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GATE 2016 ME (ME2) – Question 23

Fluid Mechanics · Differential equations of continuity and momentum, velocity potential · 1 mark · Multiple choice

The volumetric flow rate per unit depth between streamlines of stream functions $\psi_1,\psi_2$ is ______.

  1. $|\psi_1+\psi_2|$
  2. $\psi_1\psi_2$
  3. $\psi_1/\psi_2$
  4. $|\psi_1-\psi_2|$

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Correct answer: (D) $|\psi_1-\psi_2|$

Explanation

For a two-dimensional incompressible flow, streamfunction differences measure signed volume flow per unit depth. Integrating normal velocity across a connecting line gives ψ2−ψ1. The requested magnitude is therefore **|ψ1−ψ2|, D**. Adding streamfunction values depends on the arbitrary reference and cannot represent the flow.