Degree of Reaction of Turbine with Right Angled Outlet Blade Calculator

✖Guide Blade Angle For Francis Trubine is defined as the angle between the direction of the jet and the direction of motion of the plate.ⓘ Guide Blade Angle For Francis Trubine [α_f]			+10% -10%
✖Vane Angle at Inlet is the angle made by the relative velocity of jet with the direction of motion at inlet.ⓘ Vane Angle at Inlet [θ_i]			+10% -10%

✖Degree of Reaction is defined as the ratio of pressure energy change inside a runner to the total energy change inside the runner.ⓘ Degree of Reaction of Turbine with Right Angled Outlet Blade [R]

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Degree of Reaction of Turbine with Right Angled Outlet Blade Solution

STEP 0: Pre-Calculation Summary

Formula Used

Degree of Reaction = 1-cot(Guide Blade Angle For Francis Trubine)/(2*(cot(Guide Blade Angle For Francis Trubine)-cot(Vane Angle at Inlet)))
R = 1-cot(α_f)/(2*(cot(α_f)-cot(θ_i)))
This formula uses 1 Functions, 3 Variables

Functions Used

cot - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., cot(Angle)

Variables Used

Degree of Reaction - Degree of Reaction is defined as the ratio of pressure energy change inside a runner to the total energy change inside the runner.
Guide Blade Angle For Francis Trubine - (Measured in Radian) - Guide Blade Angle For Francis Trubine is defined as the angle between the direction of the jet and the direction of motion of the plate.
Vane Angle at Inlet - (Measured in Radian) - Vane Angle at Inlet is the angle made by the relative velocity of jet with the direction of motion at inlet.

STEP 1: Convert Input(s) to Base Unit

Guide Blade Angle For Francis Trubine: 11.03 Degree --> 0.192509816494938 Radian (Check conversion here)
Vane Angle at Inlet: 65 Degree --> 1.1344640137961 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R = 1-cot(α_f)/(2*(cot(α_f)-cot(θ_i))) --> 1-cot(0.192509816494938)/(2*(cot(0.192509816494938)-cot(1.1344640137961)))

Evaluating ... ...

R = 0.450008866151466

STEP 3: Convert Result to Output's Unit

0.450008866151466 --> No Conversion Required

FINAL ANSWER

0.450008866151466 ≈ 0.450009 <-- Degree of Reaction

(Calculation completed in 00.020 seconds)

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Home » Physics » Fluid Mechanics » Fluid Machinery » Turbine » Mechanical » Francis Turbine » Degree of Reaction of Turbine with Right Angled Outlet Blade

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Created by Peri Krishna Karthik

National Institute of Technology Calicut (NIT Calicut), Calicut, Kerala

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< Francis Turbine Calculators

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LaTeX 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))

Velocity of Vane at Inlet given Speed Ratio Francis Turbine

LaTeX 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 Flow Ratio

LaTeX 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))

Pressure Head given Speed Ratio in Francis Turbine

LaTeX 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)

Degree of Reaction of Turbine with Right Angled Outlet Blade Formula

LaTeX 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)))
R = 1-cot(α_f)/(2*(cot(α_f)-cot(θ_i)))

What is the significance of degree of reaction?

Degree of reaction is an important factor in designing the blades of a turbine, compressors, pumps and other turbo-machinery. It also tells about the efficiency of machine and is used for proper selection of a machine and it others for a required purpose. The degree of reaction contributes to the stage efficiency and thus used as a design parameter. Stages having 50% degree of reaction are used where the pressure drop is equally shared by the stator and the rotor for a turbine. This reduces the tendency of boundary layer separation from the blade surface avoiding large stagnation pressure losses. Stage having reaction less than half suggest that pressure drop or enthalpy drop in the rotor is less than the pressure drop in the stator for the turbine. Stage having reaction more than half suggest that pressure drop or enthalpy drop in the rotor is more than the pressure drop in the stator for the turbine.

What if degree of reaction is zero?

This is special case used for impulse turbine which suggest that entire pressure drop in the turbine is obtained in the stator. The stator performs a nozzle action converting pressure head to velocity head. It is difficult to achieve adiabatic expansion in the impulse stage, i.e. expansion only in the nozzle, due to irreversibility involved, in actual practice.

How to Calculate Degree of Reaction of Turbine with Right Angled Outlet Blade?

Degree of Reaction of Turbine with Right Angled Outlet Blade calculator uses Degree of Reaction = 1-cot(Guide Blade Angle For Francis Trubine)/(2*(cot(Guide Blade Angle For Francis Trubine)-cot(Vane Angle at Inlet))) to calculate the Degree of Reaction, The Degree of Reaction of turbine with right angled outlet blade formula is defined as the ratio of the change of pressure energy inside the runner to the change of total energy inside the runner. Degree of Reaction is denoted by R symbol.

How to calculate Degree of Reaction of Turbine with Right Angled Outlet Blade using this online calculator? To use this online calculator for Degree of Reaction of Turbine with Right Angled Outlet Blade, enter Guide Blade Angle For Francis Trubine (α_f) & Vane Angle at Inlet (θ_i) and hit the calculate button. Here is how the Degree of Reaction of Turbine with Right Angled Outlet Blade calculation can be explained with given input values -> 0.450009 = 1-cot(0.192509816494938)/(2*(cot(0.192509816494938)-cot(1.1344640137961))).

FAQ

What is Degree of Reaction of Turbine with Right Angled Outlet Blade?

The Degree of Reaction of turbine with right angled outlet blade formula is defined as the ratio of the change of pressure energy inside the runner to the change of total energy inside the runner and is represented as R = 1-cot(α_f)/(2*(cot(α_f)-cot(θ_i))) or Degree of Reaction = 1-cot(Guide Blade Angle For Francis Trubine)/(2*(cot(Guide Blade Angle For Francis Trubine)-cot(Vane Angle at Inlet))). Guide Blade Angle For Francis Trubine is defined as the angle between the direction of the jet and the direction of motion of the plate & Vane Angle at Inlet is the angle made by the relative velocity of jet with the direction of motion at inlet.

How to calculate Degree of Reaction of Turbine with Right Angled Outlet Blade?

The Degree of Reaction of turbine with right angled outlet blade formula is defined as the ratio of the change of pressure energy inside the runner to the change of total energy inside the runner is calculated using Degree of Reaction = 1-cot(Guide Blade Angle For Francis Trubine)/(2*(cot(Guide Blade Angle For Francis Trubine)-cot(Vane Angle at Inlet))). To calculate Degree of Reaction of Turbine with Right Angled Outlet Blade, you need Guide Blade Angle For Francis Trubine (α_f) & Vane Angle at Inlet (θ_i). With our tool, you need to enter the respective value for Guide Blade Angle For Francis Trubine & Vane Angle at Inlet 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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