8. The stream function for a flow with constant velocity V in the x-direction is given by =Vy and for a line source by =q/2 where q is the volumetric flow rate per unit length of the source (its "strength"). The angle runs anticlockwise from the x-axis. (a) Write down equations for the velocity components u (in the x-direction) and v (in the y-direction) in terms of q, and the radial distance from the source, r. (b) If the two flows are combined to form a Rankine half-body, show that there is a stagnation point a distance rs=b=q/2V from the source. (c) Find an equation for the Rankine half-body half-width, w, as x tends to infinity. (d) Find the flow half-width, the flow velocity and the flow direction at P, where it lies on the Rankine half-body surface and along the y-axis