GATE ME 2022 Set 2 — Question 43
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Fluid Mechanics → Fluid Kinematics & Dynamics → Applications of Bernoulli
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Question
A tube of uniform diameter is immersed in a steady flowing inviscid liquid stream of velocity , as shown in the figure. Gravitational acceleration is represented by . The volume flow rate through the tube is ______.
Correct answer
(D) (π)/(4) D² √(V² - 2gh₂)
Solution
Applying Bernoulli's equation between a point in the free stream (1) and the exit of the tube (2). Point 1 is at depth where pressure is and velocity is . Point 2 is at the exit of the tube at height above the free surface, where pressure is and velocity is . Taking the inlet level as datum: Simplifying gives:The volume flow rate is .
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