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. 350πœ‹2

  2. 750πœ‹

  3. 1000πœ‹

  4. 3000πœ‹

Show Answer

Answer :

750πœ‹

Solution :

diameter, d = 1m, r = 0.5 m, density ρ1 = 1 kg/m3, V1 = 100 m/s

Ξ” P = 10 kPa, V2 = 170 m/s

A = Ο€ r2 = 0.25Ο€ m2

mass flow rate  m Λ™ = ρ1A1V1 = 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 = m Λ™ (V2 - V1)

10 Γ— 103 Γ— 0.25Ο€ - F = 25Ο€ (70)

F = 750Ο€ N

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