Speed of Turbine given Unit Speed Solution

STEP 0: Pre-Calculation Summary
Formula Used
Working Speed = Unit Speed*sqrt(Fall Height)
N = Nu*sqrt(H)
This formula uses 1 Functions, 3 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Working Speed - (Measured in Radian per Second) - Working speed of a hydroelectric plant depends on various factors such as the design of the plant, the type of turbines used, the head and flow rate of water, and the desired electrical output.
Unit Speed - Unit speed is defined as the speed of a geometrically similar turbine working under a head of 1m.
Fall Height - (Measured in Meter) - Fall height, is an important factor in hydroelectric power generation. It refers to the vertical distance that the water falls from the intake point to the turbine.
STEP 1: Convert Input(s) to Base Unit
Unit Speed: 2.31 --> No Conversion Required
Fall Height: 250 Meter --> 250 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
N = Nu*sqrt(H) --> 2.31*sqrt(250)
Evaluating ... ...
N = 36.5243069749448
STEP 3: Convert Result to Output's Unit
36.5243069749448 Radian per Second -->348.781439901856 Revolution per Minute (Check conversion here)
FINAL ANSWER
348.781439901856 348.7814 Revolution per Minute <-- Working Speed
(Calculation completed in 00.004 seconds)

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Indian Institute of Technology,Roorlee (IITR), Roorkee
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23 Hydroelectric Power Plant Calculators

Dimensionless Specific Speed
Go Dimensionless Specific Speed = (Working Speed*sqrt(Hydroelectric Power/1000))/(sqrt(Water Density)*([g]*Fall Height)^(5/4))
Efficiency of Turbine given Energy
Go Turbine Efficiency = Energy/([g]*Water Density*Flow Rate*Fall Height*Operating Time per Year)
Energy Produced by Hydroelectric Power Plant
Go Energy = [g]*Water Density*Flow Rate*Fall Height*Turbine Efficiency*Operating Time per Year
Specific Speed of Turbine of Hydroelectric Power Plant
Go Specific Speed = (Working Speed*sqrt(Hydroelectric Power/1000))/Fall Height^(5/4)
Velocity of Jet from Nozzle
Go Velocity of Jet = Coefficient of Velocity*sqrt(2*[g]*Fall Height)
Head or Height of Fall of Water given Power
Go Fall Height = Hydroelectric Power/([g]*Water Density*Flow Rate)
Specific Speed of Single Jet Machine
Go Specific Speed of Single Jet Machine = Specific Speed of Multi Jet Machine/sqrt(Number of Jets)
Specific Speed of Multi Jet Machine
Go Specific Speed of Multi Jet Machine = sqrt(Number of Jets)*Specific Speed of Single Jet Machine
Flow Rate of Water given Power
Go Flow Rate = Hydroelectric Power/([g]*Water Density*Fall Height)
Tidal Energy
Go Tidal Power = 0.5*Area of Base*Water Density*[g]*Fall Height^2
Hydroelectric Power
Go Hydroelectric Power = [g]*Water Density*Flow Rate*Fall Height
Energy Produced by Hydroelectric Power Plant given Power
Go Energy = Hydroelectric Power*Turbine Efficiency*Operating Time per Year
Height of Fall of Pelton Wheel Turbine Power Plant
Go Fall Height = (Velocity of Jet^2)/(2*[g]*Coefficient of Velocity^2)
Diameter of Bucket
Go Bucket Circle Diameter = (60*Bucket Velocity)/(pi*Working Speed)
Speed of Bucket given Diameter and RPM
Go Bucket Velocity = (pi*Bucket Circle Diameter*Working Speed)/60
Number of Jets
Go Number of Jets = (Specific Speed of Multi Jet Machine/Specific Speed of Single Jet Machine)^2
Unit Speed of Turbine
Go Unit Speed = (Working Speed)/sqrt(Fall Height)
Speed of Turbine given Unit Speed
Go Working Speed = Unit Speed*sqrt(Fall Height)
Speed of Bucket given Angular Velocity and Radius
Go Bucket Velocity = Angular Velocity*Bucket Circle Diameter/2
Unit Power of Hydroelectric Power Plant
Go Unit Power = (Hydroelectric Power/1000)/Fall Height^(3/2)
Power given Unit Power
Go Hydroelectric Power = Unit Power*1000*Fall Height^(3/2)
Jet Ratio of Hydroelectric Power Plant
Go Jet Ratio = Bucket Circle Diameter/Nozzle Diameter
Angular Velocity of Wheel
Go Angular Velocity = (2*pi*Working Speed)/60

Speed of Turbine given Unit Speed Formula

Working Speed = Unit Speed*sqrt(Fall Height)
N = Nu*sqrt(H)

What is the range of speed of Hydro Power Plant?

Most hydro power plants use either Francis, Kaplan, or Pelton turbines, each of which has a different operating range. Generally speaking, Francis turbines operate at speeds between 100 and 600 revolutions per minute (rpm), while Kaplan turbines operate at speeds between 100 and 250 rpm. Pelton turbines, on the other hand, operate at much higher speeds, typically between 500 and 1,500 rpm.

How to Calculate Speed of Turbine given Unit Speed?

Speed of Turbine given Unit Speed calculator uses Working Speed = Unit Speed*sqrt(Fall Height) to calculate the Working Speed, The Speed of Turbine given Unit Speed formula is defined as rotational velocity of the turbine. Working Speed is denoted by N symbol.

How to calculate Speed of Turbine given Unit Speed using this online calculator? To use this online calculator for Speed of Turbine given Unit Speed, enter Unit Speed (Nu) & Fall Height (H) and hit the calculate button. Here is how the Speed of Turbine given Unit Speed calculation can be explained with given input values -> 3330.617 = 2.31*sqrt(250).

FAQ

What is Speed of Turbine given Unit Speed?
The Speed of Turbine given Unit Speed formula is defined as rotational velocity of the turbine and is represented as N = Nu*sqrt(H) or Working Speed = Unit Speed*sqrt(Fall Height). Unit speed is defined as the speed of a geometrically similar turbine working under a head of 1m & Fall height, is an important factor in hydroelectric power generation. It refers to the vertical distance that the water falls from the intake point to the turbine.
How to calculate Speed of Turbine given Unit Speed?
The Speed of Turbine given Unit Speed formula is defined as rotational velocity of the turbine is calculated using Working Speed = Unit Speed*sqrt(Fall Height). To calculate Speed of Turbine given Unit Speed, you need Unit Speed (Nu) & Fall Height (H). With our tool, you need to enter the respective value for Unit Speed & Fall Height 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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