Discussion
An ideal gas passes isothermally through a long horizontal uniform cross-section pipe under steady flow. Consider that the pressure gradient in the pipe is sufficient for a finite change in the density of the gas. If the flow of the gas is purely pressure driven and subsonic throughout, then the average flow velocity
Answer: A
The average velocity increases along the flow.
In steady flow through a uniform pipe the mass flow rate \(\rho VA\) is constant, so \(\rho V\) is constant. The flow is pressure driven, so pressure falls along the pipe, and at constant temperature an ideal gas's density \(\rho = p/RT\) falls with it. Hence \(V\) must rise.
Velocity would stay constant only for an incompressible fluid, which the question rules out by saying density changes. A decrease would need density to rise downstream. The entrance-region option describes the shape of the velocity profile, not the average velocity.
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