at the specified conditions behaves as an ideal gas.
Properties   The gas constant of air is R = 0.287 kJ/kg·K, and its specific heat ratio at 30°C is 1.4.
Analysis   We note that the speed of sound in a gas varies with temperature, which is given to be 30°C.

(a) The speed of sound in air at 30°C is determined from Eq. 2–26 to be

c = \sqrt{kRT} = \sqrt{(1.4)(0.287  kJ/kg.K)(303  K)\left(\frac{1000  m^2/s^2}{1  kJ/kg} \right) } = 349  m/s

(b) Then the Mach number becomes

Ma = \frac{V}{c} = \frac{200  m/s}{349  m/s} = 0.573

Discussion   The flow at the diffuser inlet is subsonic since Ma < 1.