Energy per Unit Mass of Pelton Turbine Solution

STEP 0: Pre-Calculation Summary
Formula Used
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
Em = (Vr1+Vr2*cos(β2))*U
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
Energy per Unit Mass of Pelton Turbine - (Measured in Joule per Kilogram) - Energy per Unit Mass of Pelton Turbine is the rate of energy transfer per unit mass to the fluid through the rotor.
Inlet Relative Velocity of Pelton Turbine - (Measured in Meter per Second) - The Inlet Relative Velocity of Pelton Turbine is a vector quantity and is quantified as the rate of displacement.
Outlet Relative Velocity of Pelton - (Measured in Meter per Second) - Outlet Relative Velocity of Pelton is a vector quantity and is quantified as the rate of displacement.
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.
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
Inlet Relative Velocity of Pelton Turbine: 13.27 Meter per Second --> 13.27 Meter per Second No Conversion Required
Outlet Relative Velocity of Pelton: 12.6 Meter per Second --> 12.6 Meter per Second No Conversion Required
Outlet Bucket Angle of Pelton: 20 Degree --> 0.3490658503988 Radian (Check conversion here)
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
Em = (Vr1+Vr2*cos(β2))*U --> (13.27+12.6*cos(0.3490658503988))*14.73
Evaluating ... ...
Em = 369.872171032627
STEP 3: Convert Result to Output's Unit
369.872171032627 Joule per Kilogram -->369.872171032627 Square Meter per Square Second (Check conversion here)
FINAL ANSWER
369.872171032627 369.8722 Square Meter per Square Second <-- Energy per Unit Mass of Pelton Turbine
(Calculation completed in 00.004 seconds)

Credits

Created by Suman Ray Pramanik
Indian Institute of Technology (IIT), Kanpur
Suman Ray Pramanik has created this Calculator and 50+ more calculators!
Verified by Anshika Arya
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

Energy per Unit Mass of Pelton Turbine Formula

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
Em = (Vr1+Vr2*cos(β2))*U

How to calculate the energy per unit of a mass of a Pelton wheel?

A Pelton wheel is an impulse type water turbine. Energy per unit mass of the Pelton turbine is the rate of energy transfer per unit mass to the fluid through the rotor. it is calculated using the relative velocities, outlet bucket angle, and bucket velocity.

How to Calculate Energy per Unit Mass of Pelton Turbine?

Energy per Unit Mass of Pelton Turbine calculator uses 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 to calculate the Energy per Unit Mass of Pelton Turbine, Energy per unit mass of Pelton turbine is the rate of energy transfer per unit mass to the fluid through the rotor. Energy per Unit Mass of Pelton Turbine is denoted by Em symbol.

How to calculate Energy per Unit Mass of Pelton Turbine using this online calculator? To use this online calculator for Energy per Unit Mass of Pelton Turbine, enter Inlet Relative Velocity of Pelton Turbine (Vr1), Outlet Relative Velocity of Pelton (Vr2), Outlet Bucket Angle of Pelton 2) & Bucket Velocity of Pelton Turbine (U) and hit the calculate button. Here is how the Energy per Unit Mass of Pelton Turbine calculation can be explained with given input values -> 369.8722 = (13.27+12.6*cos(0.3490658503988))*14.73.

FAQ

What is Energy per Unit Mass of Pelton Turbine?
Energy per unit mass of Pelton turbine is the rate of energy transfer per unit mass to the fluid through the rotor and is represented as Em = (Vr1+Vr2*cos(β2))*U or 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. The Inlet Relative Velocity of Pelton Turbine is a vector quantity and is quantified as the rate of displacement, Outlet Relative Velocity of Pelton is a vector quantity and is quantified as the rate of displacement, Outlet Bucket Angle of Pelton is the angle the bucket makes with the relative velocity at the outlet & Bucket velocity of Pelton turbine is a vector quantity and is quantified as the rate of displacement.
How to calculate Energy per Unit Mass of Pelton Turbine?
Energy per unit mass of Pelton turbine is the rate of energy transfer per unit mass to the fluid through the rotor is calculated using 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. To calculate Energy per Unit Mass of Pelton Turbine, you need Inlet Relative Velocity of Pelton Turbine (Vr1), Outlet Relative Velocity of Pelton (Vr2), Outlet Bucket Angle of Pelton 2) & Bucket Velocity of Pelton Turbine (U). With our tool, you need to enter the respective value for Inlet Relative Velocity of Pelton Turbine, Outlet Relative Velocity of Pelton, Outlet Bucket Angle of Pelton & 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.
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