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A turbine develops 900 kW when running at 200 r.p.m. The head on the turbine is 30 m. If the head on the turbine is reduced to 18 m, determine the speed of the turbine (in rpm).
Correct answer is between '154,155'. Can you explain this answer?
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A turbine develops 900 kW when running at 200 r.p.m. The head on the t...
Solution:
Given:
Power developed by the turbine, P1 = 900 kW
Speed of the turbine, N1 = 200 rpm
Head on the turbine, H1 = 30 m
New head on the turbine, H2 = 18 m
To find: Speed of the turbine, N2
Assumptions:
The turbine is operating under Francis Turbine conditions.
The change in head does not affect the efficiency of the turbine.
Formulae:
The formula to find the power developed by the turbine is given by:
P = γQH
Where,
P is the power developed by the turbine
γ is the specific weight of the fluid (taken as 9810 N/m3 for water)
Q is the discharge through the turbine
H is the head on the turbine
The specific speed of the turbine is given by:
N_s = N√Q/H^(3/4)
Where,
N is the speed of the turbine
Q is the discharge through the turbine
H is the head on the turbine
Calculation:
From the given data, we can find the discharge through the turbine for the given power and head as follows:
P1 = γQ1H1
900 × 10^3 = 9810 × Q1 × 30
Q1 = 3.06 m3/s
Using the specific speed formula, we get:
N_s1 = N1√(Q1/H1^(3/4))
200 = N1 √(3.06/30^(3/4))
N1 = 168.67 rpm
Now, using the discharge formula, we can find the discharge through the turbine for the new head as follows:
Q2 = Q1(H2/H1)
Q2 = 3.06(18/30)
Q2 = 1.84 m3/s
Using the specific speed formula, we get:
N_s2 = N2√(Q2/H2^(3/4))
N_s2 = N1√(Q2/H2^(3/4))
N2 = (N_s2/N_s1)² × N1
N2 = (18/30)^(3/4) × 200
N2 = 154.3 rpm
Therefore, the speed of the turbine is 154.3 rpm (rounded to the nearest integer).
Conclusion:
The speed of the turbine when the head is reduced from 30 m to 18 m is 154.3 rpm (rounded to the nearest integer).
Given:
Power developed by the turbine, P1 = 900 kW
Speed of the turbine, N1 = 200 rpm
Head on the turbine, H1 = 30 m
New head on the turbine, H2 = 18 m
To find: Speed of the turbine, N2
Assumptions:
The turbine is operating under Francis Turbine conditions.
The change in head does not affect the efficiency of the turbine.
Formulae:
The formula to find the power developed by the turbine is given by:
P = γQH
Where,
P is the power developed by the turbine
γ is the specific weight of the fluid (taken as 9810 N/m3 for water)
Q is the discharge through the turbine
H is the head on the turbine
The specific speed of the turbine is given by:
N_s = N√Q/H^(3/4)
Where,
N is the speed of the turbine
Q is the discharge through the turbine
H is the head on the turbine
Calculation:
From the given data, we can find the discharge through the turbine for the given power and head as follows:
P1 = γQ1H1
900 × 10^3 = 9810 × Q1 × 30
Q1 = 3.06 m3/s
Using the specific speed formula, we get:
N_s1 = N1√(Q1/H1^(3/4))
200 = N1 √(3.06/30^(3/4))
N1 = 168.67 rpm
Now, using the discharge formula, we can find the discharge through the turbine for the new head as follows:
Q2 = Q1(H2/H1)
Q2 = 3.06(18/30)
Q2 = 1.84 m3/s
Using the specific speed formula, we get:
N_s2 = N2√(Q2/H2^(3/4))
N_s2 = N1√(Q2/H2^(3/4))
N2 = (N_s2/N_s1)² × N1
N2 = (18/30)^(3/4) × 200
N2 = 154.3 rpm
Therefore, the speed of the turbine is 154.3 rpm (rounded to the nearest integer).
Conclusion:
The speed of the turbine when the head is reduced from 30 m to 18 m is 154.3 rpm (rounded to the nearest integer).
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A turbine develops 900 kW when running at 200 r.p.m. The head on the turbine is 30 m. If the head on the turbine is reduced to 18 m, determine the speed of the turbine (in rpm).Correct answer is between '154,155'. Can you explain this answer?
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A turbine develops 900 kW when running at 200 r.p.m. The head on the turbine is 30 m. If the head on the turbine is reduced to 18 m, determine the speed of the turbine (in rpm).Correct answer is between '154,155'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A turbine develops 900 kW when running at 200 r.p.m. The head on the turbine is 30 m. If the head on the turbine is reduced to 18 m, determine the speed of the turbine (in rpm).Correct answer is between '154,155'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A turbine develops 900 kW when running at 200 r.p.m. The head on the turbine is 30 m. If the head on the turbine is reduced to 18 m, determine the speed of the turbine (in rpm).Correct answer is between '154,155'. Can you explain this answer?.
A turbine develops 900 kW when running at 200 r.p.m. The head on the turbine is 30 m. If the head on the turbine is reduced to 18 m, determine the speed of the turbine (in rpm).Correct answer is between '154,155'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A turbine develops 900 kW when running at 200 r.p.m. The head on the turbine is 30 m. If the head on the turbine is reduced to 18 m, determine the speed of the turbine (in rpm).Correct answer is between '154,155'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A turbine develops 900 kW when running at 200 r.p.m. The head on the turbine is 30 m. If the head on the turbine is reduced to 18 m, determine the speed of the turbine (in rpm).Correct answer is between '154,155'. Can you explain this answer?.
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