GATE XE 2023 | Question: 25

Question

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Q. 35 & In a steady two-dimensional compressible flow, $u$ and $v$ are the $x$ - and $y$ - \\
components of flow velocity, respectively and $\rho$ is the fluid density. Among the \\
following pairs of relations, which one(s) perfectly satisfies/satisfy the definition \\
of stream function, $\psi$, for this flow? \\

• A. & $u=\frac{\partial \psi}{\partial y}$ and $v=-\frac{\partial \psi}{\partial x}$ \\
  
• B. & $u=-\frac{\partial \psi}{\partial x}$ and $v=-\frac{\partial \psi}{\partial y}$ \\
  
• C. & $\rho u=\frac{\partial \psi}{\partial y}$ and $\rho v=-\frac{\partial \psi}{\partial x}$ \\
  
• D. & $\rho u=-\frac{\partial \psi}{\partial y}$ and $\rho v=\frac{\partial \psi}{\partial x}$
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