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Dimensionless Specific Speed Formula

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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. Check FAQs

N s' = \frac{N \cdot \sqrt{\frac{P h}{1000}}}{\sqrt{ρ w} \cdot {([g] \cdot H)}^{\frac{5}{4}}}

N_s' - Dimensionless Specific Speed?N - Working Speed?P_h - Hydroelectric Power?ρ_w - Water Density?H - Fall Height?[g] - Gravitational acceleration on Earth?

Dimensionless Specific Speed Example

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Here is how the Dimensionless Specific Speed equation looks like with Values.

Here is how the Dimensionless Specific Speed equation looks like with Units.

Here is how the Dimensionless Specific Speed equation looks like.

0.0048 = \frac{350 \cdot \sqrt{\frac{5145}{1000}}}{\sqrt{1000} \cdot {(9.8066 \cdot 250)}^{\frac{5}{4}}}

0.0048 = \frac{350rev/min \cdot \sqrt{\frac{5145kW}{1000}}}{\sqrt{1000kg/m³} \cdot {(9.8066m/s² \cdot 250m)}^{\frac{5}{4}}}

0.0048 = \frac{350 \cdot \sqrt{\frac{5145}{1000}}}{\sqrt{1000} \cdot {(9.8066 \cdot 250)}^{\frac{5}{4}}}

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Dimensionless Specific Speed Solution

Follow our step by step solution on how to calculate Dimensionless Specific Speed?

FIRST Step Consider the formula

N s' = \frac{N \cdot \sqrt{\frac{P h}{1000}}}{\sqrt{ρ w} \cdot {([g] \cdot H)}^{\frac{5}{4}}}

Next Step Substitute values of Variables

∴

N s' = \frac{350rev/min \cdot \sqrt{\frac{5145kW}{1000}}}{\sqrt{1000kg/m³} \cdot {([g] \cdot 250m)}^{\frac{5}{4}}}

Next Step Substitute values of Constants

∴

N s' = \frac{350rev/min \cdot \sqrt{\frac{5145kW}{1000}}}{\sqrt{1000kg/m³} \cdot {(9.8066m/s² \cdot 250m)}^{\frac{5}{4}}}

Next Step Convert Units

∴

N s' = \frac{36.6519rad/s \cdot \sqrt{\frac{5.1E+6W}{1000}}}{\sqrt{1000kg/m³} \cdot {(9.8066m/s² \cdot 250m)}^{\frac{5}{4}}}

Next Step Prepare to Evaluate

∴

N s' = \frac{36.6519 \cdot \sqrt{\frac{5.1E+6}{1000}}}{\sqrt{1000} \cdot {(9.8066 \cdot 250)}^{\frac{5}{4}}}

Next Step Evaluate

∴

N s' = 0.00481907290495882

LAST Step Rounding Answer

∴

N s' = 0.0048

Dimensionless Specific Speed Formula Elements

Variables

Constants

Functions

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.

Symbol: N_s'

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Dimensionless 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

Water Density

Water density in a hydroelectric plant depends on the temperature and pressure conditions inside the plant.

Symbol: ρ_w

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Water Density

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

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

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 Dimensionless Specific Speed?

Dimensionless Specific Speed evaluator uses Dimensionless Specific Speed = (Working Speed*sqrt(Hydroelectric Power/1000))/(sqrt(Water Density)*([g]*Fall Height)^(5/4)) to evaluate 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 evaluate Dimensionless Specific Speed using this online evaluator? To use this online evaluator for Dimensionless Specific Speed, enter Working Speed (N), Hydroelectric Power (P_h), Water Density (ρ_w) & Fall Height (H) and hit the calculate button.

FAQs on Dimensionless Specific Speed

What is the formula to find Dimensionless Specific Speed?

The formula of Dimensionless Specific Speed is expressed as Dimensionless Specific Speed = (Working Speed*sqrt(Hydroelectric Power/1000))/(sqrt(Water Density)*([g]*Fall Height)^(5/4)). Here is an example- 0.004819 = (36.6519142900145*sqrt(5145000/1000))/(sqrt(1000)*([g]*250)^(5/4)).

How to calculate Dimensionless Specific Speed?

With Working Speed (N), Hydroelectric Power (P_h), Water Density (ρ_w) & Fall Height (H) we can find Dimensionless Specific Speed using the formula - Dimensionless Specific Speed = (Working Speed*sqrt(Hydroelectric Power/1000))/(sqrt(Water Density)*([g]*Fall Height)^(5/4)). This formula also uses Gravitational acceleration on Earth constant(s) and Square Root Function function(s).

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Dimensionless Specific Speed Formula

Dimensionless Specific Speed Example

Dimensionless Specific Speed Solution

Dimensionless Specific Speed Formula Elements

Other formulas in Hydroelectric Power Plant category

How to Evaluate Dimensionless Specific Speed?

FAQs on Dimensionless Specific Speed

Variable Name