Question

A normal shock wave propagates through stagnant air at 300K and 100kPa with a Mach number of 1.2. What is the post shock flow velocity in the lab frame of reference and the post shock pressure, and temperature? If a shock wave propagated through helium with the same pressure ratio as the air shock wave, what would its Mach number be?

Answer 1

The expression for the pressure ratio,

------------------------------------------------Eq1

whehe P₁ is post shock pressure, k is specific heat ratio which is 1.4 for air and M_a is Mach number.

Given Data;

P₀ = 100 kPa, T₀ = 300 K, M_a = 1.2

now putting all the values in equation 1

P₁ = 454 kPa

The Expression for temperature ratio for shock wave;

because shock wave duration is very small hence it is isothermal process.

T₁ = 100 K ( Post shock temperature)

The expression of Velocity Ratio:

-----------------------------------Eq2

V₀ = 1.2*432 = 518.4 m/s (432m/s the velocity of sound in air)

Putting all the values is equation2

V₁ = 322 m/s

Now if the shock wave propagates through Helium and Pressure ratio is constant:

-----------------------eq3

where KH and M_aH are the specific heat ratio and Mach no. for Helium.

Specific heat ratio for helium is 1.66

Now putting all the values in equation3

M_aH = 1.223