$2.(10$ pts$)$ Kundu $3\mathrm{.}12$

The velocity components in an unsteady plane flow are given by u $=$ x$/(1+$ t$)$

and v $=2$y$/(2+$ t$).$ Determine equations for the streamline and path lines subject

to $($x$,$ y$)=($x$0,$ y$0)$ at t $=0.$ The second answer is obtained by eliminating time from

the component path line equations.

ans. y

y$0$

$=$ x$2(1+$t$)$

$(2+$t$)$

x$0$

; y $=$ y$0$

$4(1+$ x

x$0$

$)2$