Consider a two-dimensional flow field described by a potential function v=c+ dr? - ey? where constant c=4m2.s-1, d=3s-1, e=3s-1 and x and y are the horizontal and vertical position coordinates, respectively measured in meters.

a) derive the stream function (\psi) for this flow field.

b) plot streamlines for three iso-values of \psi=1,2,3. from these iso-streamlines, comment on how velocity in this flow field changes with x, y positions.

c)determine pressure gradient at point (1, 1) located within the field if the fluid is assumed to be water. (hint: include effect of gravity acceleration which is 9.81 m. s-2. density of water can be assumed to be 998.2 kg/m3).