Pumped storage is receiving increased attention, as it is a cost-effective approach to store excess electricity...

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Pumped storage is receiving increased attention, as it is a cost-effective approach to store excess electricity generation (e.g. during the day from Photovoltaics) and to release this energy during the evening, when demand is highest. For Brisbane, a storage scheme is proposed, which has a reservoir on Mt Cootha, and a pumping/turbine station in Indooroopilly, so that water from the Brisbane river can be used. The pipe connecting the reservoir and turbine has a diameter of 2 m and wall roughness of 2 mm and is 2.5 km long. The pressure in the pipe at point A, a short distance after exit from the reservoir, at an altitude of 300 m, is 250 kPa (absolute). The pressure at point B, just before the inlet to the turbine, at an altitude of 15 m is 2500 kPa. a) In 2-3 sentences, explain why the water flows from point A at low pressure to point B at high pressure. b) Find the flow rate of water in the pipe. Hint: for part (b) you need to iterate as friction factor f and thus frictional head loss hr depend on flow rate. Use an initial guess for the friction factor of 0.02. Substitute this estimation of friction factor into the head equation and solve for velocity V, then calculate a value for f using Haaland's formula. After 2-3 iterations you should find that f and V have converged. Pumped storage is receiving increased attention, as it is a cost-effective approach to store excess electricity generation (e.g. during the day from Photovoltaics) and to release this energy during the evening, when demand is highest. For Brisbane, a storage scheme is proposed, which has a reservoir on Mt Cootha, and a pumping/turbine station in Indooroopilly, so that water from the Brisbane river can be used. The pipe connecting the reservoir and turbine has a diameter of 2 m and wall roughness of 2 mm and is 2.5 km long. The pressure in the pipe at point A, a short distance after exit from the reservoir, at an altitude of 300 m, is 250 kPa (absolute). The pressure at point B, just before the inlet to the turbine, at an altitude of 15 m is 2500 kPa. a) In 2-3 sentences, explain why the water flows from point A at low pressure to point B at high pressure. b) Find the flow rate of water in the pipe. Hint: for part (b) you need to iterate as friction factor f and thus frictional head loss hr depend on flow rate. Use an initial guess for the friction factor of 0.02. Substitute this estimation of friction factor into the head equation and solve for velocity V, then calculate a value for f using Haaland's formula. After 2-3 iterations you should find that f and V have converged.

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a Water flows from point A at low pressure to point B at high pressure because it follows the natura... View the full answer