Vane angle at inlet and outlet at extreme edge of runner Calculator

✖Flow velocity at inlet is the velocity of the flow at the entrance of the turbine.ⓘ Flow Velocity at Inlet [V_fi]			+10% -10%
✖Whirl velocity at inlet is defined as the component of velocity of jet in the direction of motion of the vane.ⓘ Whirl velocity at inlet [V_wi]			+10% -10%
✖The Velocity of Vane at Inlet is defined as the velocity of the vane at the inlet of the turbine.ⓘ Velocity of Vane at Inlet [u_i]			+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 and outlet at extreme edge of runner [θ]

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Formula

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Vane angle at inlet and outlet at extreme edge of runner

Formula

`"θ" = atan(("V"_{"fi"})/("V"_{"wi"}-"u"_{"i"}))`

Example

`"15.541°"=atan(("5.84m/s")/("31m/s"-"10m/s"))`

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Vane angle at inlet and outlet at extreme edge of runner Solution

STEP 0: Pre-Calculation Summary

Formula Used

Vane Angle = atan((Flow Velocity at Inlet)/(Whirl velocity at inlet-Velocity of Vane at Inlet))
θ = atan((V_fi)/(V_wi-u_i))
This formula uses 2 Functions, 4 Variables

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)

Variables Used

Vane Angle - (Measured in Radian) - Vane Angle at Inlet is the angle made by the relative velocity of jet with the direction of motion at inlet.
Flow Velocity at Inlet - (Measured in Meter per Second) - Flow velocity at inlet is the velocity of the flow at the entrance of the turbine.
Whirl velocity at inlet - (Measured in Meter per Second) - Whirl velocity at inlet is defined as the component of velocity of jet in the direction of motion of the vane.
Velocity of Vane at Inlet - (Measured in Meter per Second) - The Velocity of Vane at Inlet is defined as the velocity of the vane at the inlet of the turbine.

STEP 1: Convert Input(s) to Base Unit

Flow Velocity at Inlet: 5.84 Meter per Second --> 5.84 Meter per Second No Conversion Required
Whirl velocity at inlet: 31 Meter per Second --> 31 Meter per Second No Conversion Required
Velocity of Vane at Inlet: 10 Meter per Second --> 10 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = atan((V_fi)/(V_wi-u_i)) --> atan((5.84)/(31-10))

Evaluating ... ...

θ = 0.271241545811226

STEP 3: Convert Result to Output's Unit

0.271241545811226 Radian -->15.5409958035905 Degree (Check conversion here)

FINAL ANSWER

15.5409958035905 ≈ 15.541 Degree <-- Vane Angle

(Calculation completed in 00.004 seconds)

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Home » Physics » Fluid Mechanics » Fluid Machinery » Turbine » Kaplan Turbine » Vane angle at inlet and outlet at extreme edge of runner

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Created by Peri Krishna Karthik

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

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< 7 Kaplan Turbine Calculators

Diameter of hub given discharge

Go Diameter of hub = sqrt((Outer diameter of runner^2)-((4/pi)*(Volume Flow Rate/Flow Velocity at Inlet)))

Outer diameter of runner

Go Outer diameter of runner = sqrt((Volume Flow Rate/Flow Velocity at Inlet)*(4/pi)+(Diameter of hub^2))

Velocity of flow at inlet

Go Flow Velocity at Inlet = Volume Flow Rate/((pi/4)*((Outer diameter of runner^2)-(Diameter of hub^2)))

Discharge through runner

Go Volume Flow Rate = (pi/4)*((Outer diameter of runner^2)-(Diameter of hub^2))*Flow Velocity at Inlet

Vane angle at inlet and outlet at extreme edge of runner

Go Vane Angle = atan((Flow Velocity at Inlet)/(Whirl velocity at inlet-Velocity of Vane at Inlet))

Flow velocity given whirl velocity

Go Flow Velocity at Inlet = Whirl velocity at inlet*tan(Guide Blade Angle)

Whirl velocity at inlet

Go Whirl velocity at inlet = Flow Velocity at Inlet/tan(Guide Blade Angle)

Vane angle at inlet and outlet at extreme edge of runner Formula

Vane Angle = atan((Flow Velocity at Inlet)/(Whirl velocity at inlet-Velocity of Vane at Inlet))
θ = atan((V_fi)/(V_wi-u_i))

How does Kaplan turbine operate?

The Kaplan turbine is an inward flow reaction turbine, which means that the working fluid changes pressure as it moves through the turbine and gives up its energy. Power is recovered from both the hydrostatic head and from the kinetic energy of the flowing water. The design combines features of radial and axial turbines. The inlet is a scroll-shaped tube that wraps around the turbine's wicket gate. Water is directed tangentially through the wicket gate and spirals on to a propeller shaped runner, causing it to spin. The outlet is a specially shaped draft tube that helps decelerate the water and recover kinetic energy. The turbine does not need to be at the lowest point of water flow as long as the draft tube remains full of water. A higher turbine location, however, increases the suction that is imparted on the turbine blades by the draft tube. The resulting pressure drop may lead to cavitation. Kaplan turbine efficiencies are typically over 90%, but maybe lower in very low head applications.

What are the other applications of Kaplan turbine?

Kaplan turbines are widely used throughout the world for electrical power production. They cover the lowest head hydro sites and are especially suited for high flow conditions. Inexpensive microturbines on the Kaplan turbine model are manufactured for individual power production designed for 3 m of the head which can work with as little as 0.3 m of the head at a highly reduced performance provided sufficient water flow. Large Kaplan turbines are individually designed for each site to operate at the highest possible efficiency, typically over 90%. They are very expensive to design, manufacture and install, but operate for decades.

How to Calculate Vane angle at inlet and outlet at extreme edge of runner?

Vane angle at inlet and outlet at extreme edge of runner calculator uses Vane Angle = atan((Flow Velocity at Inlet)/(Whirl velocity at inlet-Velocity of Vane at Inlet)) to calculate the Vane Angle, The Vane angle at inlet and outlet at extreme edge of runner formula is used to find the angle made by the relative velocity with the direction of motion of the plate. Vane Angle is denoted by θ symbol.

How to calculate Vane angle at inlet and outlet at extreme edge of runner using this online calculator? To use this online calculator for Vane angle at inlet and outlet at extreme edge of runner, enter Flow Velocity at Inlet (V_fi), Whirl velocity at inlet (V_wi) & Velocity of Vane at Inlet (u_i) and hit the calculate button. Here is how the Vane angle at inlet and outlet at extreme edge of runner calculation can be explained with given input values -> 913.6039 = atan((5.84)/(31-10)).

FAQ

What is Vane angle at inlet and outlet at extreme edge of runner?

The Vane angle at inlet and outlet at extreme edge of runner formula is used to find the angle made by the relative velocity with the direction of motion of the plate and is represented as θ = atan((V_fi)/(V_wi-u_i)) or Vane Angle = atan((Flow Velocity at Inlet)/(Whirl velocity at inlet-Velocity of Vane at Inlet)). Flow velocity at inlet is the velocity of the flow at the entrance of the turbine, Whirl velocity at inlet is defined as the component of velocity of jet in the direction of motion of the vane & The Velocity of Vane at Inlet is defined as the velocity of the vane at the inlet of the turbine.

How to calculate Vane angle at inlet and outlet at extreme edge of runner?

The Vane angle at inlet and outlet at extreme edge of runner formula is used to find the angle made by the relative velocity with the direction of motion of the plate is calculated using Vane Angle = atan((Flow Velocity at Inlet)/(Whirl velocity at inlet-Velocity of Vane at Inlet)). To calculate Vane angle at inlet and outlet at extreme edge of runner, you need Flow Velocity at Inlet (V_fi), Whirl velocity at inlet (V_wi) & Velocity of Vane at Inlet (u_i). With our tool, you need to enter the respective value for Flow Velocity at Inlet, Whirl velocity at inlet & Velocity of Vane 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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