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Specific Speed of Turbine of Hydroelectric Power Plant Formula

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Specific Speed of a geometrically similar turbine which would produce unit power (one kilowatt) under unit head (one meter) to the point of maximum efficiency. Check FAQs

N S = \frac{N \cdot \sqrt{\frac{P h}{1000}}}{H^{\frac{5}{4}}}

N_S - Specific Speed?N - Working Speed?P_h - Hydroelectric Power?H - Fall Height?

Specific Speed of Turbine of Hydroelectric Power Plant Example

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Here is how the Specific Speed of Turbine of Hydroelectric Power Plant equation looks like with Values.

Here is how the Specific Speed of Turbine of Hydroelectric Power Plant equation looks like with Units.

Here is how the Specific Speed of Turbine of Hydroelectric Power Plant equation looks like.

25.2543 = \frac{350 \cdot \sqrt{\frac{5145}{1000}}}{250^{\frac{5}{4}}}

25.2543rev/min = \frac{350rev/min \cdot \sqrt{\frac{5145kW}{1000}}}{{250m}^{\frac{5}{4}}}

25.2543 = \frac{350 \cdot \sqrt{\frac{5145}{1000}}}{250^{\frac{5}{4}}}

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Specific Speed of Turbine of Hydroelectric Power Plant Solution

Follow our step by step solution on how to calculate Specific Speed of Turbine of Hydroelectric Power Plant?

FIRST Step Consider the formula

N S = \frac{N \cdot \sqrt{\frac{P h}{1000}}}{H^{\frac{5}{4}}}

Next Step Substitute values of Variables

∴

N S = \frac{350rev/min \cdot \sqrt{\frac{5145kW}{1000}}}{{250m}^{\frac{5}{4}}}

Next Step Convert Units

∴

N S = \frac{36.6519rad/s \cdot \sqrt{\frac{5.1E+6W}{1000}}}{{250m}^{\frac{5}{4}}}

Next Step Prepare to Evaluate

∴

N S = \frac{36.6519 \cdot \sqrt{\frac{5.1E+6}{1000}}}{250^{\frac{5}{4}}}

Next Step Evaluate

∴

N S = 2.64462647333344rad/s

Next Step Convert to Output's Unit

∴

N S = 25.2543225530482rev/min

LAST Step Rounding Answer

∴

N S = 25.2543rev/min

Specific Speed of Turbine of Hydroelectric Power Plant Formula Elements

Variables

Functions

Specific Speed

Specific Speed of a geometrically similar turbine which would produce unit power (one kilowatt) under unit head (one meter) to the point of maximum efficiency.

Symbol: N_S

Measurement: Angular VelocityUnit: rev/min

Note: Value can be positive or negative.

Formulas to find Specific Speed

Working Speed

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.

Symbol: N

Measurement: Angular VelocityUnit: rev/min

Note: Value should be greater than 0.

Formulas to find Working Speed

Hydroelectric Power

Hydroelectric Power depends on several factors such as the water flow rate, the height difference btw the water source & the turbine.

Symbol: P_h

Measurement: PowerUnit: kW

Note: Value should be greater than 0.

Formulas to find Hydroelectric Power

Fall Height

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.

Symbol: H

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Fall Height

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.

Syntax: sqrt(Number)

Other formulas in Hydroelectric Power Plant category

Go Energy Produced by Hydroelectric Power Plant

E = [g] \cdot ρ w \cdot Q \cdot H \cdot η \cdot t

Go Energy Produced by Hydroelectric Power Plant given Power

E = P h \cdot η \cdot t

Go Head or Height of Fall of Water given Power

H = \frac{P h}{[g] \cdot ρ w \cdot Q}

Go Flow Rate of Water given Power

Q = \frac{P h}{[g] \cdot ρ w \cdot H}

How to Evaluate Specific Speed of Turbine of Hydroelectric Power Plant?

Specific Speed of Turbine of Hydroelectric Power Plant evaluator uses Specific Speed = (Working Speed*sqrt(Hydroelectric Power/1000))/Fall Height^(5/4) to evaluate the Specific Speed, The Specific Speed of Turbine of Hydroelectric Power Plant formula is defined as a parameter that is used to describe the performance characteristics of the turbine in a hydroelectric power plant. It is defined as the speed at which a geometrically similar turbine of unit size would operate if it were to be used in a unit of water power under unit head. Specific Speed is denoted by N_S symbol.

How to evaluate Specific Speed of Turbine of Hydroelectric Power Plant using this online evaluator? To use this online evaluator for Specific Speed of Turbine of Hydroelectric Power Plant, enter Working Speed (N), Hydroelectric Power (P_h) & Fall Height (H) and hit the calculate button.

FAQs on Specific Speed of Turbine of Hydroelectric Power Plant

What is the formula to find Specific Speed of Turbine of Hydroelectric Power Plant?

The formula of Specific Speed of Turbine of Hydroelectric Power Plant is expressed as Specific Speed = (Working Speed*sqrt(Hydroelectric Power/1000))/Fall Height^(5/4). Here is an example- 241.161 = (36.6519142900145*sqrt(5145000/1000))/250^(5/4).

How to calculate Specific Speed of Turbine of Hydroelectric Power Plant?

With Working Speed (N), Hydroelectric Power (P_h) & Fall Height (H) we can find Specific Speed of Turbine of Hydroelectric Power Plant using the formula - Specific Speed = (Working Speed*sqrt(Hydroelectric Power/1000))/Fall Height^(5/4). This formula also uses Square Root Function function(s).

Can the Specific Speed of Turbine of Hydroelectric Power Plant be negative?

Yes, the Specific Speed of Turbine of Hydroelectric Power Plant, measured in Angular Velocity can be negative.

Which unit is used to measure Specific Speed of Turbine of Hydroelectric Power Plant?

Specific Speed of Turbine of Hydroelectric Power Plant is usually measured using the Revolution per Minute[rev/min] for Angular Velocity. Radian per Second[rev/min], Radian per Day[rev/min], Radian per Hour[rev/min] are the few other units in which Specific Speed of Turbine of Hydroelectric Power Plant can be measured.

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Specific Speed of Turbine of Hydroelectric Power Plant Formula

Specific Speed of Turbine of Hydroelectric Power Plant Example

Specific Speed of Turbine of Hydroelectric Power Plant Solution

Specific Speed of Turbine of Hydroelectric Power Plant Formula Elements

Other formulas in Hydroelectric Power Plant category

How to Evaluate Specific Speed of Turbine of Hydroelectric Power Plant?

FAQs on Specific Speed of Turbine of Hydroelectric Power Plant

Variable Name