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HYDRO-ELECTRIC POWER PLANT

Hydro-electric Power Plant • Electric power is produced by falling water that rotates a turbine. • The potential energy of water at high level is converted to mechanical energy by the turbine and the mechanical energy is converted to electrical energy by the generator. • The advantage of hydroelectric power plant is that it needs no fuel and the dam can be used as flood control and irrigation. • Most of the hydroelectric power plant are used to cope up peak loads because they can be easily started and stopped.

Basic Parts of High-Head Hydroelectric Plant

Basic Parts of High-Head Hydroelectric Plant • Reservoir – stores the water coming from the upper river or water falls.

• Headwater – the water in the reservoir. • Spillway – a weir in the reservoir which discharges excess

water so that the heads of the plant will be maintained. • Dam – the concrete structure that encloses the reservoir. • Silt Sluice – a chamber which collects the mud and through which the mud is discharged

Basic Parts of High-Head Hydroelectric Plant • Trash Rack – a screen which prevents the leaves, branches and other water contaminants to enter into the penstock.

• Valve – opens or closes the entrance of water into the penstock. • Surge Chamber – a standpipe connected to the atmosphere and attached to the penstock so that the water will be at atmospheric pressure.

• Penstock – the channel that leads the water from the reservoir to the turbine.

• Turbine – converts energy of the water into mechanical energy.

Basic Parts of High-Head Hydroelectric Plant • Generator – converts the mechanical energy of the turbine into electrical energy output.

• Draft tube – connects the turbine outlet to the tailwater so that the turbine can be set above the tailwater level.

• Tailrace – a channel which leads the water from the turbine to the tailwater.

• Tailwater – the water that is discharged from the turbine.

Run-of-the-River (Low Head) Hydroelectric Power Plant

• Pondage – the water behind the dam of a run-of-the-river hydroelectric power plant.

Pumped Storage Hydroelectric Power Plant • Pumped storage plant – is a hydroelectric plant which involves the use of off-peak energy to store water and to use the stored water to generate extra energy to cope with the peak load. Pumped storage hydroelectric plant is also termed as Hydraulic Accumulator.

Classification of Hydraulic Turbines 1. Impulse (Pelton) Turbine – high head and low flow

Classification of Hydraulic Turbines 2. Reaction Turbine a. Francis Turbine – low head and high efficiency

Classification of Hydraulic Turbines b. Propeller (Kaplan) Turbine – very low head and efficiency is lower that Francis.

Selection of Turbine Type based on head Net Head

Type of Turbine

Up to 70 ft 70 ft to 110 ft 110 ft to 800 ft 800 ft to 1300 ft 1300 ft and above

Propeller Type Propeller type or Francis Francis Type Francis or Impulse Impulse

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant Continuation…Friction Head Loss Where: f = coefficient of friction L = total length of pipe, in meters V = velocity, m/sec g = 9.81 m/sec2 D = inside diameter, meters (Friction head loss is usually expressed as a percentage of the gross head.)

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

HYDROELECTRIC POWER PLANT

PROBLEMS

Problem 1 A hydroelectric power plant having 50 sq. km reservoir area and 100 m head is used to generate power. The energy utilized by the consumers whose load is connected to the power plant during a fivehour period is 13.5x106 kW-hr. The overall generation efficiency is 75%. Find the fall in the height of water in the reservoir after 5-hour period. a. 2.13 m c. 3.21 m b. 1.32 m d. 0.53 m

Problem 2 45 kW of the shaft power is developed by a turbine working under an available head of 40 meters. Assuming hydraulic and mechanical efficiencies to be 87% and 95% respectively, what is the discharge through the turbine in m3/s? a. 0.0345 c. 1.511 b. 0.139 d. 1.234

Problem 3 A vertical draft tube is installed on a Francis turbine with a head of 38 meters at the inlet while discharge is 2.1 m3/s. The hydraulic efficiency is 0.87 and overall efficiency is 0.84. The velocities at the inlet and exit of the draft tube are 5 m/s and 1.5 m/s, respectively. The top of the draft is 1 m below the center line of the spiral casing while the tailrace (water) level is 3 m from the top of the draft tube. There is no velocity of whirl at either top or bottom of the draft tube and leakage losses are negligible. What is the power output of the turbine in kW? a. 746.9 c. 901.3 b. 632.9 d. 832.6

Problem 4 A Pelton Wheel is to be designed to run at 300 rpm under an effective head of 150 m. The ratio of the nozzle diameter to the diameter of the pitch circle is 1/12. assuming efficiency of 84%, what is the size of the wheel in meters. Assume speed ratio of 0.45. a. 1.05 b. 2.00

c. 1.55 d. 2.86

Problem 5 A hydro-electric generating station is supplied from a reservoir of capacity 6,000,000 m3 at a head of 170 m. Assume hydraulic efficiency of 80% and electrical efficiency of 90%. The fall in the reservoir level after a load of 15 MW has been supplied for 3 hours, if the area of the reservoir is 2.5 sq. km is closest to: a. 5.39 cm b. 4.32 cm

c. 5.98 cm d. 4.83 cm

Problem 6 A hydroelectric plant discharges water at the rate of 0.75 cubic meter per second and enters the turbine at 0.35 mps with a pressure of 275kPa. Runner inside diameter is 550 mm, speed is 520 rpm and the turbine efficiency is 88%. Find the turbine speed factor. a. 0.638 b. 0.386

c. 0.368 d. 0.836

Problem 7 The nozzle efficiency of a Pelton turbine is 90%. Find the velocity of water at the nozzle exit if the head is 180 meters. a. 53.48 m/s b. 65.4 m/s

c. 77.4 m/s d. 89.4 m/s

Problem 8 A hydro-electric plant in Loboc, Bohol discharges 205 ft3/sec and reduces the pressure from 50 psi to 30 psi. Determine the power output in MW.

a. 0.80 MW b. 1.20 MW

c. 1.80 MW d. 2.40 MW

Problem 9 A hydraulic turbine receives water from a reservoir at an elevation of 100 meters above it. What is the minimum water flow in kg per second to produce a steady turbine output of 50 MW?

a. 50,247 b. 50,968

c. 50,672 d. 50,465

Problem 10 The pressure drop across a turbine is 25 psi. The flow rate is 55 gallons per minute. Calculate the power output of the turbine. a. 0.802 hp b. 0.41 hp

c. 1.05 hp d. 2.54 hp

Problem 11 A reaction turbine develops 500 bhp. Flow through the turbine is 50 cfs. Water enters at 20 fps with a 100 ft pressure head. The elevation of the turbine above the tailwater level is 10 ft. Find the effective head. a. 130 ft b. 120 ft

c. 110 ft d. 116.2 ft

Problem 12 The hydraulic efficiency of hydro-electric turbine is 85%, find the discharge in liters per second. Power developed is 10,500 kW and operating under a head of 320 m.

a. 3,935 L/s b. 3,395 L/s

c. 9,533 L/s d. 5,933 L/s

Problem 13 A horizontal tube supplies 280 liters per second of water to a hydraulic turbine. The net head is 46.50 m. Determine the power supplied to the turbine.

a. 117.7 kW b. 127.7 kW

c. 137.7 kW d. 157.7 kW

Problem 14 What is the overall efficiency of the turbine if the power developed is 15,000 kW at a head of 170 meters and the nozzle discharge is 10 cubic meters per second?

a. 70.09 % b. 89.94 %

c. 79.98 % d. 90.96 %

Problem 15 If the available water power of a hydro-station is 3,500 MW and the head of water is 280 meters, determine the water rate of flow. a. 1,420 m3/sec b. 12,500 m3/sec

c. 875 m3/sec d. 1,274 m3/sec

Problem 16 What is the overall efficiency of the turbine if the power developed is 12 MW at a head of 150 meters and the nozzle discharge 10 cubic meters each second.

a. 70.65% b. 78.99%

c. 81.55% d. 89.23%

Problem 17 A reaction turbine develops 500 bhp. Flow through the turbine is 50 cfs. Water enters at 20 fps with a 100 ft pressure head. The elevation of the turbine above the tailwater level is 10 ft. What is the turbine efficiency? a. 65.8% b. 75.8%

c. 85.8% d. 90.5%

Problem 18 A river 60 m wide and 2 m deep flows at 2 m/s. If a hydro-plant develops a pressure of 300 kPa gage just before the turbine, what power in MW can be developed?

a. 40 b. 48

c. 56 d. 72

Problem 19 The difference between the head race and the tail race of a hydroelectric plant is 220 m. The friction loss through the penstock is equivalent to 10 m. Water flows at the rate of 3.0 m3/sec. Power loss due to friction in the turbine is 50 kW and the leakage loss is 0.103 m3/sec. Determine the electrical power generated in kW if the generator efficiency is 90%. a. 3966 c. 4931 b. 4255 d. 5326

Problem 20 A hydro-electric power plant has the following data: catchment area, 100 sq. km; average annual rainfall, 150 cm; run off, 90%; available head, 400 m; overall station efficiency, 80%. Calculate the power that it can develop in kw. a. 11,789 b. 10,567

c. 12,435 d. 13,435

Problem 21 In a certain municipality, a proposed hydro-electric plant site has the following data: the elevation of the head water is 500 m, tail water elevation is 390m, average annual water flow is determined to be equal to that volume flowing through a regular channel 5m wide and 1.0m deep and average velocity of 6.0 m/sec. Assuming that the plant will operate 345 days a year. Find the annual energy in kW-hr that the power site can develop if the hydraulic turbine that will be used has an efficiency of 83% and generator efficiency of 93%. Assume a head loss of 5% of the available head. a. 176,561,261 kW-hr c. 146,561,261 kW-hr b. 196,561,261 kW-hr d. 116,561,261 kW-hr

Problem 22 The water surface on the dam of a certain hydroelectric power plant in Mindanao is at an elevation of 165 m, while the water surface just at an outlet of the gate is 160 m. The head gate has an opening of 1.25m x 1.25m leading to the penstock which is fully opened. Assume 70% as coefficient of discharge. Determine (1) the quantity of water that enters the hydraulic turbine per second; and (2) the kW output of the turbine, assuming 81.5% efficiency and the turbine is 110m below the entrance of the penstock. a. (1) 6.56 m3; (2) 7890 c. (1) 10.8 m3; (2) 9,960 b. (1) 7.45 m3; (2) 8200 d. (1) 15.6 m3; (2) 12,200

Problem 23 A certain community in the mountains of Mindanao plans to put up a small hydro-electric plant to service 5 closely located barangays estimated to consume 61,320,000 kw-hr per annum. Expected flow of water is 1,700 m3/min. The most favourable location for plant fixes the tail water level at 400 m, the manufacturer of the turbine generator set have indicated the following performance data: Turbine efficiency is 85%, generator efficiency is 91%, losses in head work will not exceed 5% of the available head. Determine (1) the head water elevation (HWE); and (2) the synchronous speed of generator if the number of poles is 4, and the frequency is 60 Hz. a. (1) 434 m; (2) 1800rpm c. (1) 344 m; (2) 1200 rpm b. (1) 388 m; (2) 1500 rpm d. (1) 299 m; (2) 1000 rpm

Problem 24 (situational) A proposed hydroelectric power plant in Bohol has the following data: Elevation of normal head water…………………………… 200 m Elevation of normal tail water……………………………... 80 m Loss of head due to friction…………………………………. 10 m Turbine discharge at full gate opening…………………. 6.5 m3/sec Turbine efficiency at rated capacity…………………..... 85 % Turbine is directly connected to 60 cycle AC generator.

Problem 24 (situational) A. Determine the effective head of the hydro-electric power plant. a. 80 m c. 110 m b. 99m d. 160 m B. Find the brake power of the turbine in kW. a. 4162 kw c. 5562 kw b. 4962 kw d. 5962 kw

Problem 24 (situational) C. Find the number of poles of the generator if the rotative speed is 900 rpm. a. 2 poles c. 8 poles b. 4 poles d. 10 poles D. Find the kW output of the direct connected generator if the efficiency is 92% a. 5485 kW c. 5584 kW b. 4585 kW d. 4855 kW

Problem 25 (situational) A certain hydro storage plant in Laguna has 18,000 kW rated capacity, with a utilization factor of 70%. For a 2.0 hr peak, determine the hydraulic impoundment of water required, with frictional loss of 4 ft. Dam elevation at 130 ft and hydroelectric turbine elevation of 40 ft and a tail race at elevation 30 ft. Generator efficiency is 90% and a turbine efficiency of 80% and evaporation factor of 25%. Assume that the water is pumped from the low reservoir with friction factor of 10%, pump efficiency of 75% and motor efficiency of 84%. a. 51.3 m3/sec c. 71.3 m3/sec b. 61.3 m3/sec d. 81.3 m3/sec

Problem 25 (situational) A. How many kW-hr is required to pump the water needed to carry the peak? a. 64,911.80 c. 84,911.80 b. 74,911.80 d. 94,911.80 B. What is the overall efficiency of the hydroelectric power plant? a. 15% c. 30% b. 20% d. 38%

Problem 26 If it is desired to use a type of hydraulic turbine whose specific speed is 50 rpm to deliver 150 hp at 150 ft head, what will be the corrected speed of the unit?

a. 1143 rpm b. 1743 rpm

c. 1943 rpm d. 2143 rpm

Problem 27 A hydroelectric power station is to be constructed has an average annual rainfall of 1.5 m. The catchment area is 230 km2 with an available head of 40 m. Only 80% of the rainfall can be collected and ¾ of the impoundment water is available for power. The load factor of the station is 82%. The penstock efficiency is 95%, turbine efficiency is 80%, and generator efficiency is 90%. (1) Calculate the average power that could be generated; and (2) the installed capacity of the power station. a. (1) 2,962 kw; (2) 1,549 kw c. (1) 1,962 kw; (2) 1,949 kw b. (1) 2,762 kw; (2) 2,549 kw d. (1) 1762 kw; (2) 2,149 kw

Problem 28 (situational) An existing hydroelectric power plant has the following data and design: Gross head …………………………………………….. 49.5 ft Mean flow ……………………………………………… 75 ft3/sec Length of penstock ………………………………... 80 ft Penstock diameter …………………………………. 3.5 ft Assumptions: Coefficient of friction …………………………….. 0.020 Turbine efficiency ………………………………….. 88% Generator efficiency ……………………………… 92%

Problem 28 (situational) A. Find the net head in ft used by the turbine. a. 42 c. 49 b. 44 d. 59 B. Find the Hp developed by the turbine. a. 312 c. 367 b. 339 d. 667

Problem 28 (situational) C. Find the standard capacity of synchronous generator. a. 338 hp c. 388 hp b. 358 hp d. 489 hp D. Find the motor rpm assuming 6 poles. a. 900 rpm c. 1800 rpm b. 1200 rpm d. 2200 rpm

Problem 29 A mini-hydropower plant has an available head of 5m. The water flow is 1.25 m3/sec, efficiency of the turbine is 90%, efficiency of the generator is 92%. Determine the maximum output of the generator in kW. a. 29.5 c. 50.7 b. 42.5 d. 69.5

Problem 30 It is desired to develop a 5MW impulse turbine under an effective head of 320 m. The turbine efficiency is 85%. Velocity coefficient of the nozzle is 99%. What should be the wheel diameter assuming it is 12 times the diameter of the jet? a. 1.5 m c. 2.1 m b. 1.8 m d. 2.8 m

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Hydro-electric Power Plant • Electric power is produced by falling water that rotates a turbine. • The potential energy of water at high level is converted to mechanical energy by the turbine and the mechanical energy is converted to electrical energy by the generator. • The advantage of hydroelectric power plant is that it needs no fuel and the dam can be used as flood control and irrigation. • Most of the hydroelectric power plant are used to cope up peak loads because they can be easily started and stopped.

Basic Parts of High-Head Hydroelectric Plant

Basic Parts of High-Head Hydroelectric Plant • Reservoir – stores the water coming from the upper river or water falls.

• Headwater – the water in the reservoir. • Spillway – a weir in the reservoir which discharges excess

water so that the heads of the plant will be maintained. • Dam – the concrete structure that encloses the reservoir. • Silt Sluice – a chamber which collects the mud and through which the mud is discharged

Basic Parts of High-Head Hydroelectric Plant • Trash Rack – a screen which prevents the leaves, branches and other water contaminants to enter into the penstock.

• Valve – opens or closes the entrance of water into the penstock. • Surge Chamber – a standpipe connected to the atmosphere and attached to the penstock so that the water will be at atmospheric pressure.

• Penstock – the channel that leads the water from the reservoir to the turbine.

• Turbine – converts energy of the water into mechanical energy.

Basic Parts of High-Head Hydroelectric Plant • Generator – converts the mechanical energy of the turbine into electrical energy output.

• Draft tube – connects the turbine outlet to the tailwater so that the turbine can be set above the tailwater level.

• Tailrace – a channel which leads the water from the turbine to the tailwater.

• Tailwater – the water that is discharged from the turbine.

Run-of-the-River (Low Head) Hydroelectric Power Plant

• Pondage – the water behind the dam of a run-of-the-river hydroelectric power plant.

Pumped Storage Hydroelectric Power Plant • Pumped storage plant – is a hydroelectric plant which involves the use of off-peak energy to store water and to use the stored water to generate extra energy to cope with the peak load. Pumped storage hydroelectric plant is also termed as Hydraulic Accumulator.

Classification of Hydraulic Turbines 1. Impulse (Pelton) Turbine – high head and low flow

Classification of Hydraulic Turbines 2. Reaction Turbine a. Francis Turbine – low head and high efficiency

Classification of Hydraulic Turbines b. Propeller (Kaplan) Turbine – very low head and efficiency is lower that Francis.

Selection of Turbine Type based on head Net Head

Type of Turbine

Up to 70 ft 70 ft to 110 ft 110 ft to 800 ft 800 ft to 1300 ft 1300 ft and above

Propeller Type Propeller type or Francis Francis Type Francis or Impulse Impulse

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant Continuation…Friction Head Loss Where: f = coefficient of friction L = total length of pipe, in meters V = velocity, m/sec g = 9.81 m/sec2 D = inside diameter, meters (Friction head loss is usually expressed as a percentage of the gross head.)

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

Performance of Hydroelectric Power Plant

HYDROELECTRIC POWER PLANT

PROBLEMS

Problem 1 A hydroelectric power plant having 50 sq. km reservoir area and 100 m head is used to generate power. The energy utilized by the consumers whose load is connected to the power plant during a fivehour period is 13.5x106 kW-hr. The overall generation efficiency is 75%. Find the fall in the height of water in the reservoir after 5-hour period. a. 2.13 m c. 3.21 m b. 1.32 m d. 0.53 m

Problem 2 45 kW of the shaft power is developed by a turbine working under an available head of 40 meters. Assuming hydraulic and mechanical efficiencies to be 87% and 95% respectively, what is the discharge through the turbine in m3/s? a. 0.0345 c. 1.511 b. 0.139 d. 1.234

Problem 3 A vertical draft tube is installed on a Francis turbine with a head of 38 meters at the inlet while discharge is 2.1 m3/s. The hydraulic efficiency is 0.87 and overall efficiency is 0.84. The velocities at the inlet and exit of the draft tube are 5 m/s and 1.5 m/s, respectively. The top of the draft is 1 m below the center line of the spiral casing while the tailrace (water) level is 3 m from the top of the draft tube. There is no velocity of whirl at either top or bottom of the draft tube and leakage losses are negligible. What is the power output of the turbine in kW? a. 746.9 c. 901.3 b. 632.9 d. 832.6

Problem 4 A Pelton Wheel is to be designed to run at 300 rpm under an effective head of 150 m. The ratio of the nozzle diameter to the diameter of the pitch circle is 1/12. assuming efficiency of 84%, what is the size of the wheel in meters. Assume speed ratio of 0.45. a. 1.05 b. 2.00

c. 1.55 d. 2.86

Problem 5 A hydro-electric generating station is supplied from a reservoir of capacity 6,000,000 m3 at a head of 170 m. Assume hydraulic efficiency of 80% and electrical efficiency of 90%. The fall in the reservoir level after a load of 15 MW has been supplied for 3 hours, if the area of the reservoir is 2.5 sq. km is closest to: a. 5.39 cm b. 4.32 cm

c. 5.98 cm d. 4.83 cm

Problem 6 A hydroelectric plant discharges water at the rate of 0.75 cubic meter per second and enters the turbine at 0.35 mps with a pressure of 275kPa. Runner inside diameter is 550 mm, speed is 520 rpm and the turbine efficiency is 88%. Find the turbine speed factor. a. 0.638 b. 0.386

c. 0.368 d. 0.836

Problem 7 The nozzle efficiency of a Pelton turbine is 90%. Find the velocity of water at the nozzle exit if the head is 180 meters. a. 53.48 m/s b. 65.4 m/s

c. 77.4 m/s d. 89.4 m/s

Problem 8 A hydro-electric plant in Loboc, Bohol discharges 205 ft3/sec and reduces the pressure from 50 psi to 30 psi. Determine the power output in MW.

a. 0.80 MW b. 1.20 MW

c. 1.80 MW d. 2.40 MW

Problem 9 A hydraulic turbine receives water from a reservoir at an elevation of 100 meters above it. What is the minimum water flow in kg per second to produce a steady turbine output of 50 MW?

a. 50,247 b. 50,968

c. 50,672 d. 50,465

Problem 10 The pressure drop across a turbine is 25 psi. The flow rate is 55 gallons per minute. Calculate the power output of the turbine. a. 0.802 hp b. 0.41 hp

c. 1.05 hp d. 2.54 hp

Problem 11 A reaction turbine develops 500 bhp. Flow through the turbine is 50 cfs. Water enters at 20 fps with a 100 ft pressure head. The elevation of the turbine above the tailwater level is 10 ft. Find the effective head. a. 130 ft b. 120 ft

c. 110 ft d. 116.2 ft

Problem 12 The hydraulic efficiency of hydro-electric turbine is 85%, find the discharge in liters per second. Power developed is 10,500 kW and operating under a head of 320 m.

a. 3,935 L/s b. 3,395 L/s

c. 9,533 L/s d. 5,933 L/s

Problem 13 A horizontal tube supplies 280 liters per second of water to a hydraulic turbine. The net head is 46.50 m. Determine the power supplied to the turbine.

a. 117.7 kW b. 127.7 kW

c. 137.7 kW d. 157.7 kW

Problem 14 What is the overall efficiency of the turbine if the power developed is 15,000 kW at a head of 170 meters and the nozzle discharge is 10 cubic meters per second?

a. 70.09 % b. 89.94 %

c. 79.98 % d. 90.96 %

Problem 15 If the available water power of a hydro-station is 3,500 MW and the head of water is 280 meters, determine the water rate of flow. a. 1,420 m3/sec b. 12,500 m3/sec

c. 875 m3/sec d. 1,274 m3/sec

Problem 16 What is the overall efficiency of the turbine if the power developed is 12 MW at a head of 150 meters and the nozzle discharge 10 cubic meters each second.

a. 70.65% b. 78.99%

c. 81.55% d. 89.23%

Problem 17 A reaction turbine develops 500 bhp. Flow through the turbine is 50 cfs. Water enters at 20 fps with a 100 ft pressure head. The elevation of the turbine above the tailwater level is 10 ft. What is the turbine efficiency? a. 65.8% b. 75.8%

c. 85.8% d. 90.5%

Problem 18 A river 60 m wide and 2 m deep flows at 2 m/s. If a hydro-plant develops a pressure of 300 kPa gage just before the turbine, what power in MW can be developed?

a. 40 b. 48

c. 56 d. 72

Problem 19 The difference between the head race and the tail race of a hydroelectric plant is 220 m. The friction loss through the penstock is equivalent to 10 m. Water flows at the rate of 3.0 m3/sec. Power loss due to friction in the turbine is 50 kW and the leakage loss is 0.103 m3/sec. Determine the electrical power generated in kW if the generator efficiency is 90%. a. 3966 c. 4931 b. 4255 d. 5326

Problem 20 A hydro-electric power plant has the following data: catchment area, 100 sq. km; average annual rainfall, 150 cm; run off, 90%; available head, 400 m; overall station efficiency, 80%. Calculate the power that it can develop in kw. a. 11,789 b. 10,567

c. 12,435 d. 13,435

Problem 21 In a certain municipality, a proposed hydro-electric plant site has the following data: the elevation of the head water is 500 m, tail water elevation is 390m, average annual water flow is determined to be equal to that volume flowing through a regular channel 5m wide and 1.0m deep and average velocity of 6.0 m/sec. Assuming that the plant will operate 345 days a year. Find the annual energy in kW-hr that the power site can develop if the hydraulic turbine that will be used has an efficiency of 83% and generator efficiency of 93%. Assume a head loss of 5% of the available head. a. 176,561,261 kW-hr c. 146,561,261 kW-hr b. 196,561,261 kW-hr d. 116,561,261 kW-hr

Problem 22 The water surface on the dam of a certain hydroelectric power plant in Mindanao is at an elevation of 165 m, while the water surface just at an outlet of the gate is 160 m. The head gate has an opening of 1.25m x 1.25m leading to the penstock which is fully opened. Assume 70% as coefficient of discharge. Determine (1) the quantity of water that enters the hydraulic turbine per second; and (2) the kW output of the turbine, assuming 81.5% efficiency and the turbine is 110m below the entrance of the penstock. a. (1) 6.56 m3; (2) 7890 c. (1) 10.8 m3; (2) 9,960 b. (1) 7.45 m3; (2) 8200 d. (1) 15.6 m3; (2) 12,200

Problem 23 A certain community in the mountains of Mindanao plans to put up a small hydro-electric plant to service 5 closely located barangays estimated to consume 61,320,000 kw-hr per annum. Expected flow of water is 1,700 m3/min. The most favourable location for plant fixes the tail water level at 400 m, the manufacturer of the turbine generator set have indicated the following performance data: Turbine efficiency is 85%, generator efficiency is 91%, losses in head work will not exceed 5% of the available head. Determine (1) the head water elevation (HWE); and (2) the synchronous speed of generator if the number of poles is 4, and the frequency is 60 Hz. a. (1) 434 m; (2) 1800rpm c. (1) 344 m; (2) 1200 rpm b. (1) 388 m; (2) 1500 rpm d. (1) 299 m; (2) 1000 rpm

Problem 24 (situational) A proposed hydroelectric power plant in Bohol has the following data: Elevation of normal head water…………………………… 200 m Elevation of normal tail water……………………………... 80 m Loss of head due to friction…………………………………. 10 m Turbine discharge at full gate opening…………………. 6.5 m3/sec Turbine efficiency at rated capacity…………………..... 85 % Turbine is directly connected to 60 cycle AC generator.

Problem 24 (situational) A. Determine the effective head of the hydro-electric power plant. a. 80 m c. 110 m b. 99m d. 160 m B. Find the brake power of the turbine in kW. a. 4162 kw c. 5562 kw b. 4962 kw d. 5962 kw

Problem 24 (situational) C. Find the number of poles of the generator if the rotative speed is 900 rpm. a. 2 poles c. 8 poles b. 4 poles d. 10 poles D. Find the kW output of the direct connected generator if the efficiency is 92% a. 5485 kW c. 5584 kW b. 4585 kW d. 4855 kW

Problem 25 (situational) A certain hydro storage plant in Laguna has 18,000 kW rated capacity, with a utilization factor of 70%. For a 2.0 hr peak, determine the hydraulic impoundment of water required, with frictional loss of 4 ft. Dam elevation at 130 ft and hydroelectric turbine elevation of 40 ft and a tail race at elevation 30 ft. Generator efficiency is 90% and a turbine efficiency of 80% and evaporation factor of 25%. Assume that the water is pumped from the low reservoir with friction factor of 10%, pump efficiency of 75% and motor efficiency of 84%. a. 51.3 m3/sec c. 71.3 m3/sec b. 61.3 m3/sec d. 81.3 m3/sec

Problem 25 (situational) A. How many kW-hr is required to pump the water needed to carry the peak? a. 64,911.80 c. 84,911.80 b. 74,911.80 d. 94,911.80 B. What is the overall efficiency of the hydroelectric power plant? a. 15% c. 30% b. 20% d. 38%

Problem 26 If it is desired to use a type of hydraulic turbine whose specific speed is 50 rpm to deliver 150 hp at 150 ft head, what will be the corrected speed of the unit?

a. 1143 rpm b. 1743 rpm

c. 1943 rpm d. 2143 rpm

Problem 27 A hydroelectric power station is to be constructed has an average annual rainfall of 1.5 m. The catchment area is 230 km2 with an available head of 40 m. Only 80% of the rainfall can be collected and ¾ of the impoundment water is available for power. The load factor of the station is 82%. The penstock efficiency is 95%, turbine efficiency is 80%, and generator efficiency is 90%. (1) Calculate the average power that could be generated; and (2) the installed capacity of the power station. a. (1) 2,962 kw; (2) 1,549 kw c. (1) 1,962 kw; (2) 1,949 kw b. (1) 2,762 kw; (2) 2,549 kw d. (1) 1762 kw; (2) 2,149 kw

Problem 28 (situational) An existing hydroelectric power plant has the following data and design: Gross head …………………………………………….. 49.5 ft Mean flow ……………………………………………… 75 ft3/sec Length of penstock ………………………………... 80 ft Penstock diameter …………………………………. 3.5 ft Assumptions: Coefficient of friction …………………………….. 0.020 Turbine efficiency ………………………………….. 88% Generator efficiency ……………………………… 92%

Problem 28 (situational) A. Find the net head in ft used by the turbine. a. 42 c. 49 b. 44 d. 59 B. Find the Hp developed by the turbine. a. 312 c. 367 b. 339 d. 667

Problem 28 (situational) C. Find the standard capacity of synchronous generator. a. 338 hp c. 388 hp b. 358 hp d. 489 hp D. Find the motor rpm assuming 6 poles. a. 900 rpm c. 1800 rpm b. 1200 rpm d. 2200 rpm

Problem 29 A mini-hydropower plant has an available head of 5m. The water flow is 1.25 m3/sec, efficiency of the turbine is 90%, efficiency of the generator is 92%. Determine the maximum output of the generator in kW. a. 29.5 c. 50.7 b. 42.5 d. 69.5

Problem 30 It is desired to develop a 5MW impulse turbine under an effective head of 320 m. The turbine efficiency is 85%. Velocity coefficient of the nozzle is 99%. What should be the wheel diameter assuming it is 12 times the diameter of the jet? a. 1.5 m c. 2.1 m b. 1.8 m d. 2.8 m

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