Question $3($Unit $5)25$ marks Consider a two$-$dimensional fluid flow whose velocity field in Cartesian form at time t $0$ is given by: u $=$ e $2$t i $2$xe$$t j $($x $>0,$ y $>0).($a$)$ Is the flow $($i$)$ steady, $($ii$)$ incompressible, $($iii$)$ irrotational? $[4]($b$)$ Find the equations x$($t$)$ and y$($t$)$ of the pathline of a particle that passes through the point $(0,1)$ at time t $=0.[8]($c$)$ Write down the equations describing the stream function for the velocity vector field u$.$ Hence find the stream function for this flow, and the equations of the streamlines. $[5]($d$)$ Suppose that the fluid is inviscid with constant density $,$ and that is subject to body force $($per unit mass$),$ F $=2$e $2$t i $+2$xe$$t j$.$ Find the pressure distribution in the fluid. $[8$