Dimensionless Specific Speed Calculator

✖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.ⓘ Working Speed [N]			+10% -10%
✖Hydroelectric Power depends on several factors such as the water flow rate, the height difference btw the water source & the turbine.ⓘ Hydroelectric Power [P_h]			+10% -10%
✖Water density in a hydroelectric plant depends on the temperature and pressure conditions inside the plant.ⓘ Water Density [ρ_w]			+10% -10%
✖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.ⓘ Fall Height [H]			+10% -10%

✖Dimensionless Specific Speed is an important parameter because it provides a way to compare the performance of different pumps that have different sizes, flow rates, and head pressures.ⓘ Dimensionless Specific Speed [N_s']

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Dimensionless Specific Speed

Formula

`("N"_{"s"}"'") = ("N"*sqrt("P"_{"h"}/1000))/(sqrt("ρ"_{"w"})*("[g]"*"H")^(5/4))`

Example

`"0.004819"=("350rev/min"*sqrt("5145kW"/1000))/(sqrt("1000kg/m³")*("[g]"*"250m")^(5/4))`

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Dimensionless Specific Speed Solution

STEP 0: Pre-Calculation Summary

Formula Used

Dimensionless Specific Speed = (Working Speed*sqrt(Hydroelectric Power/1000))/(sqrt(Water Density)*([g]*Fall Height)^(5/4))
N_s' = (N*sqrt(P_h/1000))/(sqrt(ρ_w)*([g]*H)^(5/4))
This formula uses 1 Constants, 1 Functions, 5 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

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

Dimensionless Specific Speed - Dimensionless Specific Speed is an important parameter because it provides a way to compare the performance of different pumps that have different sizes, flow rates, and head pressures.
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.
Hydroelectric Power - (Measured in Watt) - Hydroelectric Power depends on several factors such as the water flow rate, the height difference btw the water source & the turbine.
Water Density - (Measured in Kilogram per Cubic Meter) - Water density in a hydroelectric plant depends on the temperature and pressure conditions inside the plant.
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

Working Speed: 350 Revolution per Minute --> 36.6519142900145 Radian per Second (Check conversion here)
Hydroelectric Power: 5145 Kilowatt --> 5145000 Watt (Check conversion here)
Water Density: 1000 Kilogram per Cubic Meter --> 1000 Kilogram per Cubic Meter No Conversion Required
Fall Height: 250 Meter --> 250 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_s' = (N*sqrt(P_h/1000))/(sqrt(ρ_w)*([g]*H)^(5/4)) --> (36.6519142900145*sqrt(5145000/1000))/(sqrt(1000)*([g]*250)^(5/4))

Evaluating ... ...

N_s' = 0.00481907290495882

STEP 3: Convert Result to Output's Unit

0.00481907290495882 --> No Conversion Required

FINAL ANSWER

0.00481907290495882 ≈ 0.004819 <-- Dimensionless Specific Speed

(Calculation completed in 00.004 seconds)

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Created by Nisarg

Indian Institute of Technology,Roorlee (IITR), Roorkee

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Verified by Parminder Singh

Chandigarh University (CU), Punjab

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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

Dimensionless Specific Speed Formula

Dimensionless Specific Speed = (Working Speed*sqrt(Hydroelectric Power/1000))/(sqrt(Water Density)*([g]*Fall Height)^(5/4))
N_s' = (N*sqrt(P_h/1000))/(sqrt(ρ_w)*([g]*H)^(5/4))

What is a Hydroelectric Power Plant?

A hydroelectric power plant is a facility that generates electricity by harnessing the energy of falling water. The basic components of a hydroelectric power plant include a dam, reservoir, turbine, generator, and transmission lines.

What is the significance of Hydroelectric Power Plant?

Hydroelectric power plants are significant because they provide a reliable, cost-effective, and clean source of renewable energy, reducing reliance on fossil fuels. They also offer energy security, flexibility, and environmental benefits, such as flood control and recreation opportunities.

How to Calculate Dimensionless Specific Speed?

Dimensionless Specific Speed calculator uses Dimensionless Specific Speed = (Working Speed*sqrt(Hydroelectric Power/1000))/(sqrt(Water Density)*([g]*Fall Height)^(5/4)) to calculate the Dimensionless Specific Speed, The Dimensionless Specific Speed formula is defined as a parameter that is used to compare the performance characteristics of different types and sizes of turbines in hydroelectric power plants, regardless of their specific dimensions or units of measurement. Dimensionless Specific Speed is denoted by N_s' symbol.

How to calculate Dimensionless Specific Speed using this online calculator? To use this online calculator for Dimensionless Specific Speed, enter Working Speed (N), Hydroelectric Power (P_h), Water Density (ρ_w) & Fall Height (H) and hit the calculate button. Here is how the Dimensionless Specific Speed calculation can be explained with given input values -> 0.004819 = (36.6519142900145*sqrt(5145000/1000))/(sqrt(1000)*([g]*250)^(5/4)).

FAQ

What is Dimensionless Specific Speed?

The Dimensionless Specific Speed formula is defined as a parameter that is used to compare the performance characteristics of different types and sizes of turbines in hydroelectric power plants, regardless of their specific dimensions or units of measurement and is represented as N_s' = (N*sqrt(P_h/1000))/(sqrt(ρ_w)*([g]*H)^(5/4)) or Dimensionless Specific Speed = (Working Speed*sqrt(Hydroelectric Power/1000))/(sqrt(Water Density)*([g]*Fall Height)^(5/4)). 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, Hydroelectric Power depends on several factors such as the water flow rate, the height difference btw the water source & the turbine, Water density in a hydroelectric plant depends on the temperature and pressure conditions inside the plant & 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 Dimensionless Specific Speed?

The Dimensionless Specific Speed formula is defined as a parameter that is used to compare the performance characteristics of different types and sizes of turbines in hydroelectric power plants, regardless of their specific dimensions or units of measurement is calculated using Dimensionless Specific Speed = (Working Speed*sqrt(Hydroelectric Power/1000))/(sqrt(Water Density)*([g]*Fall Height)^(5/4)). To calculate Dimensionless Specific Speed, you need Working Speed (N), Hydroelectric Power (P_h), Water Density (ρ_w) & Fall Height (H). With our tool, you need to enter the respective value for Working Speed, Hydroelectric Power, Water Density & 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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