Hydroelectric Power Plant Problems and Solutions

Hydroelectric Problems 1.0 Find the torque and power transferred to the buckets of an impulse wheel with α= 00, β= 1600, κ= 0.44, ∅=0.46 , Cv = 0.98, a jet diameter of 10 inches and a pitch diam eter of 10ft. Find also, the hydraulic efficiency, and expressed as a percentage of the total head, find the head loss in bucket friction, the energy head loss at discharge and the head loss in the nozzle. 2.0 A tangential turbine develops 7200 hp at 200 rpm under a head of 790 ft at an efficiency of 82 percent. (a) If the speed factor is 0.46 compute the wheel diameter, the flow, the unit speed, unit power, unti flow, and specific speed. (b) For this turbine, what would be the speed, power and flow under a head of 529 ft? (c) For a turbine having the same design, what size of wheel should be used to develop 3800 hp under a 600 ft head and what would be its speed and rate of discharge? Assume no change in efficiency. 3.0. A double-overhung impulse-turbine installation is to develop 20 000hp at 257rpm under a net head of 1120 ft. Determine N, wheel-pitch diameter and approximate jet diameter. And determine also the N and jet diameter of a single wheel with a single nozzle and in four nozzles. 4.0 The Francis turbine which the test curves are shown in Fig 21-4a and b has a 27-indiameter runner and a maximum efficiency of 88% when discharging 38.8 cfs and developing 550 bhp at 600rpm under a net head of 141.8 ft. Compute Ns, ∅ e, and Cr, assuming B/D =0.15. 5.0 A Kaplan turbine develops 10000 kW under a head of 12m when the following conditions prevail. Speed ratio=2, flow ratio=0.65, diameter of hub=0.3 times the external diameter of the vane and the overall efficiency=94 percent. Estimate (a) the speed (b)the diameter of the runner and (c) the specific speed. 6.0 A turbine is to be installed at a point where the available head is 175 ft and the available flow will average 1000cfs. What type of turbine would you recommend? Specify the operating speed and number of generator poles for 60-cycle electricity if a turbine with the highest tolerable specific speed to safeguard against cavitation is selected. Assume static draft head of 10ft and 90 percent turbine efficiency. Approximately what size of turbine is required? 7.0 A Pelton wheel of 12-ft pitch diameter operates under a net head of 2000 ft. Estimate the speed, power output and flow rate for best efficiency if the nozzle exit diameter is 4 in. 8.0 A Pelton wheel is to be selected to drive a generator at 600 rpm. The water jet is 75 mm in diameter and has a velocity of 100m/s. With the blade angle at 170°, the ratio of vane speed to initial jet speed at 0.47, and neglecting losses, determine (α) diameter of wheel to entreline of buckets (vanes), (b) power developed, and (c) kinetic energy per newton remaining in fluid. 9.0 A turbine is to operate at 400 rpm under a net head of 1320 ft. If a single 6-inches diameter water jet is used, find the specific speed of this machine assuming Cv = 0.98, ∅=0.45, and n = 0.85. Find the required pitch diameter of the wheel. 10.0 A Pelton type turbine was installed 30m below the head gate of the penstock. The head loss due to friction is 15 percent of the given elevation. The length of the penstock is 80m and the coefficient of friction is 0.00093. Determine the power output in KW.