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Power Extracted by Rotor given Power Coefficient of Wind Machine Formula

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Power Extracted by Rotor is the rate at which mechanical energy is extracted by the rotor from the wind stream by reducing its kinetic energy. Check FAQs

P e = C p \cdot (0.5 \cdot ρ \cdot π \cdot (R^{2}) \cdot {V ∞}^{3})

P_e - Power Extracted by Rotor?C_p - Power Coefficient of Wind Machine?ρ - Density of Air?R - Rotor Radius?V_∞ - Free Stream Wind Speed?π - Archimedes' constant?

Power Extracted by Rotor given Power Coefficient of Wind Machine Example

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Here is how the Power Extracted by Rotor given Power Coefficient of Wind Machine equation looks like with Values.

Here is how the Power Extracted by Rotor given Power Coefficient of Wind Machine equation looks like with Units.

Here is how the Power Extracted by Rotor given Power Coefficient of Wind Machine equation looks like.

39.8084 = 0.4 \cdot (0.5 \cdot 1.293 \cdot 3.1416 \cdot (7^{2}) \cdot 10^{3})

39.8084kW = 0.4 \cdot (0.5 \cdot 1.293kg/m³ \cdot 3.1416 \cdot ({7m}^{2}) \cdot {10m/s}^{3})

39.8084 = 0.4 \cdot (0.5 \cdot 1.293 \cdot 3.1416 \cdot (7^{2}) \cdot 10^{3})

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Power Extracted by Rotor given Power Coefficient of Wind Machine Solution

Follow our step by step solution on how to calculate Power Extracted by Rotor given Power Coefficient of Wind Machine?

FIRST Step Consider the formula

P e = C p \cdot (0.5 \cdot ρ \cdot π \cdot (R^{2}) \cdot {V ∞}^{3})

Next Step Substitute values of Variables

∴

P e = 0.4 \cdot (0.5 \cdot 1.293kg/m³ \cdot π \cdot ({7m}^{2}) \cdot {10m/s}^{3})

Next Step Substitute values of Constants

∴

P e = 0.4 \cdot (0.5 \cdot 1.293kg/m³ \cdot 3.1416 \cdot ({7m}^{2}) \cdot {10m/s}^{3})

Next Step Prepare to Evaluate

∴

P e = 0.4 \cdot (0.5 \cdot 1.293 \cdot 3.1416 \cdot (7^{2}) \cdot 10^{3})

Next Step Evaluate

∴

P e = 39808.3771506977W

Next Step Convert to Output's Unit

∴

P e = 39.8083771506977kW

LAST Step Rounding Answer

∴

P e = 39.8084kW

Power Extracted by Rotor given Power Coefficient of Wind Machine Formula Elements

Variables

Constants

Power Extracted by Rotor

Power Extracted by Rotor is the rate at which mechanical energy is extracted by the rotor from the wind stream by reducing its kinetic energy.

Symbol: P_e

Measurement: PowerUnit: kW

Note: Value should be greater than 0.

Formulas to find Power Extracted by Rotor

Power Coefficient of Wind Machine

Power Coefficient of Wind Machine is defined as the ratio of the power extracted by the rotor to the power available in the wind stream.

Symbol: C_p

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 0.6.

Formulas to find Power Coefficient of Wind Machine

Density of Air

Density of Air is the mass of air per unit volume; it decreases with altitude due to lower pressure.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density of Air

Rotor Radius

Rotor Radius is the radius of rotation of the rotor.

Symbol: R

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Rotor Radius

Free Stream Wind Speed

Free Stream Wind Speed is the velocity of the free stream which is the air far upstream of an aerodynamic body i.e. before the body has a chance to deflect, slow down or compress the air.

Symbol: V_∞

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Free Stream Wind Speed

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 Other Renewable Energy Sources category

Go Power Coefficient of Wind Machine

C p = \frac{P e}{0.5 \cdot ρ \cdot π \cdot R^{2} \cdot {V ∞}^{3}}

Go Lift Coefficient of Blade of Wind Rotor

C L = \frac{L}{0.5 \cdot ρ vc \cdot π \cdot R^{2} \cdot {V ∞}^{2}}

Go Lift Force given Lift Coefficient of Blade

L = C L \cdot 0.5 \cdot ρ vc \cdot π \cdot R^{2} \cdot {V ∞}^{2}

Go Drag Coefficient of Blade of Wind Rotor

C D = \frac{F D}{0.5 \cdot ρ vc \cdot π \cdot R^{2} \cdot {V ∞}^{2}}

How to Evaluate Power Extracted by Rotor given Power Coefficient of Wind Machine?

Power Extracted by Rotor given Power Coefficient of Wind Machine evaluator uses Power Extracted by Rotor = Power Coefficient of Wind Machine*(0.5*Density of Air*pi*(Rotor Radius^2)*Free Stream Wind Speed^3) to evaluate the Power Extracted by Rotor, The Power Extracted by Rotor given Power Coefficient of Wind Machine is defined as the rate at which mechanical energy is extracted by the rotor from the wind stream by reducing its kinetic energy. Power Extracted by Rotor is denoted by P_e symbol.

How to evaluate Power Extracted by Rotor given Power Coefficient of Wind Machine using this online evaluator? To use this online evaluator for Power Extracted by Rotor given Power Coefficient of Wind Machine, enter Power Coefficient of Wind Machine (C_p), Density of Air (ρ), Rotor Radius (R) & Free Stream Wind Speed (V_∞) and hit the calculate button.

FAQs on Power Extracted by Rotor given Power Coefficient of Wind Machine

What is the formula to find Power Extracted by Rotor given Power Coefficient of Wind Machine?

The formula of Power Extracted by Rotor given Power Coefficient of Wind Machine is expressed as Power Extracted by Rotor = Power Coefficient of Wind Machine*(0.5*Density of Air*pi*(Rotor Radius^2)*Free Stream Wind Speed^3). Here is an example- 0.039808 = 0.4*(0.5*1.293*pi*(7^2)*10^3).

How to calculate Power Extracted by Rotor given Power Coefficient of Wind Machine?

With Power Coefficient of Wind Machine (C_p), Density of Air (ρ), Rotor Radius (R) & Free Stream Wind Speed (V_∞) we can find Power Extracted by Rotor given Power Coefficient of Wind Machine using the formula - Power Extracted by Rotor = Power Coefficient of Wind Machine*(0.5*Density of Air*pi*(Rotor Radius^2)*Free Stream Wind Speed^3). This formula also uses Archimedes' constant .

Can the Power Extracted by Rotor given Power Coefficient of Wind Machine be negative?

No, the Power Extracted by Rotor given Power Coefficient of Wind Machine, measured in Power cannot be negative.

Which unit is used to measure Power Extracted by Rotor given Power Coefficient of Wind Machine?

Power Extracted by Rotor given Power Coefficient of Wind Machine is usually measured using the Kilowatt[kW] for Power. Watt[kW], Milliwatt[kW], Microwatt[kW] are the few other units in which Power Extracted by Rotor given Power Coefficient of Wind Machine can be measured.

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Power Extracted by Rotor given Power Coefficient of Wind Machine Formula

Power Extracted by Rotor given Power Coefficient of Wind Machine Example

Power Extracted by Rotor given Power Coefficient of Wind Machine Solution

Power Extracted by Rotor given Power Coefficient of Wind Machine Formula Elements

Other formulas in Other Renewable Energy Sources category

How to Evaluate Power Extracted by Rotor given Power Coefficient of Wind Machine?

FAQs on Power Extracted by Rotor given Power Coefficient of Wind Machine

Variable Name