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The pressure , velocity and temperature just upstream of normal shock wave in air are 100 kPa(abs), 660 m/s and 20 respectively.

Calculate pressure, velocity and temperature just downstream of the shock wave. [Take ratio of specific heat k=1.4 and gas constant R=287 J/(kg.k)].

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Data:-

Upstream conditions:

v1=660m/s,P1=110kPa=100×103N/m2

k=1.4,T1=20C=20+273=253K,R=287J/kgK

To find:-

P2=?,V2=?,T2=?

Solution:-

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Sonic speed at upstream

c1=K.R.T1=1.9×287×253=318.83m/s

Upstream mach number

M1=v1c1=660318.83=2.07

Velocity at downstream, v2

v2v1=(K1)M21+2(K+1)M21

v2660=(1.41)2.072+2(1.4+1)2.072

v2=238.4m/s

Pressure at downstream, P2

P2P1=2KM21(K1)K+1

P2100×103=2×1.4×2.072(1.41)1.4+1

P2=483.238×103N/m2

Temperature at downstream, T2

T2T1=[(K1)M21+2][2KM21(K1)](K+1)2M21

T2253=[(1.41)2.072+2][2×1.4×2.072(1.41)](1.4+1)2×2.072

T2=441.53K

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