Work Done per Second on Runner by Water for Right Angled Outlet Blade Angle Solution

STEP 0: Pre-Calculation Summary
Formula Used
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
W = ρf*Qf*u1*Vw1
This formula uses 5 Variables
Variables Used
Work Done per Second by Francis Turbine - (Measured in Watt) - Work Done per Second by Francis Turbine is defined as the amount of work that is done by the Francis turbine in a given unit of time.
Density of Fluid in Francis Turbine - (Measured in Kilogram per Cubic Meter) - The Density of Fluid in Francis Turbine is the corresponding density of the fluid at the given conditions in the franchise turbine.
Volume Flow Rate for Francis Turbine - (Measured in Cubic Meter per Second) - Volume Flow Rate for Francis Turbine is the volume of fluid that passes per unit of time.
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.
Whirl Velocity at Inlet of Francis Turbine - (Measured in Meter per Second) - Whirl Velocity at Inlet of Francis Turbine is the tangential component of absolute velocity at the blade inlet.
STEP 1: Convert Input(s) to Base Unit
Density of Fluid in Francis Turbine: 1000 Kilogram per Cubic Meter --> 1000 Kilogram per Cubic Meter No Conversion Required
Volume Flow Rate for Francis Turbine: 1.5 Cubic Meter per Second --> 1.5 Cubic Meter per Second No Conversion Required
Velocity of Vane at Inlet for Francis Turbine: 9.45 Meter per Second --> 9.45 Meter per Second No Conversion Required
Whirl Velocity at Inlet of Francis Turbine: 12.93 Meter per Second --> 12.93 Meter per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
W = ρf*Qf*u1*Vw1 --> 1000*1.5*9.45*12.93
Evaluating ... ...
W = 183282.75
STEP 3: Convert Result to Output's Unit
183282.75 Watt -->183.28275 Kilowatt (Check conversion here)
FINAL ANSWER
183.28275 183.2827 Kilowatt <-- Work Done per Second by Francis Turbine
(Calculation completed in 00.004 seconds)

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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))))

Work Done per Second on Runner by Water for Right Angled Outlet Blade Angle Formula

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
W = ρf*Qf*u1*Vw1

What are the main components of a Francis turbine?

The main components are spiral casing, guide and stay vanes, runner blades, draft tube. The spiral casing also known as the volute casing or scroll case, has numerous openings at regular intervals which convert fluid's pressure energy into kinetic and allow the working fluid to impinge on the blades of the runner. This maintains a constant velocity despite the fact that numerous openings have been provided for the fluid to enter the blades, as the cross-sectional area of this casing decreases uniformly along the circumference. Guide and stay vanes convert the pressure energy of the fluid into kinetic energy. Runner blades are the centers where the fluid strikes and the tangential force of the impact produces torque causing the shaft of the turbine to rotate. Attention to blade angles at inlet and outlet is necessary, as these are major parameters affecting power production. The draft tube's primary function is to reduce the velocity of discharged water to minimize the loss of kinetic energy at the outlet.

What is the purpose of draft tube?

The efficiency of a reaction turbine, such as a Francis Turbine, increases with the increase in pressure difference between inlet and outlet pressures. As inlet pressure can't be increased further, since the inlet head of the turbine remains constant, the only way to improve efficiency is to decrease the outlet pressure and to create a negative head at the outlet. This is where Draft tubes comes into picture. Draft tubes are of different shapes and sizes, depending upon the magnitude of negative head to be produced at the outlet of the turbine. A draft tube can be imagined as a component with increasing area of cross section starting from the outlet of the turbine, to the tail race. Cross sections may be circular, rectangular, square or a specially designed one like a Siphon draft tube etc.

How to Calculate Work Done per Second on Runner by Water for Right Angled Outlet Blade Angle?

Work Done per Second on Runner by Water for Right Angled Outlet Blade Angle calculator uses 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 to calculate the Work Done per Second by Francis Turbine, The work done per second on runner by water for right angled outlet blade angle formula can be used to evaluate the work done by the water on the runner in a second which is a measure of the capacity of the turbine. Work Done per Second by Francis Turbine is denoted by W symbol.

How to calculate Work Done per Second on Runner by Water for Right Angled Outlet Blade Angle using this online calculator? To use this online calculator for Work Done per Second on Runner by Water for Right Angled Outlet Blade Angle, enter Density of Fluid in Francis Turbine f), Volume Flow Rate for Francis Turbine (Qf), Velocity of Vane at Inlet for Francis Turbine (u1) & Whirl Velocity at Inlet of Francis Turbine (Vw1) and hit the calculate button. Here is how the Work Done per Second on Runner by Water for Right Angled Outlet Blade Angle calculation can be explained with given input values -> 0.183283 = 1000*1.5*9.45*12.93.

FAQ

What is Work Done per Second on Runner by Water for Right Angled Outlet Blade Angle?
The work done per second on runner by water for right angled outlet blade angle formula can be used to evaluate the work done by the water on the runner in a second which is a measure of the capacity of the turbine and is represented as W = ρf*Qf*u1*Vw1 or 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. The Density of Fluid in Francis Turbine is the corresponding density of the fluid at the given conditions in the franchise turbine, Volume Flow Rate for Francis Turbine is the volume of fluid that passes per unit of time, Velocity of Vane at Inlet for Francis Turbine is defined as the velocity of the vane at the inlet of the turbine & Whirl Velocity at Inlet of Francis Turbine is the tangential component of absolute velocity at the blade inlet.
How to calculate Work Done per Second on Runner by Water for Right Angled Outlet Blade Angle?
The work done per second on runner by water for right angled outlet blade angle formula can be used to evaluate the work done by the water on the runner in a second which is a measure of the capacity of the turbine is calculated using 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. To calculate Work Done per Second on Runner by Water for Right Angled Outlet Blade Angle, you need Density of Fluid in Francis Turbine f), Volume Flow Rate for Francis Turbine (Qf), Velocity of Vane at Inlet for Francis Turbine (u1) & Whirl Velocity at Inlet of Francis Turbine (Vw1). With our tool, you need to enter the respective value for 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 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 Work Done per Second by Francis Turbine?
In this formula, Work Done per Second by Francis Turbine uses 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. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • 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 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)
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