At a certain point at the beach, the coastline makes a right-angle bend, as shown in Fig...

At a certain point at the beach, the coastline makes a right-angle bend, as shown in Fig. P6.43a. The flow of salt water in this bend can be approximated by the potential flow of an incompressible fluid in a right-angle corner. (a) Show that the stream function for this flow is where A is a positive constant. (b) A freshwater reservoir is located in the corner. The salt water is to be kept away from the reservoir to avoid any possible seepage of salt water into the freshwater (Fig. P6.43b). The freshwater source can be approximated as a line source having a strength m, where m is the volume rate of flow (per unit length) emanating from the source. Determine m if the salt water is not to get closer than a distance L to the corner. Hint: Find the value of m (in terms of A and L) so that a stagnation point occurs at Y = L. (c) The streamline passing through the stagnation point would represent the line dividing the freshwater from the salt water. Plot this streamline.