Consider steady, incompressible, laminar flow that is two$-$dimensional in the x$-$y plane. Ignore gravity effects and units. The x$-$component of velocity is u $=-5$x$+3.$ Do not be concerned with units.

$($a$)$ Calculate the y$-$component of velocity, v$.$

$($b$)$ Regardless of your answer to Part $($a$),$ set v$=5$y$+2,$ and calculate the stream function psi$($x$,$y$).$

$($c$)$ Generate an expression for the pressure field associated with this velocity field, i$.$e$.,$ calculate P$($x$,$y$).$ Is this a valid steady, two$-$dimensional, incompressible, laminar flow field? Explain. Hint: To calculate the pressure field, you will need to write out both the x and y components of the Navier$-$Stokes equation, reduce them as much as possible, and then integrate them to calculate P$($x$,$y$),$ noting that the pressure derivatives are partial derivatives, so the integration must be handled carefully, as discussed in class.

Solve each part of this question and show all work.