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2. You are tasked with evaluating the performance of a small-scale hydropower system. Water is collected from a mountain reservoir and directed through a system to generate electricity for a rural community. Note: Show all calculations clearly. Assume all values are ideal unless stated otherwise. Use the following information to perform your analysis: 2.1 The hydropower system draws water from a reservoir through an intake with a cross- sectional area of 25 m*. The water flows at a velocity of 3.2 m/s. Calculate the flow rate Q of the water. (3) 2.2 The water flows into a penstock, which transports the water to a turbine located 85 meters below the intake. Assume the mass flow rate m is derived from the density of water p=1000kg/m?. Calculate the potential energy per second (in Joules/second) delivered to the turbine. (4) 2.3 The turbine extracts the potential energy from the water and converts it into mechanical energy. The turbine has an angular velocity of 12 radians/sec and a torque output of 5800 Nm. Calculate the power output P of the turbine. (3) 2.4 The turbine drives a generator that converts mechanical energy into electrical energy with an efficiency of 92%. Calculate the electrical power output Priecc from the generator. (3) 2.5 The electricity is transmitted through power lines with a transmission efficiency of 87%. Calculate the final power available to consumers. (3) 2.6 Calculate the overall efficiency of the hydropower system as a percentage. (4) 2.7 Consider the implications of your results above and discuss briefly (35 lines) how efficiency might be improved in a real-world setup