GATE ME 2022 Set 1 — Question 44
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Fluid Mechanics → Fluid Kinematics & Dynamics → Continuity & Momentum Equations
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Question
Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter . At one location in the pipe, the density and velocity are and , respectively. At a downstream location in the pipe, the velocity is . If the pressure drop between these two locations is , the force exerted by the gas on the pipe between these two locations is ____________ N.
Correct answer
(B) 750π
Solution
Using the momentum equation for the control volume of the pipe:
Since diameter is constant, .
Mass flow rate .
Pressure drop .
.
The force exerted by the gas on the pipe is equal and opposite, so .
Since diameter is constant, .
Mass flow rate .
Pressure drop .
.
The force exerted by the gas on the pipe is equal and opposite, so .
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