Francis Turbine Speed Ratio Calculator

✖Velocity of Vane at Inlet For Francis Turbine is defined as the velocity of the vane at the inlet of the turbine.ⓘ Velocity of Vane at Inlet For Francis Turbine [u₁]			+10% -10%
✖Acceleration Due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration Due to Gravity [g]			+10% -10%
✖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.ⓘ Head at Inlet of Francis Turbine [H_i]			+10% -10%

✖Speed Ratio of Francis Turbine is the ratio of tangential velocity to the theoretical velocity.ⓘ Francis Turbine Speed Ratio [K_u]

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Francis Turbine Speed Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
K_u = u₁/(sqrt(2*g*H_i))
This formula uses 1 Functions, 4 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

Speed Ratio of Francis Turbine - Speed Ratio of Francis Turbine is the ratio of tangential velocity to the theoretical velocity.
Velocity of Vane at Inlet For Francis Turbine - (Measured in Meter per Second) - Velocity of Vane at Inlet For Francis Turbine is defined as the velocity of the vane at the inlet of the turbine.
Acceleration Due to Gravity - (Measured in Meter per Square Second) - Acceleration Due to Gravity is acceleration gained by an object because of gravitational force.
Head at Inlet of Francis Turbine - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Velocity of Vane at Inlet For Francis Turbine: 9.45 Meter per Second --> 9.45 Meter per Second No Conversion Required
Acceleration Due to Gravity: 9.81 Meter per Square Second --> 9.81 Meter per Square Second No Conversion Required
Head at Inlet of Francis Turbine: 10.5 Meter --> 10.5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_u = u₁/(sqrt(2*g*H_i)) --> 9.45/(sqrt(2*9.81*10.5))

Evaluating ... ...

K_u = 0.658396718196643

STEP 3: Convert Result to Output's Unit

0.658396718196643 --> No Conversion Required

FINAL ANSWER

0.658396718196643 ≈ 0.658397 <-- Speed Ratio of Francis Turbine

(Calculation completed in 00.006 seconds)

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Created by Parul Keshav

National Institute of Technology (NIT), Srinagar

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National Institute Of Technology (NIT), Hamirpur

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< Francis Turbine Calculators

Francis Turbine Speed Ratio

LaTeX Go 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))

Velocity of Vane at Inlet given Speed Ratio Francis Turbine

LaTeX Go Velocity of Vane at Inlet For Francis Turbine = Speed Ratio of Francis Turbine*sqrt(2*Acceleration Due to Gravity*Head at Inlet of Francis Turbine)

Francis Turbine Flow Ratio

LaTeX Go Flow Ratio of Francis Turbine = Velocity of Flow at Inlet of Francis Turbine/(sqrt(2*Acceleration Due to Gravity*Head at Inlet of Francis Turbine))

Pressure Head given Speed Ratio in Francis Turbine

LaTeX Go Head at Inlet of Francis Turbine = ((Velocity of Vane at Inlet For Francis Turbine/Speed Ratio of Francis Turbine)^2)/(2*Acceleration Due to Gravity)

Francis Turbine Speed Ratio Formula

LaTeX Go

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))
K_u = u₁/(sqrt(2*g*H_i))

what is Tip speed Ratio?

The Tip Speed Ratio (TSR) is an extremely important factor in wind turbine design. TSR refers to the ratio between the wind speed and the speed of the tips of the wind turbine blades.

How to Calculate Francis Turbine Speed Ratio?

Francis Turbine Speed Ratio calculator 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 calculate 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 calculate Francis Turbine Speed Ratio using this online calculator? To use this online calculator 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. Here is how the Francis Turbine Speed Ratio calculation can be explained with given input values -> 0.658397 = 9.45/(sqrt(2*9.81*10.5)).

FAQ

What is Francis Turbine Speed Ratio?

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 and is represented as K_u = u₁/(sqrt(2*g*H_i)) or 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)). Velocity of Vane at Inlet For Francis Turbine is defined as the velocity of the vane at the inlet of the turbine, Acceleration Due to Gravity is acceleration gained by an object because of gravitational force & 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.

How to calculate Francis Turbine Speed Ratio?

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 is calculated using 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 calculate Francis Turbine Speed Ratio, you need Velocity of Vane at Inlet For Francis Turbine (u₁), Acceleration Due to Gravity (g) & Head at Inlet of Francis Turbine (H_i). With our tool, you need to enter the respective value for Velocity of Vane at Inlet For Francis Turbine, Acceleration Due to Gravity & Head at Inlet of Francis Turbine 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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