Question 2 A long municipal discharge pipe can be modelled as a source of strength m. The pipe is placed at a distance b from the bottom of a deep containment tank as shown in Figure 2. The city engineers want to drain the tank, but do not want to interrupt the discharge during the operation. The drain can be modelled as a sink of strength -2m placed at the centre of the tank directly below the pipe, as shown in the figure. The city supervisor is concerned about the forces generated on the pipe. Your consulting company is asked to estimate these forces using potential flow theory. Drain: Sink strength -2m discharge pipe: source strength m Figure 2: Cross-sectional view of discharge pipe next to a tank bed with a drain. Assuming that the waste water density is the same as the water in the discharge tank, that the tank bed is flat, that the fluid velocity far from the discharge is negligible, and that the free surface effects can be neglected, determine: (a) The stream function that will represent this flow. (b) Verify that the tank bed is correctly simulated. (c) The velocity distribution along the tank bed. (d) The forces acting on the discharge pipe.