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Francis Turbine Speed Ratio Formula

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Speed Ratio of Francis Turbine is the ratio of tangential velocity to the theoretical velocity. Check FAQs

K u = \frac{u 1}{\sqrt{2 \cdot g \cdot H i}}

K_u - Speed Ratio of Francis Turbine?u₁ - Velocity of Vane at Inlet For Francis Turbine?g - Acceleration Due to Gravity?H_i - Head at Inlet of Francis Turbine?

Francis Turbine Speed Ratio Example

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Here is how the Francis Turbine Speed Ratio equation looks like with Values.

Here is how the Francis Turbine Speed Ratio equation looks like with Units.

Here is how the Francis Turbine Speed Ratio equation looks like.

0.6584 = \frac{9.45}{\sqrt{2 \cdot 9.81 \cdot 10.5}}

0.6584 = \frac{9.45m/s}{\sqrt{2 \cdot 9.81m/s² \cdot 10.5m}}

0.6584 = \frac{9.45}{\sqrt{2 \cdot 9.81 \cdot 10.5}}

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Francis Turbine Speed Ratio Solution

Follow our step by step solution on how to calculate Francis Turbine Speed Ratio?

FIRST Step Consider the formula

K u = \frac{u 1}{\sqrt{2 \cdot g \cdot H i}}

Next Step Substitute values of Variables

∴

K u = \frac{9.45m/s}{\sqrt{2 \cdot 9.81m/s² \cdot 10.5m}}

Next Step Prepare to Evaluate

∴

K u = \frac{9.45}{\sqrt{2 \cdot 9.81 \cdot 10.5}}

Next Step Evaluate

∴

K u = 0.658396718196643

LAST Step Rounding Answer

∴

K u = 0.6584

Francis Turbine Speed Ratio Formula Elements

Variables

Functions

Speed Ratio of Francis Turbine

Speed Ratio of Francis Turbine is the ratio of tangential velocity to the theoretical velocity.

Symbol: K_u

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Speed Ratio of Francis Turbine

Velocity of Vane at Inlet For Francis Turbine

Velocity of Vane at Inlet For Francis Turbine is defined as the velocity of the vane at the inlet of the turbine.

Symbol: u₁

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Velocity of Vane at Inlet For Francis Turbine

Acceleration Due to Gravity

Acceleration Due to Gravity is acceleration gained by an object because of gravitational force.

Symbol: g

Measurement: AccelerationUnit: m/s²

Note: Value should be greater than 0.

Formulas to find Acceleration Due to Gravity

Head at Inlet of Francis Turbine

Head at Inlet of Francis Turbine is defined as the height of the water column at the inlet of the Francis turbine. It represents the energy of fluid at the inlet.

Symbol: H_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Head at Inlet of Francis Turbine

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 Francis Turbine category

Go Velocity of Vane at Inlet given Speed Ratio Francis Turbine

u 1 = K u \cdot \sqrt{2 \cdot g \cdot H i}

Go Pressure Head given Speed Ratio in Francis Turbine

H i = \frac{{(\frac{u 1}{K u})}^{2}}{2 \cdot g}

Go Francis Turbine Flow Ratio

K f = \frac{V f1}{\sqrt{2 \cdot g \cdot H i}}

Go Velocity of Flow at Inlet given Flow Ratio in Francis Turbine

V f1 = K f \cdot \sqrt{2 \cdot g \cdot H i}

How to Evaluate Francis Turbine Speed Ratio?

Francis Turbine Speed Ratio evaluator uses Speed Ratio of Francis Turbine = Velocity of Vane at Inlet For Francis Turbine/(sqrt(2*Acceleration Due to Gravity*Head at Inlet of Francis Turbine)) to evaluate the Speed Ratio of Francis Turbine, Francis Turbine Speed Ratio is the ratio of the actual rotational speed of the turbine to the ideal rotational speed for maximum efficiency. It helps in assessing how closely the turbine operates to its optimal speed for power generation. Speed Ratio of Francis Turbine is denoted by K_u symbol.

How to evaluate Francis Turbine Speed Ratio using this online evaluator? To use this online evaluator for Francis Turbine Speed Ratio, enter Velocity of Vane at Inlet For Francis Turbine (u₁), Acceleration Due to Gravity (g) & Head at Inlet of Francis Turbine (H_i) and hit the calculate button.

FAQs on Francis Turbine Speed Ratio

What is the formula to find Francis Turbine Speed Ratio?

The formula of Francis Turbine Speed Ratio is expressed as Speed Ratio of Francis Turbine = Velocity of Vane at Inlet For Francis Turbine/(sqrt(2*Acceleration Due to Gravity*Head at Inlet of Francis Turbine)). Here is an example- 0.658397 = 9.45/(sqrt(2*9.81*10.5)).

How to calculate Francis Turbine Speed Ratio?

With Velocity of Vane at Inlet For Francis Turbine (u₁), Acceleration Due to Gravity (g) & Head at Inlet of Francis Turbine (H_i) we can find Francis Turbine Speed Ratio using the formula - Speed Ratio of Francis Turbine = Velocity of Vane at Inlet For Francis Turbine/(sqrt(2*Acceleration Due to Gravity*Head at Inlet of Francis Turbine)). This formula also uses Square Root (sqrt) function(s).

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Francis Turbine Speed Ratio Formula

Francis Turbine Speed Ratio Example

Francis Turbine Speed Ratio Solution

Francis Turbine Speed Ratio Formula Elements

Other formulas in Francis Turbine category

How to Evaluate Francis Turbine Speed Ratio?

FAQs on Francis Turbine Speed Ratio

Variable Name