• # question_answer In a two-dimensional fluid flow,$u=6x+xy.$ which one of the following gives the component of the velocity to satisfy the continuity equation? A) $6x+xy$                     B) $6+xy$C) $-\,\left( 6x+xy \right)$              D) $-\,\left( 6y+\frac{1}{2}\,{{y}^{2}} \right)$

$u=6x+xy$ Continuity equation in two-dimension is: $\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0$ $u=\frac{\partial \phi }{\partial x},$ $v=\frac{\partial \phi }{\partial y}$ $\frac{\partial v}{\partial y}=6+y$ A. $\frac{\partial v}{\partial y}=x\frac{\partial }{+\,1}$ $6+y+x\ne 0$ B. $\frac{\partial v}{\partial y}=x,$ $6+y+x\ne 0$ C. $\frac{\partial v}{\partial y}=-\,\,(6+x)=-\,\,(6+x)$ $6+y-6-6x\ne 0$ $(6+y)-(6+y)=0)$