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The velocity field in an incompressible flow is \( \mathbf{v} = axy\hat{i} + v_y\hat{j} + \beta\hat{k} \), where \( \hat{i} \), \( \hat{j} \), and \( \hat{k} \) are unit vectors in the \( (x, y, z) \) Cartesian coordinate system. Given that \( a \) and \( \beta \) are constants, and \( v_y = 0 \) at \( y = 0 \), the correct expression for \( v_y \) is:
The velocity field in an incompressible flow is \( \mathbf{v} = axy\hat{i} + v_y\hat{j} + \beta\hat{k} \), where \( \hat{i} \), \( \hat{j} \), and \( \hat{k} \) are unit vectors in the \( (x, y, z) \) Cartesian coordinate system. Given that \( a \) and \( \beta \) are constants, and \( v_y = 0 \) at \( y = 0 \), the correct expression for \( v_y \) is:
Updated On: Jul 17, 2024
- \(-\frac{axy}{2}\)
- \(-\frac{ay^2}{2}\)
- \(\frac{ay^2}{2}\)
- \(\frac{axy}{2}\)
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The Correct Option is B
Solution and Explanation
The correct option is (B) :\(-\frac{ay^2}{2}\)
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