Chapter 13, Problem 6P

Water flows through a 7.5 m diameter penstock on a dam at a flow rate of 113 m3/s. The total head available for the turbine is 18.4 m. The specifiic weight of water is 9810 N/m3.   What is the power generated by the turbine?

Water is pumped at a flow rate of 15 m3/s from the lower reservoir through a pipe with a diameter of 1.50 m. How much power does the water need to be powered to produce this much flow?

Water is pumped 14.5 km from a reservoir at elevation 30 m to another reservoirat elevation 70 m. The steel pipeline connecting the reservoirs has a nominal diameter of 1400mm (the actual inside diameter is 1372 mm) with C = 90. If the flow is 1.18 m3/s, the pumpingefficiency is 82%, and electricity costs $0.14/kWh. Assuming that the density of water is 1000kg/m3, what will be the monthly power bill? Sketch the hydraulic and energy grade lines.

At a proposed hydroelectric power plant site, the average elevation of headwater is 600m and the tailwater elevation is 480m. The average annual water flow is determined to be equal to that volume flowing through a rectangular channel 4m wide and 0.5m deep and average velocity of 5.5m/s. Assuming the plant will operate 350 days/year, find the energy kwh that the plant site can developed if the hydraulic turbine that will be used has an efficiency of 78% and generator efficiency of 90%. Consider a headwork loss of 4% of the available head.

Water is flowing in a 90° triangular channel at a depth of 39 cm. A hydraulic jump occurs. The depth after the jump is 126 cm. a. What is the discharge?b. What is the decrease in specific energy caused by the jump?c. What is the head loss in kW?

Compute the minimum water horsepower of a pump needed to pump-out water at a rate of 300 gpm with a total head of 6 m. The pump efficiency is about 60%.

What is the cost to pump 1000 liters of water to the top of a 30 m high water tank? Assume a pumping efficiency of 50% and an electrical cost of $0.15 per KW-h. P(h2O) = 1000 ?g/m^3 .   1 m^3 = 1000 liters

Two reservoirs A and B have elevations of 250 m and 100 m, respectively. It is connected by a pipe having adiameter of 250 mm and a length of 100 m. A turbine, with an efficiency of 0.95, which is installed at a point inbetween A and B, is used to supply 233 kW of electric power to a nearby community. If the total head loss as watertravelled from reservoir A to B is 25 m, determine the discharge inside the pipe in liters per second.

Determine the total energy production of a run-of-river plant having an total efficiency of 85%. It receives flow by means of a penstock, 400m long with 1.2m diameter, and f=0.015 in Darcy-Weisbach equation. The available head is 200m and seasonal fluctuations of upstream and downstream water levels are ignored. The flow duration data are tabulated as below.