Air is isentropically expanded from a large chamber in which

Air is isentropically expanded from a large chamber in which the pressure is 10000 kPa and the temperature is 50 C until the mach number reaches a value of 2. A normal shock wave then occurs in the flow. Following the shock wave, the air is isentropically decelerated until the velocity is again essentially zero. Find the pressure and temperature that then exists.

Solution

Given :

Air undergoes Isentrophic Expansion

P₀₁ = 10000 kPa = 10000* 10³ N/m²

T01 = 50 C = 50 + 273 = 323 K

Mach no before Shock = 2

To Find :

Stagnation pressure and temperatures after Shock.

The condition before and after a normal shock is shown in the folloowing figure.

Now at M= 2 , from the isentrophic flow tables we get

T₁/T_{o1 = 0.555}

_{we get T1 = 0.555 * 323 = 179.26 K}

P₁/P_{01 = 0.128}

_{we get P1 = 0.128 * 10,000 = 1280 kPa}

_{From Normal Shock table at Mx = 2,}

_{we get}

_{Py/Px = 4.5}

_{Py = 4.5 * 1280 = 5760 kPa}

_{Ty/Tx = 1.687}

_{Ty = 1.687 * 179.26 = 302.41 K}

_{Poy/ Px = 5.641}

_{P oy = 5.641 * 5760 = 32,492.16 k Pa}

_{To2 =To1}

_{so To2 = 323 K}

_Answers:

_{stagnation Pressure = 32,492.16 kPa}

_{Stagnation temperature = 50 C}