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Water falls from a height 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy how much power is generated by the turbine?
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Water falls from a height 60 m at the rate of 15 kg/s to operate a tur...
Power generated by the turbine is,
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Introduction
To calculate the power generated by the turbine, we need to find the potential energy of the falling water and account for the energy losses due to friction.
1. Potential Energy Calculation
- The potential energy (PE) of water falling from a height can be calculated using the formula:
PE = m × g × h
Where:
- m = mass flow rate (kg/s)
- g = acceleration due to gravity (approximately 9.81 m/s²)
- h = height (m)
- Given:
- m = 15 kg/s
- h = 60 m
- Calculation:
PE = 15 kg/s × 9.81 m/s² × 60 m
PE = 8829 J/s or Watts (since 1 J/s = 1 W)
2. Accounting for Energy Losses
- The energy losses due to frictional forces are 10% of the potential energy. Therefore, the usable energy is:
Usable Energy = PE - (0.10 × PE)
Usable Energy = 8829 W - (0.10 × 8829 W)
Usable Energy = 8829 W - 882.9 W
Usable Energy = 7946.1 W
3. Power Generated by the Turbine
- The power generated by the turbine, accounting for losses, is approximately:
Power = 7946.1 W
This indicates that the turbine can generate around 7946 Watts or approximately 7.95 kW of power, after factoring in the friction losses.
To calculate the power generated by the turbine, we need to find the potential energy of the falling water and account for the energy losses due to friction.
1. Potential Energy Calculation
- The potential energy (PE) of water falling from a height can be calculated using the formula:
PE = m × g × h
Where:
- m = mass flow rate (kg/s)
- g = acceleration due to gravity (approximately 9.81 m/s²)
- h = height (m)
- Given:
- m = 15 kg/s
- h = 60 m
- Calculation:
PE = 15 kg/s × 9.81 m/s² × 60 m
PE = 8829 J/s or Watts (since 1 J/s = 1 W)
2. Accounting for Energy Losses
- The energy losses due to frictional forces are 10% of the potential energy. Therefore, the usable energy is:
Usable Energy = PE - (0.10 × PE)
Usable Energy = 8829 W - (0.10 × 8829 W)
Usable Energy = 8829 W - 882.9 W
Usable Energy = 7946.1 W
3. Power Generated by the Turbine
- The power generated by the turbine, accounting for losses, is approximately:
Power = 7946.1 W
This indicates that the turbine can generate around 7946 Watts or approximately 7.95 kW of power, after factoring in the friction losses.
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Water falls from a height 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy how much power is generated by the turbine?
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Water falls from a height 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy how much power is generated by the turbine? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Water falls from a height 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy how much power is generated by the turbine? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water falls from a height 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy how much power is generated by the turbine?.
Water falls from a height 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy how much power is generated by the turbine? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Water falls from a height 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy how much power is generated by the turbine? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water falls from a height 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy how much power is generated by the turbine?.
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