GATE ME 2026 Set 1 — Question 25
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Fluid Mechanics → Compressible Flow → Continuity & Momentum Equations
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Question
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
Correct answer
(A) increases along the flow
Solution
For isothermal flow of an ideal gas in a constant area pipe (), the continuity equation is . From the ideal gas law, . Since the process is isothermal (), . As the gas flows through the pipe, friction causes the pressure to decrease along the flow direction. Consequently, the density also decreases. To satisfy the continuity equation , the average flow velocity must increase along the flow.
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