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Vane Angle at Inlet from Degree of Reaction Formula

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Vane Angle at Inlet is the angle made by the relative velocity of jet with the direction of motion at inlet. Check FAQs

θ i = a \cot (\cot (α f) \cdot (1 - \frac{1}{2 \cdot (1 - R)}))

θ_i - Vane Angle at Inlet?α_f - Guide Blade Angle For Francis Trubine?R - Degree of Reaction?

Vane Angle at Inlet from Degree of Reaction Example

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Here is how the Vane Angle at Inlet from Degree of Reaction equation looks like with Values.

Here is how the Vane Angle at Inlet from Degree of Reaction equation looks like with Units.

Here is how the Vane Angle at Inlet from Degree of Reaction equation looks like.

64.9965 = a \cot (\cot (11.03) \cdot (1 - \frac{1}{2 \cdot (1 - 0.45)}))

64.9965° = a \cot (\cot (11.03°) \cdot (1 - \frac{1}{2 \cdot (1 - 0.45)}))

64.9965 = a \cot (\cot (11.03) \cdot (1 - \frac{1}{2 \cdot (1 - 0.45)}))

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Vane Angle at Inlet from Degree of Reaction Solution

Follow our step by step solution on how to calculate Vane Angle at Inlet from Degree of Reaction?

FIRST Step Consider the formula

θ i = a \cot (\cot (α f) \cdot (1 - \frac{1}{2 \cdot (1 - R)}))

Next Step Substitute values of Variables

∴

θ i = a \cot (\cot (11.03°) \cdot (1 - \frac{1}{2 \cdot (1 - 0.45)}))

Next Step Convert Units

∴

θ i = a \cot (\cot (0.1925rad) \cdot (1 - \frac{1}{2 \cdot (1 - 0.45)}))

Next Step Prepare to Evaluate

∴

θ i = a \cot (\cot (0.1925) \cdot (1 - \frac{1}{2 \cdot (1 - 0.45)}))

Next Step Evaluate

∴

θ i = 1.13440226038694rad

Next Step Convert to Output's Unit

∴

θ i = 64.9964617902845°

LAST Step Rounding Answer

∴

θ i = 64.9965°

Vane Angle at Inlet from Degree of Reaction Formula Elements

Variables

Functions

Vane Angle at Inlet

Vane Angle at Inlet is the angle made by the relative velocity of jet with the direction of motion at inlet.

Symbol: θ_i

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Vane Angle at Inlet

Guide Blade Angle For Francis Trubine

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.

Symbol: α_f

Measurement: AngleUnit: °

Note: Value should be less than 361.

Formulas to find Guide Blade Angle For Francis Trubine

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.

Symbol: R

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Degree of Reaction

cot

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: cot(Angle)

acot

The ACOT function calculates the arccotangent of a given number which is an angle given in radians from 0 (zero) to pi.

Syntax: acot(Number)

Other formulas in Francis Turbine category

Go Francis Turbine Speed Ratio

K u = \frac{u 1}{\sqrt{2 \cdot g \cdot H i}}

Go Velocity of Vane at Inlet given Speed Ratio Francis Turbine

u 1 = K u \cdot \sqrt{2 \cdot g \cdot H i}

Go Pressure Head given Speed Ratio in Francis Turbine

H i = \frac{{(\frac{u 1}{K u})}^{2}}{2 \cdot g}

Go Francis Turbine Flow Ratio

K f = \frac{V f1}{\sqrt{2 \cdot g \cdot H i}}

How to Evaluate Vane Angle at Inlet from Degree of Reaction?

Vane Angle at Inlet from Degree of Reaction evaluator uses Vane Angle at Inlet = acot(cot(Guide Blade Angle For Francis Trubine)*(1-1/(2*(1-Degree of Reaction)))) to evaluate the Vane Angle at Inlet, The Vane angle at inlet from degree of reaction formula is used to find the vane angle at inlet of a francis turbine with right angled outlet blade angle. Vane Angle at Inlet is denoted by θ_i symbol.

How to evaluate Vane Angle at Inlet from Degree of Reaction using this online evaluator? To use this online evaluator for Vane Angle at Inlet from Degree of Reaction, enter Guide Blade Angle For Francis Trubine (α_f) & Degree of Reaction (R) and hit the calculate button.

FAQs on Vane Angle at Inlet from Degree of Reaction

What is the formula to find Vane Angle at Inlet from Degree of Reaction?

The formula of Vane Angle at Inlet from Degree of Reaction is expressed as Vane Angle at Inlet = acot(cot(Guide Blade Angle For Francis Trubine)*(1-1/(2*(1-Degree of Reaction)))). Here is an example- 3724.023 = acot(cot(0.192509816494938)*(1-1/(2*(1-0.45)))).

How to calculate Vane Angle at Inlet from Degree of Reaction?

With Guide Blade Angle For Francis Trubine (α_f) & Degree of Reaction (R) we can find Vane Angle at Inlet from Degree of Reaction using the formula - Vane Angle at Inlet = acot(cot(Guide Blade Angle For Francis Trubine)*(1-1/(2*(1-Degree of Reaction)))). This formula also uses Cotangent (cot), Inverse cotangent (acot) function(s).

Can the Vane Angle at Inlet from Degree of Reaction be negative?

No, the Vane Angle at Inlet from Degree of Reaction, measured in Angle cannot be negative.

Which unit is used to measure Vane Angle at Inlet from Degree of Reaction?

Vane Angle at Inlet from Degree of Reaction is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Vane Angle at Inlet from Degree of Reaction can be measured.

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