Question

A plane flow has velocity components $u=\frac{x}{T_1},v=\frac{-y}{T_2}andw=0$ along x, y and z directions respectively, where $T_1(\ne 0)and{T}_2(\ne 0)$ are constants having the dimension of time. The given flow is incompressible if

• A. $T_1=-T_2$
• B. $T_1=-\frac{T_2}{2}$
• C. $T_1=\frac{T_2}{2}$
• D. $T_1=T_2$

Answer 1

The correct option is D $T_1=T_2$

For a flow to exist
$\Rightarrow \frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0$
$\Rightarrow \frac{1}{T_1}-\frac{1}{T_2}=0$
$\Rightarrow T_1=T_2$