• # question_answer If $u=ax$ and $v=-\,ay$ give the velocity distribution for a two-dimensional flow, what is the equation of a stream line passing through the point (3, 1)? A) $xy=3$                       B) $x+y=4$C) $x+3y=6$                   D) ${{x}^{2}}y=9$

The equation of stream line is: $\frac{dx}{u}=\frac{dy}{v}$ $\frac{dx}{ax}=\frac{dy}{-\,av}$             $\frac{1}{a}\,In\,x=-\,\,\frac{1}{a}\,In\,\,\,y+c$             The stream line passes through point (3, 1) $\frac{1}{a}\,In\,3=-\,\frac{1}{a}\,In+c=0+c$ $c=\frac{1}{a}\,In\,3$ $\frac{1}{a}\,In\,x=-\,\frac{1}{a}\,In\,y+\frac{1}{a}\,In\,3$             Or $In\,x=-\,\,In\,y+In\,3$             $In\,x+In\,y=In\,3$             $In\,xy=In\,3$             $xy=3$