Wheel Efficiency of Pelton Turbine Solution

STEP 0: Pre-Calculation Summary
Formula Used
Wheel Efficiency of Pelton Turbine = (2*(1+K Factor for Pelton*cos(Outlet Bucket Angle of Pelton))*(Velocity of Pelton Jet-Bucket Velocity of Pelton Turbine)*Bucket Velocity of Pelton Turbine)/(Velocity of Pelton Jet^2)
ηw = (2*(1+k*cos(β2))*(V1-U)*U)/(V1^2)
This formula uses 1 Functions, 5 Variables
Functions Used
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
Variables Used
Wheel Efficiency of Pelton Turbine - The Wheel Efficiency of Pelton Turbine is the ratio of the power developed to the available power.
K Factor for Pelton - K Factor for Pelton is the ratio of the outlet relative velocity to the inlet relative velocity.
Outlet Bucket Angle of Pelton - (Measured in Radian) - Outlet Bucket Angle of Pelton is the angle the bucket makes with the relative velocity at the outlet.
Velocity of Pelton Jet - (Measured in Meter per Second) - The velocity of Pelton jet is a vector quantity and is given as the rate of change of displacement.
Bucket Velocity of Pelton Turbine - (Measured in Meter per Second) - Bucket velocity of Pelton turbine is a vector quantity and is quantified as the rate of displacement.
STEP 1: Convert Input(s) to Base Unit
K Factor for Pelton: 0.95 --> No Conversion Required
Outlet Bucket Angle of Pelton: 20 Degree --> 0.3490658503988 Radian (Check conversion here)
Velocity of Pelton Jet: 28 Meter per Second --> 28 Meter per Second No Conversion Required
Bucket Velocity of Pelton Turbine: 14.73 Meter per Second --> 14.73 Meter per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ηw = (2*(1+k*cos(β2))*(V1-U)*U)/(V1^2) --> (2*(1+0.95*cos(0.3490658503988))*(28-14.73)*14.73)/(28^2)
Evaluating ... ...
ηw = 0.943780974241338
STEP 3: Convert Result to Output's Unit
0.943780974241338 --> No Conversion Required
FINAL ANSWER
0.943780974241338 0.943781 <-- Wheel Efficiency of Pelton Turbine
(Calculation completed in 00.004 seconds)

Credits

Created by Suman Ray Pramanik
Indian Institute of Technology (IIT), Kanpur
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National Institute Of Technology (NIT), Hamirpur
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14 Pelton Turbine Calculators

Power of Pelton Turbine given Velocity
Go Power of Pelton Turbine = (1+K Factor for Pelton*cos(Outlet Bucket Angle of Pelton))*Mass Density*Volume Flow Rate for Pelton Turbine*Bucket Velocity of Pelton Turbine*(Velocity of Pelton Jet-Bucket Velocity of Pelton Turbine)
Wheel Efficiency of Pelton Turbine
Go Wheel Efficiency of Pelton Turbine = (2*(1+K Factor for Pelton*cos(Outlet Bucket Angle of Pelton))*(Velocity of Pelton Jet-Bucket Velocity of Pelton Turbine)*Bucket Velocity of Pelton Turbine)/(Velocity of Pelton Jet^2)
Power of Pelton Turbine
Go Power of Pelton Turbine = (1+K Factor for Pelton*cos(Outlet Bucket Angle of Pelton))*Mass Density*Volume Flow Rate for Pelton Turbine*Bucket Velocity of Pelton Turbine*Inlet Relative Velocity of Pelton Turbine
Energy per Unit Mass of Pelton Turbine
Go Energy per Unit Mass of Pelton Turbine = (Inlet Relative Velocity of Pelton Turbine+Outlet Relative Velocity of Pelton*cos(Outlet Bucket Angle of Pelton))*Bucket Velocity of Pelton Turbine
Tangential Component of Outlet Velocity in Pelton Turbine
Go Tangential Outlet Velocity of Pelton = Bucket Velocity of Pelton Turbine-Outlet Relative Velocity of Pelton*cos(Outlet Bucket Angle of Pelton)
Wheel Efficiency of Pelton Turbine given Power
Go Wheel Efficiency of Pelton Turbine = (2*Power of Pelton Turbine)/(Mass Density*Volume Flow Rate for Pelton Turbine*Velocity of Pelton Jet^2)
Energy per Unit Mass of Pelton
Go Energy per Unit Mass of Pelton = (Tangential Inlet Velocity of Pelton-Tangential Outlet Velocity of Pelton)*Bucket Velocity of Pelton Turbine
Coefficient of Velocity for Pelton Wheel
Go Coefficient of Velocity for Pelton = Velocity of Pelton Jet/sqrt(2*[g]*Pelton Head)
Absolute Velocity of Pelton Jet
Go Velocity of Pelton Jet = Coefficient of Velocity for Pelton*sqrt(2*[g]*Pelton Head)
Pelton Head
Go Pelton Head = Velocity of Pelton Jet^2/(2*[g]*Coefficient of Velocity for Pelton^2)
Tangential Component of Inlet Velocity in Pelton Turbine
Go Tangential Inlet Velocity of Pelton = Inlet Relative Velocity of Pelton Turbine+Bucket Velocity of Pelton Turbine
Inlet Relative Velocity of Pelton
Go Inlet Relative Velocity of Pelton Turbine = Velocity of Pelton Jet-Bucket Velocity of Pelton Turbine
Bucket Velocity of Pelton Turbine
Go Bucket Velocity of Pelton Turbine = Velocity of Pelton Jet-Inlet Relative Velocity of Pelton Turbine
Outlet Relative Velocity of Pelton
Go Outlet Relative Velocity of Pelton = K Factor for Pelton*Inlet Relative Velocity of Pelton Turbine

Wheel Efficiency of Pelton Turbine Formula

Wheel Efficiency of Pelton Turbine = (2*(1+K Factor for Pelton*cos(Outlet Bucket Angle of Pelton))*(Velocity of Pelton Jet-Bucket Velocity of Pelton Turbine)*Bucket Velocity of Pelton Turbine)/(Velocity of Pelton Jet^2)
ηw = (2*(1+k*cos(β2))*(V1-U)*U)/(V1^2)

What is wheel efficiency?

The wheel efficiency of a Pelton turbine is the ratio of the power developed to the available power. For a Pelton turbine, it is given as the ratio of the power transmitted by the fluid to the power input to the wheel.

How to Calculate Wheel Efficiency of Pelton Turbine?

Wheel Efficiency of Pelton Turbine calculator uses Wheel Efficiency of Pelton Turbine = (2*(1+K Factor for Pelton*cos(Outlet Bucket Angle of Pelton))*(Velocity of Pelton Jet-Bucket Velocity of Pelton Turbine)*Bucket Velocity of Pelton Turbine)/(Velocity of Pelton Jet^2) to calculate the Wheel Efficiency of Pelton Turbine, The wheel efficiency of Pelton turbine is the ratio of the power developed to the available power. Wheel Efficiency of Pelton Turbine is denoted by ηw symbol.

How to calculate Wheel Efficiency of Pelton Turbine using this online calculator? To use this online calculator for Wheel Efficiency of Pelton Turbine, enter K Factor for Pelton (k), Outlet Bucket Angle of Pelton 2), Velocity of Pelton Jet (V1) & Bucket Velocity of Pelton Turbine (U) and hit the calculate button. Here is how the Wheel Efficiency of Pelton Turbine calculation can be explained with given input values -> 0.943781 = (2*(1+0.95*cos(0.3490658503988))*(28-14.73)*14.73)/(28^2).

FAQ

What is Wheel Efficiency of Pelton Turbine?
The wheel efficiency of Pelton turbine is the ratio of the power developed to the available power and is represented as ηw = (2*(1+k*cos(β2))*(V1-U)*U)/(V1^2) or Wheel Efficiency of Pelton Turbine = (2*(1+K Factor for Pelton*cos(Outlet Bucket Angle of Pelton))*(Velocity of Pelton Jet-Bucket Velocity of Pelton Turbine)*Bucket Velocity of Pelton Turbine)/(Velocity of Pelton Jet^2). K Factor for Pelton is the ratio of the outlet relative velocity to the inlet relative velocity, Outlet Bucket Angle of Pelton is the angle the bucket makes with the relative velocity at the outlet, The velocity of Pelton jet is a vector quantity and is given as the rate of change of displacement & Bucket velocity of Pelton turbine is a vector quantity and is quantified as the rate of displacement.
How to calculate Wheel Efficiency of Pelton Turbine?
The wheel efficiency of Pelton turbine is the ratio of the power developed to the available power is calculated using Wheel Efficiency of Pelton Turbine = (2*(1+K Factor for Pelton*cos(Outlet Bucket Angle of Pelton))*(Velocity of Pelton Jet-Bucket Velocity of Pelton Turbine)*Bucket Velocity of Pelton Turbine)/(Velocity of Pelton Jet^2). To calculate Wheel Efficiency of Pelton Turbine, you need K Factor for Pelton (k), Outlet Bucket Angle of Pelton 2), Velocity of Pelton Jet (V1) & Bucket Velocity of Pelton Turbine (U). With our tool, you need to enter the respective value for K Factor for Pelton, Outlet Bucket Angle of Pelton, Velocity of Pelton Jet & Bucket Velocity of Pelton Turbine and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Wheel Efficiency of Pelton Turbine?
In this formula, Wheel Efficiency of Pelton Turbine uses K Factor for Pelton, Outlet Bucket Angle of Pelton, Velocity of Pelton Jet & Bucket Velocity of Pelton Turbine. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Wheel Efficiency of Pelton Turbine = (2*Power of Pelton Turbine)/(Mass Density*Volume Flow Rate for Pelton Turbine*Velocity of Pelton Jet^2)
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