Power Extracted by Rotor given Power Coefficient of Wind Machine Calculator

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✖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.ⓘ Power Coefficient of Wind Machine [C_p]			+10% -10%
✖Density of Air is the mass of air per unit volume; it decreases with altitude due to lower pressure.ⓘ Density of Air [ρ]			+10% -10%
✖Rotor Radius is the radius of rotation of the rotor.ⓘ Rotor Radius [R]			+10% -10%
✖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.ⓘ Free Stream Wind Speed [V_∞]			+10% -10%

✖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.ⓘ Power Extracted by Rotor given Power Coefficient of Wind Machine [P_e]

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Formula

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Power Extracted by Rotor given Power Coefficient of Wind Machine

Formula

`"P"_{"e"} = "C"_{"p"}*(0.5*"ρ"*pi*("R"^2)*"V"_{"∞"}^3)`

Example

`"39.80838kW"="0.4"*(0.5*"1.293kg/m³"*pi*(("7m")^2)*("10m/s")^3)`

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Power Extracted by Rotor given Power Coefficient of Wind Machine Solution

STEP 0: Pre-Calculation Summary

Formula Used

Power Extracted by Rotor = Power Coefficient of Wind Machine*(0.5*Density of Air*pi*(Rotor Radius^2)*Free Stream Wind Speed^3)
P_e = C_p*(0.5*ρ*pi*(R^2)*V_∞^3)
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Power Extracted by Rotor - (Measured in Watt) - 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.
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.
Density of Air - (Measured in Kilogram per Cubic Meter) - Density of Air is the mass of air per unit volume; it decreases with altitude due to lower pressure.
Rotor Radius - (Measured in Meter) - Rotor Radius is the radius of rotation of the rotor.
Free Stream Wind Speed - (Measured in Meter per Second) - 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.

STEP 1: Convert Input(s) to Base Unit

Power Coefficient of Wind Machine: 0.4 --> No Conversion Required
Density of Air: 1.293 Kilogram per Cubic Meter --> 1.293 Kilogram per Cubic Meter No Conversion Required
Rotor Radius: 7 Meter --> 7 Meter No Conversion Required
Free Stream Wind Speed: 10 Meter per Second --> 10 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_e = C_p*(0.5*ρ*pi*(R^2)*V_∞^3) --> 0.4*(0.5*1.293*pi*(7^2)*10^3)

Evaluating ... ...

P_e = 39808.3771506977

STEP 3: Convert Result to Output's Unit

39808.3771506977 Watt -->39.8083771506977 Kilowatt (Check conversion here)

FINAL ANSWER

39.8083771506977 ≈ 39.80838 Kilowatt <-- Power Extracted by Rotor

(Calculation completed in 00.020 seconds)

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< 12 Other Renewable Energy Sources Calculators

Free Stream Wind Speed given Drag Coefficient

Go Free Stream Wind Speed = sqrt(Drag Force/(0.5*Density of air VC*pi*Rotor Radius^2*Drag Coefficient))

Power Extracted by Rotor given Power Coefficient of Wind Machine

Go Power Extracted by Rotor = Power Coefficient of Wind Machine*(0.5*Density of Air*pi*(Rotor Radius^2)*Free Stream Wind Speed^3)

Power Coefficient of Wind Machine

Go Power Coefficient of Wind Machine = Power Extracted by Rotor/(0.5*Density of Air*pi*Rotor Radius^2*Free Stream Wind Speed^3)

Lift Coefficient of Blade of Wind Rotor

Go Lift Coefficient of Blade of Wind Rotor = Lift Force/(0.5*Density of air VC*pi*Rotor Radius^2*Free Stream Wind Speed^2)

Lift Force given Lift Coefficient of Blade

Go Lift Force = Lift Coefficient of Blade of Wind Rotor*0.5*Density of air VC*pi*Rotor Radius^2*Free Stream Wind Speed^2

Drag Coefficient of Blade of Wind Rotor

Go Drag Coefficient = Drag Force/(0.5*Density of air VC*pi*Rotor Radius^2*Free Stream Wind Speed^2)

Solidity of Wind Machine

Go Solidity of Wind Machine = (Number of Blades in Wind turbine*Mean Chord of Blades)/(pi*Rotor Radius)

Number of Blades of Wind Turbine given Solidity of Wind Turbine

Go Number of Blades in Wind turbine = (Solidity of Wind Machine*pi*Rotor Radius)/Mean Chord of Blades

Mean Chord of Blades given Solidity of Wind Machine

Go Mean Chord of Blades = (Solidity of Wind Machine*pi*Rotor Radius)/Number of Blades in Wind turbine

Angular Velocity of Rotor given Tip Speed Ratio

Go Angular Velocity of Rotor = (Tip Speed Ratio*Free Stream Wind Speed)/Rotor Radius

Rotor Radius given Tip Speed Ratio

Go Rotor Radius = (Tip Speed Ratio*Free Stream Wind Speed)/Angular Velocity of Rotor

Tip Speed Ratio

Go Tip Speed Ratio = (Angular Velocity of Rotor*Rotor Radius)/Free Stream Wind Speed

Power Extracted by Rotor given Power Coefficient of Wind Machine Formula

Power Extracted by Rotor = Power Coefficient of Wind Machine*(0.5*Density of Air*pi*(Rotor Radius^2)*Free Stream Wind Speed^3)
P_e = C_p*(0.5*ρ*pi*(R^2)*V_∞^3)

How much wind speed does it take to power a wind turbine?

A typical modern turbine will start to generate electricity when wind speeds reach six to nine miles per hour (mph), known as the cut-in speed. Turbines will shut down if the wind is blowing too hard (roughly 55 miles an hour) to prevent equipment damage.

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

Power Extracted by Rotor given Power Coefficient of Wind Machine calculator 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 calculate 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 calculate Power Extracted by Rotor given Power Coefficient of Wind Machine using this online calculator? To use this online calculator 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. Here is how the Power Extracted by Rotor given Power Coefficient of Wind Machine calculation can be explained with given input values -> 0.039808 = 0.4*(0.5*1.293*pi*(7^2)*10^3).

FAQ

What is Power Extracted by Rotor given Power Coefficient of Wind Machine?

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 and is represented as P_e = C_p*(0.5*ρ*pi*(R^2)*V_∞^3) or Power Extracted by Rotor = Power Coefficient of Wind Machine*(0.5*Density of Air*pi*(Rotor Radius^2)*Free Stream Wind Speed^3). 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, Density of Air is the mass of air per unit volume; it decreases with altitude due to lower pressure, Rotor Radius is the radius of rotation of the rotor & 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.

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

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 is calculated using Power Extracted by Rotor = Power Coefficient of Wind Machine*(0.5*Density of Air*pi*(Rotor Radius^2)*Free Stream Wind Speed^3). To calculate Power Extracted by Rotor given Power Coefficient of Wind Machine, you need Power Coefficient of Wind Machine (C_p), Density of Air (ρ), Rotor Radius (R) & Free Stream Wind Speed (V_∞). With our tool, you need to enter the respective value for Power Coefficient of Wind Machine, Density of Air, Rotor Radius & Free Stream Wind Speed 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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