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 :

  1. 350𝜋2

  2. 750𝜋

  3. 1000𝜋

  4. 3000𝜋

Show Answer

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  m ˙ = 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 = m ˙ (V2 - V1)

10 × 103 × 0.25π - F = 25π (70)

F = 750π N

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