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 ρ1 = 1 kg/m3, V1 = 100 m/s
Δ P = 10 kPa, V2 = 170 m/s
A = π r2 = 0.25π m2
mass flow rate = ρ1A1V1 = 1× 0.25π × 100 = 25π
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 × 103 × 0.25π - F = 25π (70)
F = 750π N
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