GATE CE 2015 Set 1 — Question 26
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Water Resources Engineering → Fluid Kinematics & Dynamics → Continuity Equation
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Question
In a two-dimensional steady flow field, in a certain region of the - plane, the velocity component in the -direction is given by and the density varies as . Which of the following is a valid expression for the velocity component in the -direction, ?
Correct answer
(C) v_y = -xy
Solution
For a steady two-dimensional flow, the continuity equation is given by:Given and , we have:Substituting this into the continuity equation:Integrating with respect to :For , a valid expression is . Thus, option (C) is correct.
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