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A Kaplan turbine has a runner of diameter 4.0 m. The diameter of the hub is 1.6 m. If the velocity of flow and the swirl velocity at the inlet side of the blade at the hub are 6.0 m/s and 10.0 m/s, respectively, the flow and swirl velocities at the inlet side of the tip are, respectively:
- a)15.0 m/s and 10.0 m/s
- b)6.0 m/s and 25.0 m/s
- c)6.0 m/s and 4.0 m/s
- d)2.5 m/s and 10.0 m/s
Correct answer is option 'C'. Can you explain this answer?
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A Kaplan turbine has a runner of diameter 4.0 m. The diameter of the ...
Since the area of flow remains the same.
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The flow velocity remains the same throughout.
Hence Vf2 = Vf1 = 6 m/s
D1 = 1.6; D2 = 4; u2 = 10m/s
Hence u1 = 4 m/s
Most Upvoted Answer
A Kaplan turbine has a runner of diameter 4.0 m. The diameter of the ...
Solution:
Given,
Diameter of the runner = 4.0 m
Diameter of the hub = 1.6 m
Velocity of flow at the inlet side of the hub = 6.0 m/s
Swirl velocity at the inlet side of the hub = 10.0 m/s
To find:
The flow and swirl velocities at the inlet side of the tip.
Approach:
1. Use the continuity equation to find the velocity of flow at the tip.
2. Use the principle of conservation of angular momentum to find the swirl velocity at the tip.
HTML bold tag:
Continuity equation:
The continuity equation states that the mass flow rate through any cross-section of the runner remains constant.
mass flow rate = ρAv
where
ρ = density of the fluid
A = area of cross-section
v = velocity of flow
The area of cross-section of the runner at the hub and tip can be assumed to be circular.
Area of cross-section at the hub = πDh²/4
Area of cross-section at the tip = πDt²/4
where
Dh = diameter of the hub
Dt = diameter of the tip
Using the continuity equation,
ρAv = ρAv'
where
A = πDh²/4
v = 6.0 m/s (given)
v' = velocity of flow at the tip
v' = (Dh/Dt)²v
v' = (1.6/4.0)²(6.0)
v' = 1.44 m/s
Therefore, the velocity of flow at the inlet side of the tip is 1.44 m/s.
Principle of conservation of angular momentum:
The principle of conservation of angular momentum states that the sum of the angular momentum of a fluid element and the angular momentum of the runner remains constant.
ρπD²h/4(vr + vθ)Dh/2 = ρπD²t/4(vr' + vθ')Dt/2
where
vr = radial velocity at the hub
vθ = tangential velocity at the hub
vr' = radial velocity at the tip
vθ' = tangential velocity at the tip
At the hub, the fluid enters the runner with a swirl velocity of 10.0 m/s. However, at the tip, the fluid should exit with no swirl velocity (i.e., vθ' = 0). Therefore, the change in swirl velocity should take place only due to the change in radius.
vr' = vr(Dh/Dt)
vθ' = vθ(Dh/Dt) + (Dt/2 - Dh/2)(vr/Dh)
Substituting the given values,
vr' = 10.0(1.6/4.0)
vr' = 4.0 m/s
vθ' = 10.0(1.6/4.0) + (4.0/2 - 1.6/2)(6.0/1.6)
vθ' = 6.0 m/s
Therefore, the
Given,
Diameter of the runner = 4.0 m
Diameter of the hub = 1.6 m
Velocity of flow at the inlet side of the hub = 6.0 m/s
Swirl velocity at the inlet side of the hub = 10.0 m/s
To find:
The flow and swirl velocities at the inlet side of the tip.
Approach:
1. Use the continuity equation to find the velocity of flow at the tip.
2. Use the principle of conservation of angular momentum to find the swirl velocity at the tip.
HTML bold tag:
Continuity equation:
The continuity equation states that the mass flow rate through any cross-section of the runner remains constant.
mass flow rate = ρAv
where
ρ = density of the fluid
A = area of cross-section
v = velocity of flow
The area of cross-section of the runner at the hub and tip can be assumed to be circular.
Area of cross-section at the hub = πDh²/4
Area of cross-section at the tip = πDt²/4
where
Dh = diameter of the hub
Dt = diameter of the tip
Using the continuity equation,
ρAv = ρAv'
where
A = πDh²/4
v = 6.0 m/s (given)
v' = velocity of flow at the tip
v' = (Dh/Dt)²v
v' = (1.6/4.0)²(6.0)
v' = 1.44 m/s
Therefore, the velocity of flow at the inlet side of the tip is 1.44 m/s.
Principle of conservation of angular momentum:
The principle of conservation of angular momentum states that the sum of the angular momentum of a fluid element and the angular momentum of the runner remains constant.
ρπD²h/4(vr + vθ)Dh/2 = ρπD²t/4(vr' + vθ')Dt/2
where
vr = radial velocity at the hub
vθ = tangential velocity at the hub
vr' = radial velocity at the tip
vθ' = tangential velocity at the tip
At the hub, the fluid enters the runner with a swirl velocity of 10.0 m/s. However, at the tip, the fluid should exit with no swirl velocity (i.e., vθ' = 0). Therefore, the change in swirl velocity should take place only due to the change in radius.
vr' = vr(Dh/Dt)
vθ' = vθ(Dh/Dt) + (Dt/2 - Dh/2)(vr/Dh)
Substituting the given values,
vr' = 10.0(1.6/4.0)
vr' = 4.0 m/s
vθ' = 10.0(1.6/4.0) + (4.0/2 - 1.6/2)(6.0/1.6)
vθ' = 6.0 m/s
Therefore, the
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A Kaplan turbine has a runner of diameter 4.0 m. The diameter of the hub is 1.6 m. If the velocity of flow and the swirl velocity at the inlet side of the blade at the hub are 6.0 m/s and 10.0 m/s, respectively, the flow and swirl velocities at the inlet side of the tip are, respectively:a)15.0 m/s and 10.0 m/sb)6.0 m/s and 25.0 m/sc)6.0 m/s and 4.0 m/sd)2.5 m/s and 10.0 m/sCorrect answer is option 'C'. Can you explain this answer?
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A Kaplan turbine has a runner of diameter 4.0 m. The diameter of the hub is 1.6 m. If the velocity of flow and the swirl velocity at the inlet side of the blade at the hub are 6.0 m/s and 10.0 m/s, respectively, the flow and swirl velocities at the inlet side of the tip are, respectively:a)15.0 m/s and 10.0 m/sb)6.0 m/s and 25.0 m/sc)6.0 m/s and 4.0 m/sd)2.5 m/s and 10.0 m/sCorrect answer is option 'C'. 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 Kaplan turbine has a runner of diameter 4.0 m. The diameter of the hub is 1.6 m. If the velocity of flow and the swirl velocity at the inlet side of the blade at the hub are 6.0 m/s and 10.0 m/s, respectively, the flow and swirl velocities at the inlet side of the tip are, respectively:a)15.0 m/s and 10.0 m/sb)6.0 m/s and 25.0 m/sc)6.0 m/s and 4.0 m/sd)2.5 m/s and 10.0 m/sCorrect answer is option 'C'. 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 Kaplan turbine has a runner of diameter 4.0 m. The diameter of the hub is 1.6 m. If the velocity of flow and the swirl velocity at the inlet side of the blade at the hub are 6.0 m/s and 10.0 m/s, respectively, the flow and swirl velocities at the inlet side of the tip are, respectively:a)15.0 m/s and 10.0 m/sb)6.0 m/s and 25.0 m/sc)6.0 m/s and 4.0 m/sd)2.5 m/s and 10.0 m/sCorrect answer is option 'C'. Can you explain this answer?.
A Kaplan turbine has a runner of diameter 4.0 m. The diameter of the hub is 1.6 m. If the velocity of flow and the swirl velocity at the inlet side of the blade at the hub are 6.0 m/s and 10.0 m/s, respectively, the flow and swirl velocities at the inlet side of the tip are, respectively:a)15.0 m/s and 10.0 m/sb)6.0 m/s and 25.0 m/sc)6.0 m/s and 4.0 m/sd)2.5 m/s and 10.0 m/sCorrect answer is option 'C'. 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 Kaplan turbine has a runner of diameter 4.0 m. The diameter of the hub is 1.6 m. If the velocity of flow and the swirl velocity at the inlet side of the blade at the hub are 6.0 m/s and 10.0 m/s, respectively, the flow and swirl velocities at the inlet side of the tip are, respectively:a)15.0 m/s and 10.0 m/sb)6.0 m/s and 25.0 m/sc)6.0 m/s and 4.0 m/sd)2.5 m/s and 10.0 m/sCorrect answer is option 'C'. 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 Kaplan turbine has a runner of diameter 4.0 m. The diameter of the hub is 1.6 m. If the velocity of flow and the swirl velocity at the inlet side of the blade at the hub are 6.0 m/s and 10.0 m/s, respectively, the flow and swirl velocities at the inlet side of the tip are, respectively:a)15.0 m/s and 10.0 m/sb)6.0 m/s and 25.0 m/sc)6.0 m/s and 4.0 m/sd)2.5 m/s and 10.0 m/sCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A Kaplan turbine has a runner of diameter 4.0 m. The diameter of the hub is 1.6 m. If the velocity of flow and the swirl velocity at the inlet side of the blade at the hub are 6.0 m/s and 10.0 m/s, respectively, the flow and swirl velocities at the inlet side of the tip are, respectively:a)15.0 m/s and 10.0 m/sb)6.0 m/s and 25.0 m/sc)6.0 m/s and 4.0 m/sd)2.5 m/s and 10.0 m/sCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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A Kaplan turbine has a runner of diameter 4.0 m. The diameter of the hub is 1.6 m. If the velocity of flow and the swirl velocity at the inlet side of the blade at the hub are 6.0 m/s and 10.0 m/s, respectively, the flow and swirl velocities at the inlet side of the tip are, respectively:a)15.0 m/s and 10.0 m/sb)6.0 m/s and 25.0 m/sc)6.0 m/s and 4.0 m/sd)2.5 m/s and 10.0 m/sCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A Kaplan turbine has a runner of diameter 4.0 m. The diameter of the hub is 1.6 m. If the velocity of flow and the swirl velocity at the inlet side of the blade at the hub are 6.0 m/s and 10.0 m/s, respectively, the flow and swirl velocities at the inlet side of the tip are, respectively:a)15.0 m/s and 10.0 m/sb)6.0 m/s and 25.0 m/sc)6.0 m/s and 4.0 m/sd)2.5 m/s and 10.0 m/sCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A Kaplan turbine has a runner of diameter 4.0 m. The diameter of the hub is 1.6 m. If the velocity of flow and the swirl velocity at the inlet side of the blade at the hub are 6.0 m/s and 10.0 m/s, respectively, the flow and swirl velocities at the inlet side of the tip are, respectively:a)15.0 m/s and 10.0 m/sb)6.0 m/s and 25.0 m/sc)6.0 m/s and 4.0 m/sd)2.5 m/s and 10.0 m/sCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A Kaplan turbine has a runner of diameter 4.0 m. The diameter of the hub is 1.6 m. If the velocity of flow and the swirl velocity at the inlet side of the blade at the hub are 6.0 m/s and 10.0 m/s, respectively, the flow and swirl velocities at the inlet side of the tip are, respectively:a)15.0 m/s and 10.0 m/sb)6.0 m/s and 25.0 m/sc)6.0 m/s and 4.0 m/sd)2.5 m/s and 10.0 m/sCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice GATE tests.
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