You are requested to design a fountain, as shown in the figure, such that the water jet would reach a height of 5m above a platform placed 10m higher than the pump. The nozzle exit diameter is 1cm, while the pipe diameter is 4cm with roughness of 0.8mm. The loss due to the bend is Le/D=15, and the losses due to the nozzle and valve are KN-1.45 and Kv=0.85, respectively. (g=10ms2, Pa=100kPa, pw=10kgm, w=10kg.sm) [35%] 2.5m Valve 19m Platform Pump 30m m15m 5m Nozzle 10m (a) Calculate the required water velocity at the nozzle exit. (b) Calculate the average water velocity in the pipe and the corresponding Reynolds number. (c) Determine the friction factor for the pipe flow. (d) Estimate the absolute pressure needed at the pump outlet. (Hint: Bernoulli between the pump outlet and the nozzle exit) (e) Estimate the gage pressure at the pump inlet. (Hint: Bernoulli between the pump inlet and the water tank free surface. (f) Calculate the pump output power required for the water delivery