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In a hydro project, a turbine is mounted in such a way that it acquires a head of 52 m. The water discharge in the feeding penstock with the flow rate of 4000 l/s. If the head loss of 6 m takes place in the penstock and the power of 900 kW is extracted from the turbine, The hydraulic efficiency of the turbine can be considered as 90 %. What should be the residual head loss of the turbine? (Take g = 10 m/s2)
- a)12 m
- b)15 m
- c)21 m
- d)52 m
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
In a hydro project, a turbine is mounted in such a way that it acquire...
Concept:
The power extracted by the turbine,
P = ηh × ρ × Q × g × h - (1)
Now, apply Bernoulli's equation for the turbine,
Where,
H = Available head, h = The head used for the power generation through the turbine, Q = volume flow rate, ηh = the hydraulic efficiency of the turbine, hresidual = Residual head loss at the exit of the turbine, hl,penstock = The head loss in the penstock
Calculation:
Given:
Q = 4000 l/s = 4 m3/s, hl,penstock = 6 m, P = 900 kW, ηh = 90 %, H = 52 m
Using equation (1),
⇒ 900 × 103 = 0.90 × 1000 × 10 × 4 × h
⇒ h = 25 m
Using equation (2),
⇒ 52 = 6 + 25 + hresidual
⇒ hresidual = 21 m
The power extracted by the turbine,
P = ηh × ρ × Q × g × h - (1)
Now, apply Bernoulli's equation for the turbine,
Where,
H = Available head, h = The head used for the power generation through the turbine, Q = volume flow rate, ηh = the hydraulic efficiency of the turbine, hresidual = Residual head loss at the exit of the turbine, hl,penstock = The head loss in the penstock
Calculation:
Given:
Q = 4000 l/s = 4 m3/s, hl,penstock = 6 m, P = 900 kW, ηh = 90 %, H = 52 m
Using equation (1),
⇒ 900 × 103 = 0.90 × 1000 × 10 × 4 × h
⇒ h = 25 m
Using equation (2),
⇒ 52 = 6 + 25 + hresidual
⇒ hresidual = 21 m
Most Upvoted Answer
In a hydro project, a turbine is mounted in such a way that it acquire...
Concept:
The power extracted by the turbine,
P = ηh × ρ × Q × g × h - (1)
Now, apply Bernoulli's equation for the turbine,
Where,
H = Available head, h = The head used for the power generation through the turbine, Q = volume flow rate, ηh = the hydraulic efficiency of the turbine, hresidual = Residual head loss at the exit of the turbine, hl,penstock = The head loss in the penstock
Calculation:
Given:
Q = 4000 l/s = 4 m3/s, hl,penstock = 6 m, P = 900 kW, ηh = 90 %, H = 52 m
Using equation (1),
⇒ 900 × 103 = 0.90 × 1000 × 10 × 4 × h
⇒ h = 25 m
Using equation (2),
⇒ 52 = 6 + 25 + hresidual
⇒ hresidual = 21 m
The power extracted by the turbine,
P = ηh × ρ × Q × g × h - (1)
Now, apply Bernoulli's equation for the turbine,
Where,
H = Available head, h = The head used for the power generation through the turbine, Q = volume flow rate, ηh = the hydraulic efficiency of the turbine, hresidual = Residual head loss at the exit of the turbine, hl,penstock = The head loss in the penstock
Calculation:
Given:
Q = 4000 l/s = 4 m3/s, hl,penstock = 6 m, P = 900 kW, ηh = 90 %, H = 52 m
Using equation (1),
⇒ 900 × 103 = 0.90 × 1000 × 10 × 4 × h
⇒ h = 25 m
Using equation (2),
⇒ 52 = 6 + 25 + hresidual
⇒ hresidual = 21 m
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Community Answer
In a hydro project, a turbine is mounted in such a way that it acquire...
Given:
- Head of the turbine, h = 52 m
- Water discharge in the feeding penstock, Q = 4000 l/s = 4 m³/s
- Head loss in the penstock, h_loss = 6 m
- Power extracted from the turbine, P = 900 kW
- Hydraulic efficiency of the turbine, η = 90%
- Acceleration due to gravity, g = 10 m/s²
To find:
The residual head loss of the turbine.
Solution:
1. Convert the water discharge from liters per second to cubic meters per second:
1 liter = 0.001 cubic meters
Therefore, Q = 4000 * 0.001 = 4 m³/s
2. Calculate the net head available at the turbine:
Net head = Total head - Head loss
Net head = 52 m - 6 m = 46 m
3. Calculate the hydraulic power output of the turbine:
Hydraulic Power = ρ * g * Q * Net head
Where ρ is the density of water.
Assuming the density of water as ρ = 1000 kg/m³,
Hydraulic Power = 1000 * 10 * 4 * 46 = 1840000 W = 1840 kW
4. Calculate the actual power output of the turbine:
Actual Power = Hydraulic Power * Hydraulic Efficiency
Actual Power = 1840 kW * 0.90 = 1656 kW
5. Calculate the residual head loss:
Residual head loss = Total head - Net head
Residual head loss = 52 m - 46 m = 6 m
Therefore, the residual head loss of the turbine is 6 m. Hence, option (c) is correct.
- Head of the turbine, h = 52 m
- Water discharge in the feeding penstock, Q = 4000 l/s = 4 m³/s
- Head loss in the penstock, h_loss = 6 m
- Power extracted from the turbine, P = 900 kW
- Hydraulic efficiency of the turbine, η = 90%
- Acceleration due to gravity, g = 10 m/s²
To find:
The residual head loss of the turbine.
Solution:
1. Convert the water discharge from liters per second to cubic meters per second:
1 liter = 0.001 cubic meters
Therefore, Q = 4000 * 0.001 = 4 m³/s
2. Calculate the net head available at the turbine:
Net head = Total head - Head loss
Net head = 52 m - 6 m = 46 m
3. Calculate the hydraulic power output of the turbine:
Hydraulic Power = ρ * g * Q * Net head
Where ρ is the density of water.
Assuming the density of water as ρ = 1000 kg/m³,
Hydraulic Power = 1000 * 10 * 4 * 46 = 1840000 W = 1840 kW
4. Calculate the actual power output of the turbine:
Actual Power = Hydraulic Power * Hydraulic Efficiency
Actual Power = 1840 kW * 0.90 = 1656 kW
5. Calculate the residual head loss:
Residual head loss = Total head - Net head
Residual head loss = 52 m - 46 m = 6 m
Therefore, the residual head loss of the turbine is 6 m. Hence, option (c) is correct.
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In a hydro project, a turbine is mounted in such a way that it acquires a head of 52 m. The water discharge in the feeding penstock with the flow rate of 4000 l/s. If the head loss of 6 m takes place in the penstock and the power of 900 kW is extracted from the turbine, The hydraulic efficiency of the turbine can be considered as 90 %. What should be the residual head loss of the turbine? (Take g = 10 m/s2)a)12 mb)15 mc)21 md)52 mCorrect answer is option 'C'. Can you explain this answer?
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In a hydro project, a turbine is mounted in such a way that it acquires a head of 52 m. The water discharge in the feeding penstock with the flow rate of 4000 l/s. If the head loss of 6 m takes place in the penstock and the power of 900 kW is extracted from the turbine, The hydraulic efficiency of the turbine can be considered as 90 %. What should be the residual head loss of the turbine? (Take g = 10 m/s2)a)12 mb)15 mc)21 md)52 mCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about In a hydro project, a turbine is mounted in such a way that it acquires a head of 52 m. The water discharge in the feeding penstock with the flow rate of 4000 l/s. If the head loss of 6 m takes place in the penstock and the power of 900 kW is extracted from the turbine, The hydraulic efficiency of the turbine can be considered as 90 %. What should be the residual head loss of the turbine? (Take g = 10 m/s2)a)12 mb)15 mc)21 md)52 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a hydro project, a turbine is mounted in such a way that it acquires a head of 52 m. The water discharge in the feeding penstock with the flow rate of 4000 l/s. If the head loss of 6 m takes place in the penstock and the power of 900 kW is extracted from the turbine, The hydraulic efficiency of the turbine can be considered as 90 %. What should be the residual head loss of the turbine? (Take g = 10 m/s2)a)12 mb)15 mc)21 md)52 mCorrect answer is option 'C'. Can you explain this answer?.
In a hydro project, a turbine is mounted in such a way that it acquires a head of 52 m. The water discharge in the feeding penstock with the flow rate of 4000 l/s. If the head loss of 6 m takes place in the penstock and the power of 900 kW is extracted from the turbine, The hydraulic efficiency of the turbine can be considered as 90 %. What should be the residual head loss of the turbine? (Take g = 10 m/s2)a)12 mb)15 mc)21 md)52 mCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about In a hydro project, a turbine is mounted in such a way that it acquires a head of 52 m. The water discharge in the feeding penstock with the flow rate of 4000 l/s. If the head loss of 6 m takes place in the penstock and the power of 900 kW is extracted from the turbine, The hydraulic efficiency of the turbine can be considered as 90 %. What should be the residual head loss of the turbine? (Take g = 10 m/s2)a)12 mb)15 mc)21 md)52 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a hydro project, a turbine is mounted in such a way that it acquires a head of 52 m. The water discharge in the feeding penstock with the flow rate of 4000 l/s. If the head loss of 6 m takes place in the penstock and the power of 900 kW is extracted from the turbine, The hydraulic efficiency of the turbine can be considered as 90 %. What should be the residual head loss of the turbine? (Take g = 10 m/s2)a)12 mb)15 mc)21 md)52 mCorrect answer is option 'C'. Can you explain this answer?.
Solutions for In a hydro project, a turbine is mounted in such a way that it acquires a head of 52 m. The water discharge in the feeding penstock with the flow rate of 4000 l/s. If the head loss of 6 m takes place in the penstock and the power of 900 kW is extracted from the turbine, The hydraulic efficiency of the turbine can be considered as 90 %. What should be the residual head loss of the turbine? (Take g = 10 m/s2)a)12 mb)15 mc)21 md)52 mCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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