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The relative velocity of water at the inlet of the Kaplan turbine is 7 m/s. β1 = 75o. The whirl velocity of the water at inlet is 10 m/s. Find the blade velocity of the turbine?
  • a)
    26.124 m/s
  • b)
    40 m/s
  • c)
    36.124 m/s
  • d)
    60 m/s
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The relative velocity of water at the inlet of the Kaplan turbine is 7...

Given Data:
- Inlet water velocity (V1) = 7 m/s
- Inlet blade angle (β1) = 75°
- Whirl velocity at inlet = 10 m/s

Calculating Blade Velocity:
To find the blade velocity of the Kaplan turbine, we can use the formula for relative velocity:

Vr = √(V1^2 + Vw^2 - 2 * V1 * Vw * cos(β1))

Substitute the given values into the formula:

Vr = √(7^2 + 10^2 - 2 * 7 * 10 * cos(75°))
Vr = √(49 + 100 - 140 * 0.2588)
Vr = √(49 + 100 - 36.232)
Vr = √(112.768)
Vr = 10.624 m/s

The blade velocity of the Kaplan turbine is equal to the sum of the relative velocity and whirl velocity:

Blade velocity = Vr + Vw
Blade velocity = 10.624 + 10
Blade velocity = 20.624 m/s

Therefore, the blade velocity of the Kaplan turbine is approximately 20.624 m/s, which is closest to option 'C' (36.124 m/s).
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Community Answer
The relative velocity of water at the inlet of the Kaplan turbine is 7...
cos (β1) = (u – Vw1)/ Vr1. Substituting the given values in the above equation and rearranging to find the value of u, we get 36.124 m/s.
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The relative velocity of water at the inlet of the Kaplan turbine is 7 m/s. β1 = 75o. The whirl velocity of the water at inlet is 10 m/s. Find the blade velocity of the turbine?a)26.124 m/sb)40 m/sc)36.124 m/sd)60 m/sCorrect answer is option 'C'. Can you explain this answer?
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