Pressure Head given Speed Ratio in Francis Turbine Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
Hi = ((u1/Ku)^2)/(2*g)
This formula uses 4 Variables
Variables Used
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.
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.
Speed Ratio of Francis Turbine - The Speed Ratio of Francis Turbine is the ratio of tangential velocity to the theoretical velocity.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration Due to Gravity is acceleration gained by an object because of gravitational force.
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
Speed Ratio of Francis Turbine: 0.658 --> No Conversion Required
Acceleration due to Gravity: 9.81 Meter per Square Second --> 9.81 Meter per Square Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Hi = ((u1/Ku)^2)/(2*g) --> ((9.45/0.658)^2)/(2*9.81)
Evaluating ... ...
Hi = 10.5126650358625
STEP 3: Convert Result to Output's Unit
10.5126650358625 Meter --> No Conversion Required
FINAL ANSWER
10.5126650358625 ā‰ˆ 10.51267 Meter <-- Head at Inlet of Francis Turbine
(Calculation completed in 00.020 seconds)

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National Institute of Technology (NIT), Srinagar
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18 Francis Turbine Calculators

Volume Flow Rate of Obtuse Angled Outlet Bladed Francis Turbine given Work Done per Second
Go Volume Flow Rate for Francis Turbine = Work Done per Second by Francis Turbine/(Density of Fluid in Francis Turbine*(Whirl Velocity at Inlet of Francis Turbine*Velocity of Vane at Inlet for Francis Turbine-Whirl Velocity at Outlet of Francis Turbine*Velocity of Vane at Outlet for Francis Turbine))
Volume Flow Rate of Acute Angled Francis Turbine given Work Done Per Second on Runner
Go Volume Flow Rate for Francis Turbine = Work Done per Second by Francis Turbine/(Density of Fluid in Francis Turbine*(Whirl Velocity at Inlet of Francis Turbine*Velocity of Vane at Inlet for Francis Turbine+Whirl Velocity at Outlet of Francis Turbine*Velocity of Vane at Outlet for Francis Turbine))
Work Done per Second on Runner by Water for Acute Angled Outlet Blade
Go Work Done per Second by Francis Turbine = Density of Fluid in Francis Turbine*Volume Flow Rate for Francis Turbine*(Whirl Velocity at Inlet of Francis Turbine*Velocity of Vane at Inlet for Francis Turbine+Whirl Velocity at Outlet of Francis Turbine*Velocity of Vane at Outlet for Francis Turbine)
Work Done per sec on Runner by Water for Obtuse Angled Outlet Blade
Go Work Done per Second by Francis Turbine = Density of Fluid in Francis Turbine*Volume Flow Rate for Francis Turbine*(Whirl Velocity at Inlet of Francis Turbine*Velocity of Vane at Inlet for Francis Turbine-Whirl Velocity at Outlet of Francis Turbine*Velocity of Vane at Outlet for Francis Turbine)
Hydraulic Efficiency of Francis Turbine with Obtuse Angled Outlet Blade
Go Hydraulic Efficiency of Francis Turbine = (Whirl Velocity at Inlet of Francis Turbine*Velocity of Vane at Inlet for Francis Turbine-Whirl Velocity at Outlet of Francis Turbine*Velocity of Vane at Outlet for Francis Turbine)/(Acceleration due to Gravity*Net Francis Turbine Head)
Hydraulic Efficiency of Francis Turbine with Acute Angled Outlet Blade
Go Hydraulic Efficiency of Francis Turbine = (Whirl Velocity at Inlet of Francis Turbine*Velocity of Vane at Inlet for Francis Turbine+Whirl Velocity at Outlet of Francis Turbine*Velocity of Vane at Outlet for Francis Turbine)/(Acceleration due to Gravity*Net Francis Turbine Head)
Volume Flow Rate of Right Angled Outlet Bladed Francis Turbine given Work Done per Second
Go Volume Flow Rate for Francis Turbine = Work Done per Second by Francis Turbine/(Density of Fluid in Francis Turbine*Velocity of Vane at Inlet for Francis Turbine*Whirl Velocity at Inlet of Francis Turbine)
Work Done per Second on Runner by Water for Right Angled Outlet Blade Angle
Go Work Done per Second by Francis Turbine = Density of Fluid in Francis Turbine*Volume Flow Rate for Francis Turbine*Velocity of Vane at Inlet for Francis Turbine*Whirl Velocity at Inlet of Francis Turbine
Degree of Reaction of Turbine with Right Angled Outlet Blade
Go Degree of Reaction = 1-cot(Guide Blade Angle for Francis Trubine)/(2*(cot(Guide Blade Angle for Francis Trubine)-cot(Vane Angle at Inlet)))
Hydraulic Efficiency of Francis Turbine with Right Angled Outlet Blade
Go Hydraulic Efficiency of Francis Turbine = (Whirl Velocity at Inlet of Francis Turbine*Velocity of Vane at Inlet for Francis Turbine)/(Acceleration due to Gravity*Net Francis Turbine Head)
Velocity of Vane at Inlet given Speed Ratio Francis Turbine
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 Speed Ratio
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))
Francis Turbine Flow Ratio
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))
Velocity of Flow at Inlet given Flow Ratio in Francis Turbine
Go Velocity of Flow at Inlet of Francis Turbine = Flow Ratio of Francis Turbine*sqrt(2*Acceleration due to Gravity*Head at Inlet of Francis Turbine)
Pressure Head given Speed Ratio in Francis Turbine
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)
Pressure Head given Flow Ratio in Francis Turbine
Go Head at Inlet of Francis Turbine = ((Velocity of Flow at Inlet of Francis Turbine/Flow Ratio of Francis Turbine)^2)/(2*Acceleration due to Gravity)
Guide Blade Angle given Degree of Reaction
Go Guide Blade Angle for Francis Trubine = acot(cot(Vane Angle at Inlet)/(1-1/(2*(1-Degree of Reaction))))
Vane Angle at Inlet from Degree of Reaction
Go Vane Angle at Inlet = acot(cot(Guide Blade Angle for Francis Trubine)*(1-1/(2*(1-Degree of Reaction))))

Pressure Head given Speed Ratio in Francis Turbine Formula

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)
Hi = ((u1/Ku)^2)/(2*g)

Where is Francis turbine used?

A Francis turbine is a type of reaction turbine used most frequently in medium- or large-scale hydroelectric plants. These turbines can be used for heads as low as 2 meters and as high as 300 meters.

How to Calculate Pressure Head given Speed Ratio in Francis Turbine?

Pressure Head given Speed Ratio in Francis Turbine calculator uses 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) to calculate the Head at Inlet of Francis Turbine, The Pressure head given speed Ratio in Francis turbine is the height of a liquid column that corresponds to a particular pressure exerted by the liquid column on the base of its container. Head at Inlet of Francis Turbine is denoted by Hi symbol.

How to calculate Pressure Head given Speed Ratio in Francis Turbine using this online calculator? To use this online calculator for Pressure Head given Speed Ratio in Francis Turbine, enter Velocity of Vane at Inlet for Francis Turbine (u1), Speed Ratio of Francis Turbine (Ku) & Acceleration due to Gravity (g) and hit the calculate button. Here is how the Pressure Head given Speed Ratio in Francis Turbine calculation can be explained with given input values -> 10.52339 = ((9.45/0.658)^2)/(2*9.81).

FAQ

What is Pressure Head given Speed Ratio in Francis Turbine?
The Pressure head given speed Ratio in Francis turbine is the height of a liquid column that corresponds to a particular pressure exerted by the liquid column on the base of its container and is represented as Hi = ((u1/Ku)^2)/(2*g) or 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). Velocity of Vane at Inlet for Francis Turbine is defined as the velocity of the vane at the inlet of the turbine, The Speed Ratio of Francis Turbine is the ratio of tangential velocity to the theoretical velocity & Acceleration Due to Gravity is acceleration gained by an object because of gravitational force.
How to calculate Pressure Head given Speed Ratio in Francis Turbine?
The Pressure head given speed Ratio in Francis turbine is the height of a liquid column that corresponds to a particular pressure exerted by the liquid column on the base of its container is calculated using 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). To calculate Pressure Head given Speed Ratio in Francis Turbine, you need Velocity of Vane at Inlet for Francis Turbine (u1), Speed Ratio of Francis Turbine (Ku) & Acceleration due to Gravity (g). With our tool, you need to enter the respective value for Velocity of Vane at Inlet for Francis Turbine, Speed Ratio of Francis Turbine & Acceleration due to Gravity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Head at Inlet of Francis Turbine?
In this formula, Head at Inlet of Francis Turbine uses Velocity of Vane at Inlet for Francis Turbine, Speed Ratio of Francis Turbine & Acceleration due to Gravity. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Head at Inlet of Francis Turbine = ((Velocity of Flow at Inlet of Francis Turbine/Flow Ratio of Francis Turbine)^2)/(2*Acceleration due to Gravity)
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