Velocity of Vane at Inlet given Speed Ratio Francis Turbine Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
u1 = Ku*sqrt(2*g*Hi)
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
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.
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
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
Head at Inlet of Francis Turbine: 10.5 Meter --> 10.5 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
u1 = Ku*sqrt(2*g*Hi) --> 0.658*sqrt(2*9.81*10.5)
Evaluating ... ...
u1 = 9.44430588449993
STEP 3: Convert Result to Output's Unit
9.44430588449993 Meter per Second --> No Conversion Required
FINAL ANSWER
9.44430588449993 ā‰ˆ 9.444306 Meter per Second <-- Velocity of Vane at Inlet for Francis Turbine
(Calculation completed in 00.004 seconds)

Credits

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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))))

Velocity of Vane at Inlet given Speed Ratio Francis Turbine Formula

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)
u1 = Ku*sqrt(2*g*Hi)

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 Velocity of Vane at Inlet given Speed Ratio Francis Turbine?

Velocity of Vane at Inlet given Speed Ratio Francis Turbine calculator uses 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) to calculate the Velocity of Vane at Inlet for Francis Turbine, The Velocity of vane at inlet given speed Ratio Francis turbine is defined as the velocity of the vane at the inlet of the turbine. Velocity of Vane at Inlet for Francis Turbine is denoted by u1 symbol.

How to calculate Velocity of Vane at Inlet given Speed Ratio Francis Turbine using this online calculator? To use this online calculator for Velocity of Vane at Inlet given Speed Ratio Francis Turbine, enter Speed Ratio of Francis Turbine (Ku), Acceleration due to Gravity (g) & Head at Inlet of Francis Turbine (Hi) and hit the calculate button. Here is how the Velocity of Vane at Inlet given Speed Ratio Francis Turbine calculation can be explained with given input values -> 9.439491 = 0.658*sqrt(2*9.81*10.5) .

FAQ

What is Velocity of Vane at Inlet given Speed Ratio Francis Turbine?
The Velocity of vane at inlet given speed Ratio Francis turbine is defined as the velocity of the vane at the inlet of the turbine and is represented as u1 = Ku*sqrt(2*g*Hi) or 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). 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 & 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 Velocity of Vane at Inlet given Speed Ratio Francis Turbine?
The Velocity of vane at inlet given speed Ratio Francis turbine is defined as the velocity of the vane at the inlet of the turbine is calculated using 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). To calculate Velocity of Vane at Inlet given Speed Ratio Francis Turbine, you need Speed Ratio of Francis Turbine (Ku), Acceleration due to Gravity (g) & Head at Inlet of Francis Turbine (Hi). With our tool, you need to enter the respective value for Speed Ratio of 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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