Problem $3$

a$)$ Consider a planar flow in the xy plane. The $y-$component of velocity in a steady and incompressible flow is $v=$Axy$(x^2-y^2)$ where $A=3m^{-3}{s}^{-1}$ and x and y are measured in meters. Find a possible x$-$component of the velocity for this flow field. Show detailed work.

b$)$ For an incompressible flow in the r$-$ plane, the $r$ component of velocity is given as

$V_r=-\frac{A}{r^2}cos$

Determine a possible $$ component of the velocity. Hint. Look up the grad operator in cylindrical coordinates. Show detailed work.

Governing Equation$($s$)$