written 6.0 years ago by | • modified 4.9 years ago |
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)].
written 6.0 years ago by | • modified 4.9 years ago |
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)].
written 6.0 years ago by |
Data:-
Upstream conditions:
v1=660m/s,P1=110kPa=100×103N/m2
k=1.4,T1=−20∘C=−20+273=253K,R=287J/kgK
To find:-
P2=?,V2=?,T2=?
Solution:-
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=(K−1)M21+2(K+1)M21
v2660=(1.4−1)2.072+2(1.4+1)2.072
∴v2=238.4m/s
Pressure at downstream, P2
P2P1=2KM21−(K−1)K+1
P2100×103=2×1.4×2.072−(1.4−1)1.4+1
P2=483.238×103N/m2
Temperature at downstream, T2
T2T1=[(K−1)M21+2][2KM21−(K−1)](K+1)2M21
T2253=[(1.4−1)2.072+2][2×1.4×2.072−(1.4−1)](1.4+1)2×2.072
T2=441.53K