Problem 3: Analyzing a pump system A pump steadily draws water from a pond at a volumetric flow rate of 0.83 m3/min through a pipe having a 12 cm diameter inlet. The water is delivered through a hose terminated by a converging nozzel. The nozzel exit has a diameter of 3 cm and is located 10 m above the pipe inlet. Water enters at 20 C, 1 atm and exits with no significant change in temperature or pressure. The magnitude of the rate of heat transfer from the pump to the surroundings is 5% of the power input. The acceleration of gravity is 9.81 m/s. Determine: a- The velocity of the water at the inlet and exit, each in m/s, and b- the power required by the pump in kW. 10 m Pump- T₁-20°C P₁=1 atm D, 12 cm (AV), 0.83 m/min D₁ = 3 cm