GATE ME 2021 Set 2 — Question 21
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Fluid Mechanics → Fluid Kinematics & Dynamics → Continuity & Momentum Equations
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Question
For a two-dimensional, incompressible flow having velocity components and in the and directions, respectively, the expressioncan be simplified to
Correct answer
(D) u (∂ u)/(∂ x) + v (∂ u)/(∂ y)
Solution
Given the expression: Using the product rule for differentiation:Adding them together:For a two-dimensional, incompressible flow, the continuity equation is:Substituting this into the simplified expression:Therefore, option (D) is correct.
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