Volume Flow Rate of Acute Angled Francis Turbine given Work Done Per Second on Runner Calculator

✖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.ⓘ Work Done per Second by Francis Turbine [W]			+10% -10%
✖The Density of Fluid in Francis Turbine is the corresponding density of the fluid at the given conditions in the franchise turbine.ⓘ Density of Fluid in Francis Turbine [ρ_f]			+10% -10%
✖Whirl Velocity at Inlet of Francis Turbine is the tangential component of absolute velocity at the blade inlet.ⓘ Whirl Velocity at Inlet of Francis Turbine [V_w1]			+10% -10%
✖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%
✖Whirl Velocity at Outlet of Francis Turbine is defined as the component of velocity of the jet in the direction of motion of the vane at the outlet.ⓘ Whirl Velocity at Outlet of Francis Turbine [V_w2]			+10% -10%
✖The Velocity of Vane at Outlet for Francis Turbine is defined as the tangential velocity of the vane at the jet outlet.ⓘ Velocity of Vane at Outlet for Francis Turbine [u₂]			+10% -10%

✖Volume Flow Rate for Francis Turbine is the volume of fluid that passes per unit of time.ⓘ Volume Flow Rate of Acute Angled Francis Turbine given Work Done Per Second on Runner [Q_f]

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Volume Flow Rate of Acute Angled Francis Turbine given Work Done Per Second on Runner

Formula

`"Q"_{"f"} = "W"/("ρ"_{"f"}*("V"_{"w1"}*"u"_{"1"}+"V"_{"w2"}*"u"_{"2"}))`

Example

`"1.173163m³/s"="183kW"/("1000kg/m³"*("12.93m/s"*"9.45m/s"+"6.5m/s"*"5.2m/s"))`

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Volume Flow Rate of Acute Angled Francis Turbine given Work Done Per Second on Runner Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
Q_f = W/(ρ_f*(V_w1*u₁+V_w2*u₂))
This formula uses 7 Variables

Variables Used

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.
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.
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.
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 Outlet of Francis Turbine - (Measured in Meter per Second) - Whirl Velocity at Outlet of Francis Turbine is defined as the component of velocity of the jet in the direction of motion of the vane at the outlet.
Velocity of Vane at Outlet for Francis Turbine - (Measured in Meter per Second) - The Velocity of Vane at Outlet for Francis Turbine is defined as the tangential velocity of the vane at the jet outlet.

STEP 1: Convert Input(s) to Base Unit

Work Done per Second by Francis Turbine: 183 Kilowatt --> 183000 Watt (Check conversion here)
Density of Fluid in Francis Turbine: 1000 Kilogram per Cubic Meter --> 1000 Kilogram per Cubic Meter No Conversion Required
Whirl Velocity at Inlet of Francis Turbine: 12.93 Meter per Second --> 12.93 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 Outlet of Francis Turbine: 6.5 Meter per Second --> 6.5 Meter per Second No Conversion Required
Velocity of Vane at Outlet for Francis Turbine: 5.2 Meter per Second --> 5.2 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_f = W/(ρ_f*(V_w1*u₁+V_w2*u₂)) --> 183000/(1000*(12.93*9.45+6.5*5.2))

Evaluating ... ...

Q_f = 1.17316340627674

STEP 3: Convert Result to Output's Unit

1.17316340627674 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

1.17316340627674 ≈ 1.173163 Cubic Meter per Second <-- Volume Flow Rate for Francis Turbine

(Calculation completed in 00.004 seconds)

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Home » Physics » Fluid Mechanics » Fluid Machinery » Turbine » Francis Turbine » Volume Flow Rate of Acute Angled Francis Turbine given Work Done Per Second on Runner

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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))))

Volume Flow Rate of Acute Angled Francis Turbine given Work Done Per Second on Runner Formula

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 Volume Flow Rate of Acute Angled Francis Turbine given Work Done Per Second on Runner?

Volume Flow Rate of Acute Angled Francis Turbine given Work Done Per Second on Runner calculator uses 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)) to calculate the Volume Flow Rate for Francis Turbine, The Volume flow rate of acute angled Francis turbine given work done per second on runner formula is used to find the volume flow rate when the work done per second and inlet and outlet vane and whirl velocities are known. Volume Flow Rate for Francis Turbine is denoted by Q_f symbol.

How to calculate Volume Flow Rate of Acute Angled Francis Turbine given Work Done Per Second on Runner using this online calculator? To use this online calculator for Volume Flow Rate of Acute Angled Francis Turbine given Work Done Per Second on Runner, enter Work Done per Second by Francis Turbine (W), Density of Fluid in Francis Turbine (ρ_f), Whirl Velocity at Inlet of Francis Turbine (V_w1), Velocity of Vane at Inlet for Francis Turbine (u₁), Whirl Velocity at Outlet of Francis Turbine (V_w2) & Velocity of Vane at Outlet for Francis Turbine (u₂) and hit the calculate button. Here is how the Volume Flow Rate of Acute Angled Francis Turbine given Work Done Per Second on Runner calculation can be explained with given input values -> 1.173163 = 183000/(1000*(12.93*9.45+6.5*5.2)).

FAQ

What is Volume Flow Rate of Acute Angled Francis Turbine given Work Done Per Second on Runner?

The Volume flow rate of acute angled Francis turbine given work done per second on runner formula is used to find the volume flow rate when the work done per second and inlet and outlet vane and whirl velocities are known and is represented as Q_f = W/(ρ_f*(V_w1*u₁+V_w2*u₂)) or 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 by Francis Turbine is defined as the amount of work that is done by the Francis turbine in a given unit of time, The Density of Fluid in Francis Turbine is the corresponding density of the fluid at the given conditions in the franchise turbine, Whirl Velocity at Inlet of Francis Turbine is the tangential component of absolute velocity at the blade inlet, 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 Outlet of Francis Turbine is defined as the component of velocity of the jet in the direction of motion of the vane at the outlet & The Velocity of Vane at Outlet for Francis Turbine is defined as the tangential velocity of the vane at the jet outlet.

How to calculate Volume Flow Rate of Acute Angled Francis Turbine given Work Done Per Second on Runner?

The Volume flow rate of acute angled Francis turbine given work done per second on runner formula is used to find the volume flow rate when the work done per second and inlet and outlet vane and whirl velocities are known is calculated using 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)). To calculate Volume Flow Rate of Acute Angled Francis Turbine given Work Done Per Second on Runner, you need Work Done per Second by Francis Turbine (W), Density of Fluid in Francis Turbine (ρ_f), Whirl Velocity at Inlet of Francis Turbine (V_w1), Velocity of Vane at Inlet for Francis Turbine (u₁), Whirl Velocity at Outlet of Francis Turbine (V_w2) & Velocity of Vane at Outlet for Francis Turbine (u₂). With our tool, you need to enter the respective value for 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 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 Volume Flow Rate for Francis Turbine?

In this formula, Volume Flow Rate for Francis Turbine uses 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. We can use 2 other way(s) to calculate the same, which is/are as follows -

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 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)

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