Question
Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m3 and 100 m/s, respectively. At a downstream location in the pipe, the velocity is 170 m/s. If the pressure drop between these two locations is 10 kPa, the force exerted by the gas on the pipe between these two locations is ____________ N.
Options :
350π2
750π
1000π
3000π
Answer :
750π
Solution :
diameter, d = 1m, r = 0.5 m, density Ο1 = 1 kg/m3, V1 = 100 m/s
Ξ P = 10 kPa, V2 = 170 m/s
A = Ο r2 = 0.25Ο m2
mass flow rate = Ο1A1V1 = 1Γ 0.25Ο Γ 100 = 25Ο
F = force exerted by gas, it is a body force.
Fp = (P1 - P2)A it is a pressure force
Using momentum equation
(P1 - P2) A - F = (V2 - V1)
10 Γ 103 Γ 0.25Ο - F = 25Ο (70)
F = 750Ο N
Copyright Β© 2026 Crey All Rights Reserved