GATE 2025 ME – Question 50
Consider a velocity field $\vec{V} = 3z\,\hat{i} + 0\,\hat{j} + Cx\,\hat{k}$, where $C$ is a constant. If the flow is irrotational, the value of $C$ is ________ (rounded off to 1 decimal place).
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Correct answer: 2.98 to 3.02
Explanation
For irrotational flow the curl of the velocity must be zero. The $y$-component of the curl is $\frac{\partial V_x}{\partial z} - \frac{\partial V_z}{\partial x} = 3 - C$. Setting this to zero gives $C = 3.0$.