Hydraulic Efficiency of Francis Turbine with Right Angled Outlet Blade Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
ηh = (Vw1*u1)/(g*Hf)
This formula uses 5 Variables
Variables Used
Hydraulic Efficiency of Francis Turbine - The Hydraulic Efficiency of Francis Turbine is the measure of the amount of work input that is converted into useful work output.
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.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration Due to Gravity is acceleration gained by an object because of gravitational force.
Net Francis Turbine Head - (Measured in Meter) - The Net Francis Turbine Head is defined as the net water head in the turbine.
STEP 1: Convert Input(s) to Base Unit
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
Acceleration due to Gravity: 9.81 Meter per Square Second --> 9.81 Meter per Square Second No Conversion Required
Net Francis Turbine Head: 21.9 Meter --> 21.9 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ηh = (Vw1*u1)/(g*Hf) --> (12.93*9.45)/(9.81*21.9)
Evaluating ... ...
ηh = 0.568744501696619
STEP 3: Convert Result to Output's Unit
0.568744501696619 --> No Conversion Required
FINAL ANSWER
0.568744501696619 0.568745 <-- Hydraulic Efficiency of Francis Turbine
(Calculation completed in 00.020 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))))

Hydraulic Efficiency of Francis Turbine with Right Angled Outlet Blade Formula

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)
ηh = (Vw1*u1)/(g*Hf)

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 Hydraulic Efficiency of Francis Turbine with Right Angled Outlet Blade?

Hydraulic Efficiency of Francis Turbine with Right Angled Outlet Blade calculator uses 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) to calculate the Hydraulic Efficiency of Francis Turbine, Hydraulic efficiency of Francis turbine with right angled outlet blade formula is defined as the ratio of runner power i.e., the power delivered by water to the runner and the water power. Hydraulic Efficiency of Francis Turbine is denoted by ηh symbol.

How to calculate Hydraulic Efficiency of Francis Turbine with Right Angled Outlet Blade using this online calculator? To use this online calculator for Hydraulic Efficiency of Francis Turbine with Right Angled Outlet Blade, enter Whirl Velocity at Inlet of Francis Turbine (Vw1), Velocity of Vane at Inlet for Francis Turbine (u1), Acceleration due to Gravity (g) & Net Francis Turbine Head (Hf) and hit the calculate button. Here is how the Hydraulic Efficiency of Francis Turbine with Right Angled Outlet Blade calculation can be explained with given input values -> 0.569325 = (12.93*9.45)/(9.81*21.9).

FAQ

What is Hydraulic Efficiency of Francis Turbine with Right Angled Outlet Blade?
Hydraulic efficiency of Francis turbine with right angled outlet blade formula is defined as the ratio of runner power i.e., the power delivered by water to the runner and the water power and is represented as ηh = (Vw1*u1)/(g*Hf) or 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). 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, Acceleration Due to Gravity is acceleration gained by an object because of gravitational force & The Net Francis Turbine Head is defined as the net water head in the turbine.
How to calculate Hydraulic Efficiency of Francis Turbine with Right Angled Outlet Blade?
Hydraulic efficiency of Francis turbine with right angled outlet blade formula is defined as the ratio of runner power i.e., the power delivered by water to the runner and the water power is calculated using 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). To calculate Hydraulic Efficiency of Francis Turbine with Right Angled Outlet Blade, you need Whirl Velocity at Inlet of Francis Turbine (Vw1), Velocity of Vane at Inlet for Francis Turbine (u1), Acceleration due to Gravity (g) & Net Francis Turbine Head (Hf). With our tool, you need to enter the respective value for Whirl Velocity at Inlet of Francis Turbine, Velocity of Vane at Inlet for Francis Turbine, Acceleration due to Gravity & Net Francis Turbine Head 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 Hydraulic Efficiency of Francis Turbine?
In this formula, Hydraulic Efficiency of Francis Turbine uses Whirl Velocity at Inlet of Francis Turbine, Velocity of Vane at Inlet for Francis Turbine, Acceleration due to Gravity & Net Francis Turbine Head. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • 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 = (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)
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