10. At a certain point at the beach, the coast line makes a right angle bend, as shown in part (a) of the below figure. The flow of salt water in this bend can be approximated by the potential flow of an incompressible fluid about a right-angle corner. X Fresh water source Salt water Dividing streamline Fresh water (a) (b) a) Show that the stream function 2 Axy represents this corner flow, where A is a known positive constant. b) Now, a fresh-water reservoir is placed in the corner as shown in part (b) of the figure. By introducing (ejecting) fresh water from the reservoir, the salt water is to be kept away from the coast. The fresh-water reservoir can be approximated as a line source having a strength m. Determine m if the salt water is not to get closer than a distance L to the corner (as shown). c) Determine the equation of the dividing streamline separating the fresh water from the salt water. d) Determine the volumetric flow rate (per depth) with which fresh water is injected from the corner reservoir. Also determine the volumetric flow rate per unit depth with which the fresh water flows between the dividing streamline and the beach. e) A swimmer on the x axis side of the beach wants to swim in fresh water up to a distance of 0.5 L in a direction normal to the coast. What is the farthest distance from the corner (the x-position) at which this swimmer can begin her swim? Calculate this distance as a fraction of L (e.g. 0.43L) and for accuracy, use 2 digits beyond the decimal point for the fraction. -1 (Ans. b) 4AL, c) 2L tan () + 2xy : = TL or r sin20 + 2L0 = L, d) AL, ) 2.79L)