Question 1 (10 points). An irrigation pump is used to draw water from a reservoir and deliver it to an irrigation ditch at a mass flow rate of 20kg/s. The inflow from the reservoir and the outflow to the ditch are through pipes of diameters 10 cm and 7.5 cm respectively. If the water temperature is 15C at the inlet and 20C at the outlet, the outlet is 100 m higher than the inlet and one fifth of the of the input power to the pump is lost as heat transfer to the surroundings, find the power that must be supplied to the pump. Neglect the kinetic energy of the water in your analysis.