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Discharge through runner Formula

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Volume Flow Rate is the volume of fluid that passes per unit of time. Check FAQs

Q = \frac{π}{4} \cdot ({D o}^{2} - {D b}^{2}) \cdot V fi

Q - Volume Flow Rate?D_o - Outer Diameter of Runner?D_b - Diameter of Hub?V_fi - Flow Velocity at Inlet?π - Archimedes' constant?

Discharge through runner Example

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Here is how the Discharge through runner equation looks like with Values.

Here is how the Discharge through runner equation looks like with Units.

Here is how the Discharge through runner equation looks like.

42.1405 = \frac{3.1416}{4} \cdot ({3.5}^{2} - {1.75}^{2}) \cdot 5.84

42.1405m³/s = \frac{3.1416}{4} \cdot ({3.5m}^{2} - {1.75m}^{2}) \cdot 5.84m/s

42.1405 = \frac{3.1416}{4} \cdot ({3.5}^{2} - {1.75}^{2}) \cdot 5.84

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Discharge through runner Solution

Follow our step by step solution on how to calculate Discharge through runner?

FIRST Step Consider the formula

Q = \frac{π}{4} \cdot ({D o}^{2} - {D b}^{2}) \cdot V fi

Next Step Substitute values of Variables

∴

Q = \frac{π}{4} \cdot ({3.5m}^{2} - {1.75m}^{2}) \cdot 5.84m/s

Next Step Substitute values of Constants

∴

Q = \frac{3.1416}{4} \cdot ({3.5m}^{2} - {1.75m}^{2}) \cdot 5.84m/s

Next Step Prepare to Evaluate

∴

Q = \frac{3.1416}{4} \cdot ({3.5}^{2} - {1.75}^{2}) \cdot 5.84

Next Step Evaluate

∴

Q = 42.1405384570901m³/s

LAST Step Rounding Answer

∴

Q = 42.1405m³/s

Discharge through runner Formula Elements

Variables

Constants

Volume Flow Rate

Volume Flow Rate is the volume of fluid that passes per unit of time.

Symbol: Q

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Volume Flow Rate

Outer Diameter of Runner

Outer Diameter of Runner is the diameter of the outer surface of the runner.

Symbol: D_o

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Outer Diameter of Runner

Diameter of Hub

Diameter of Hub is the diameter of the surface of the hub which is adjacent to the fluid flow.

Symbol: D_b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diameter of Hub

Flow Velocity at Inlet

Flow Velocity at Inlet is the velocity of the flow at the entrance of the turbine.

Symbol: V_fi

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Flow Velocity at Inlet

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Kaplan Turbine category

Go Outer diameter of runner

D o = \sqrt{\frac{Q}{V fi} \cdot \frac{4}{π} + {D b}^{2}}

Go Diameter of hub given discharge

D b = \sqrt{{D o}^{2} - (\frac{4}{π} \cdot \frac{Q}{V fi})}

Go Velocity of flow at inlet

V fi = \frac{Q}{\frac{π}{4} \cdot ({D o}^{2} - {D b}^{2})}

Go Whirl velocity at inlet

V wi = \frac{V fi}{\tan (α)}

How to Evaluate Discharge through runner?

Discharge through runner evaluator uses Volume Flow Rate = pi/4*(Outer Diameter of Runner^2-Diameter of Hub^2)*Flow Velocity at Inlet to evaluate the Volume Flow Rate, The Discharge through runner formula is defined as the amount of fluid passing through the runner in a given unit of time. Volume Flow Rate is denoted by Q symbol.

How to evaluate Discharge through runner using this online evaluator? To use this online evaluator for Discharge through runner, enter Outer Diameter of Runner (D_o), Diameter of Hub (D_b) & Flow Velocity at Inlet (V_fi) and hit the calculate button.

FAQs on Discharge through runner

What is the formula to find Discharge through runner?

The formula of Discharge through runner is expressed as Volume Flow Rate = pi/4*(Outer Diameter of Runner^2-Diameter of Hub^2)*Flow Velocity at Inlet. Here is an example- 42.14054 = pi/4*(3.5^2-1.75^2)*5.84.

How to calculate Discharge through runner?

With Outer Diameter of Runner (D_o), Diameter of Hub (D_b) & Flow Velocity at Inlet (V_fi) we can find Discharge through runner using the formula - Volume Flow Rate = pi/4*(Outer Diameter of Runner^2-Diameter of Hub^2)*Flow Velocity at Inlet. This formula also uses Archimedes' constant .

Can the Discharge through runner be negative?

No, the Discharge through runner, measured in Volumetric Flow Rate cannot be negative.

Which unit is used to measure Discharge through runner?

Discharge through runner is usually measured using the Cubic Meter per Second[m³/s] for Volumetric Flow Rate. Cubic Meter per Day[m³/s], Cubic Meter per Hour[m³/s], Cubic Meter per Minute[m³/s] are the few other units in which Discharge through runner can be measured.

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Discharge through runner Formula

Discharge through runner Example

Discharge through runner Solution

Discharge through runner Formula Elements

Other formulas in Kaplan Turbine category

How to Evaluate Discharge through runner?

FAQs on Discharge through runner

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