Q$2.$ Given the velocity field, vec$(V)=(u_0+bx)hat()-(by)hat(),$ where $u_0$ is constant, find the following: $(7$ marks$)$

$($a$)$ Equation of streamline

$($b$)$ acceleration vector if $u_0=0\mathrm{.}5$;$b=1\mathrm{.}2$

$($c$)$ Is the flow field in $($b$)$ steady or unsteady?

$($d$)$ Determine the coordinates of the stagnation point.

$($e$)$ Difference between a pathline and streakline for a steady flow.

$($f$)$ A stationary probe is placed in a fluid flow and measures pressure and temperature as functions of time at one location in the flow $($as shown in Figure $2).$ Is this a Lagrangian or an Eulerian measurement? Explain.