A velocity field is given by
u = 3 y ; v = -3 x
over the range 0
Take the density as 1 and the "depth" (in the z direction) as 1.
a) Verify that this field is incompressible
b) Evaluate the mass flow rate out through each of the four sides of the box and show that the sum of these is 0.
c) Plot the velocity vectors using Matlabs' quiver function
d) Find and plot the streamlines coming out of the left and bottom boundaries, x=0 and y=0
e) Find the net force exerted on the fluid inside the box by summing the momentum flow rates out through each of the four sides of the box.