GATE Mechanical Engineering (ME) 2018 Shift 1 Solved Paper

This has to be solved through options
Continuity equation for $2\mathit{D}$ incompressible flow
$\frac{\partial \mathit{U}}{\partial \mathit{x}}+\frac{\partial \mathit{v}}{\partial \mathit{y}}=0$
$\frac{\partial \left(\mathit{A}\mathit{x}\right)}{\partial \mathit{x}}+\frac{\partial \left(-\mathit{A}\mathit{y}\right)}{\partial \mathit{y}}=0$
$\mathit{A}-\mathit{A}=0$
It satisfies continuity equation.
⇒ As $\overline{\mathit{V}}=\mathit{A}\mathit{x}\stackrel{\wedge }{\mathit{i}}-\mathit{A}\mathit{y}\stackrel{\wedge }{\mathit{j}}$
As $\mathit{y}\to \mathit{\infty }$ velocity vector field will not be defined along y axis.
So flow will be along $\mathit{x}$-axis i.e. 1-D flow.
$\Rightarrow$ Stream line equation for $2\mathit{D}$
$\frac{\mathit{d}\mathit{x}}{\mathit{u}}=\frac{\mathit{d}\mathit{y}}{\mathit{v}}$
$\frac{\mathit{d}\mathit{x}}{\mathit{A}\mathit{x}}=\frac{\mathit{d}\mathit{y}}{-\mathit{A}\mathit{y}}$
In x = -In y + In c
In xy = In c
$\mathit{x}\mathit{y}=\mathit{c}\to$ streamline equation