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A large turbine generates a power of 1000 kW under a head of 50 m. A 1/5th model of a hydraulic turbine is tested against a head of 10 m. The power developed (kW) and the discharge flow rate (m3/s) by the model are
- a)10.41, 0.0364
- b)10.41, 2.038
- c)3.578, 2.038
- d)3.578, 0.0364
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A large turbine generates a power of 1000 kW under a head of 50 m. A 1...
Given
Pp = 1000 kW
Hp = 50 m
Pp = ρgQpHp
We know that head coefficient,
and the power coefficient
and distance flow rate, Qm
Pm = ρgQmHm
Most Upvoted Answer
A large turbine generates a power of 1000 kW under a head of 50 m. A 1...
Given:
Large turbine power (P1) = 1000 kW
Large turbine head (H1) = 50 m
Model turbine head (H2) = 10 m
To find:
Power developed by the model turbine (P2)
Discharge flow rate by the model turbine (Q2)
Formula:
The power developed by a turbine is given by the equation:
P = ρ × g × Q × H
Where:
P is the power developed by the turbine
ρ is the density of the fluid
g is the acceleration due to gravity
Q is the discharge flow rate
H is the head
We can rearrange the equation to solve for Q:
Q = P / (ρ × g × H)
Assuming that the density of the fluid and the acceleration due to gravity remain constant, we can use the equation to compare the power and discharge flow rate of the large turbine and the model turbine.
Calculations:
Let's assume the discharge flow rate of the large turbine is Q1.
Using the equation, we can write:
Q1 = P1 / (ρ × g × H1)
Since the model turbine is a 1/5th scale model, the head and the discharge flow rate will be proportional to the large turbine.
Therefore, we can write:
H2 = H1 / 5
Q2 = Q1 / 5
Substituting the values, we get:
H2 = 10 m
Q2 = Q1 / 5
Now, we need to find the values of Q1 and Q2.
Using the equation for the large turbine, we can write:
Q1 = P1 / (ρ × g × H1)
Substituting the given values, we get:
Q1 = 1000 kW / (ρ × g × 50 m)
Similarly, using the equation for the model turbine, we can write:
Q2 = P2 / (ρ × g × H2)
Substituting the given values, we get:
Q2 = P2 / (ρ × g × 10 m)
Since the density of the fluid and the acceleration due to gravity remain constant, we can compare the ratios of Q1 and Q2:
Q2 / Q1 = (P2 / (ρ × g × 10 m)) / (P1 / (ρ × g × 50 m))
Simplifying the equation, we get:
Q2 / Q1 = P2 / P1 * (50 m / 10 m)
Q2 / Q1 = P2 / P1 * 5
Given that Q2 / Q1 = 1/5 (because it is a 1/5th scale model), we can solve for P2:
1/5 = P2 / P1 * 5
P2 = P1 / 25
Substituting the values, we get:
P2 = 1000 kW / 25
P2 = 40 kW
Therefore, the power developed by the model turbine is 40 kW (option D).
Since the discharge flow rate of the model turbine is 1/5th of the large turbine, we can calculate the discharge flow rate:
Q2 = Q1 / 5
Substituting the values, we get:
Q2 = 2.038 m3/s
Therefore, the discharge flow rate of the model turbine is 2
Large turbine power (P1) = 1000 kW
Large turbine head (H1) = 50 m
Model turbine head (H2) = 10 m
To find:
Power developed by the model turbine (P2)
Discharge flow rate by the model turbine (Q2)
Formula:
The power developed by a turbine is given by the equation:
P = ρ × g × Q × H
Where:
P is the power developed by the turbine
ρ is the density of the fluid
g is the acceleration due to gravity
Q is the discharge flow rate
H is the head
We can rearrange the equation to solve for Q:
Q = P / (ρ × g × H)
Assuming that the density of the fluid and the acceleration due to gravity remain constant, we can use the equation to compare the power and discharge flow rate of the large turbine and the model turbine.
Calculations:
Let's assume the discharge flow rate of the large turbine is Q1.
Using the equation, we can write:
Q1 = P1 / (ρ × g × H1)
Since the model turbine is a 1/5th scale model, the head and the discharge flow rate will be proportional to the large turbine.
Therefore, we can write:
H2 = H1 / 5
Q2 = Q1 / 5
Substituting the values, we get:
H2 = 10 m
Q2 = Q1 / 5
Now, we need to find the values of Q1 and Q2.
Using the equation for the large turbine, we can write:
Q1 = P1 / (ρ × g × H1)
Substituting the given values, we get:
Q1 = 1000 kW / (ρ × g × 50 m)
Similarly, using the equation for the model turbine, we can write:
Q2 = P2 / (ρ × g × H2)
Substituting the given values, we get:
Q2 = P2 / (ρ × g × 10 m)
Since the density of the fluid and the acceleration due to gravity remain constant, we can compare the ratios of Q1 and Q2:
Q2 / Q1 = (P2 / (ρ × g × 10 m)) / (P1 / (ρ × g × 50 m))
Simplifying the equation, we get:
Q2 / Q1 = P2 / P1 * (50 m / 10 m)
Q2 / Q1 = P2 / P1 * 5
Given that Q2 / Q1 = 1/5 (because it is a 1/5th scale model), we can solve for P2:
1/5 = P2 / P1 * 5
P2 = P1 / 25
Substituting the values, we get:
P2 = 1000 kW / 25
P2 = 40 kW
Therefore, the power developed by the model turbine is 40 kW (option D).
Since the discharge flow rate of the model turbine is 1/5th of the large turbine, we can calculate the discharge flow rate:
Q2 = Q1 / 5
Substituting the values, we get:
Q2 = 2.038 m3/s
Therefore, the discharge flow rate of the model turbine is 2
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A large turbine generates a power of 1000 kW under a head of 50 m. A 1/5th model of a hydraulic turbine is tested against a head of 10 m. The power developed (kW) and the discharge flow rate (m3/s) by the model area)10.41, 0.0364b)10.41, 2.038c)3.578, 2.038d)3.578, 0.0364Correct answer is option 'D'. Can you explain this answer?
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A large turbine generates a power of 1000 kW under a head of 50 m. A 1/5th model of a hydraulic turbine is tested against a head of 10 m. The power developed (kW) and the discharge flow rate (m3/s) by the model area)10.41, 0.0364b)10.41, 2.038c)3.578, 2.038d)3.578, 0.0364Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A large turbine generates a power of 1000 kW under a head of 50 m. A 1/5th model of a hydraulic turbine is tested against a head of 10 m. The power developed (kW) and the discharge flow rate (m3/s) by the model area)10.41, 0.0364b)10.41, 2.038c)3.578, 2.038d)3.578, 0.0364Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A large turbine generates a power of 1000 kW under a head of 50 m. A 1/5th model of a hydraulic turbine is tested against a head of 10 m. The power developed (kW) and the discharge flow rate (m3/s) by the model area)10.41, 0.0364b)10.41, 2.038c)3.578, 2.038d)3.578, 0.0364Correct answer is option 'D'. Can you explain this answer?.
A large turbine generates a power of 1000 kW under a head of 50 m. A 1/5th model of a hydraulic turbine is tested against a head of 10 m. The power developed (kW) and the discharge flow rate (m3/s) by the model area)10.41, 0.0364b)10.41, 2.038c)3.578, 2.038d)3.578, 0.0364Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A large turbine generates a power of 1000 kW under a head of 50 m. A 1/5th model of a hydraulic turbine is tested against a head of 10 m. The power developed (kW) and the discharge flow rate (m3/s) by the model area)10.41, 0.0364b)10.41, 2.038c)3.578, 2.038d)3.578, 0.0364Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A large turbine generates a power of 1000 kW under a head of 50 m. A 1/5th model of a hydraulic turbine is tested against a head of 10 m. The power developed (kW) and the discharge flow rate (m3/s) by the model area)10.41, 0.0364b)10.41, 2.038c)3.578, 2.038d)3.578, 0.0364Correct answer is option 'D'. Can you explain this answer?.
Solutions for A large turbine generates a power of 1000 kW under a head of 50 m. A 1/5th model of a hydraulic turbine is tested against a head of 10 m. The power developed (kW) and the discharge flow rate (m3/s) by the model area)10.41, 0.0364b)10.41, 2.038c)3.578, 2.038d)3.578, 0.0364Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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