GATE ME 2024 Set 1 — Question 16
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Fluid Mechanics → Fluid Kinematics & Dynamics → Continuity & Momentum Equations
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Question
The velocity field of a two-dimensional, incompressible flow is given bywhere and denote the unit vectors in and directions, respectively. If , then is
Correct answer
(C) 3
Solution
For a two-dimensional incompressible flow, the continuity equation is given by:Given the velocity field , we have:
Calculating the partial derivative of with respect to :Substituting this into the continuity equation:Integrating with respect to :Using the boundary condition :Thus, the expression for is:Now, find :Therefore, the correct option is (C).
Calculating the partial derivative of with respect to :Substituting this into the continuity equation:Integrating with respect to :Using the boundary condition :Thus, the expression for is:Now, find :Therefore, the correct option is (C).
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