The relationship \(\frac{\mathrm{d} v}{\mathrm{~d} x}=\frac{\mathrm{du}}{\mathrm{dy}}\) is valid for_____.

Concept:

Angular velocity for two-dimensional flow:

\(ω=\begin {vmatrix} i & j \\ {\partial \over \partial x} & {\partial \over \partial y} \\ u & v \end {vmatrix}\)

ω = \({\partial v\over \partial x}-{\partial u\over \partial y}\)

If the angular velocity is zero (ω = 0) then the flow will be irrotational.

0 = \({\partial v\over \partial x}-{\partial u\over \partial y}\)

\({\partial v\over \partial x}-{\partial u\over \partial y}\)

The relationship \(\frac{\mathrm{d} v}{\mathrm{~d} x}=\frac{\mathrm{du}}{\mathrm{dy}}\) is valid for irrotational flow. Hence option (1) is the correct answer.