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Q#1 Fluid Kinematics GATE CH 2024 MCQ +1 mark -0.33 marks

The velocity field in an incompressible flow is \(\vec{v} = \alpha xy \hat{i} + v_y \hat{j} + \beta \hat{k},\){ and } \hat{k}\)  where \(\hat{i}, \hat{j} \text{ and } \hat{k}\)  are unit-vectors in the (𝑥, 𝑦, 𝑧) cartesian coordinate system. Given that 𝛼 and 𝛽 are constants and \(v_y\) = 0  at 𝑦 = 0, the correct expression for \(v_y\) is

\(\frac{-\alpha xy}{2}\)

\(\frac{-\alpha y^2}{2}\)

\(\frac{\alpha y^2}{2}\)

\(\frac{\alpha xy}{2}\)

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