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Power Extracted by Rotor given Power Coefficient of Wind Machine Calculator

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✖Power Coefficient of Wind Machine is a measure of the efficiency of a wind turbine in converting wind energy into mechanical energy.ⓘ Power Coefficient of Wind Machine [C_p]			+10% -10%
✖Density of Air is the mass of air per unit volume, typically measured in kilograms per cubic meter.ⓘ Density of Air [ρ]			+10% -10%
✖Rotor Radius is the distance from the axis of rotation to the tip of the blade in a rotor.ⓘ Rotor Radius [R]			+10% -10%
✖Free Stream Wind Speed is the speed of wind that occurs naturally in the atmosphere, unaffected by any obstacles or wind turbines.ⓘ Free Stream Wind Speed [V_∞]			+10% -10%

✖Power Extracted by Rotor is the amount of energy harnessed from energy sources, such as wind, hydro, or geothermal power, converted into usable electricity.ⓘ Power Extracted by Rotor given Power Coefficient of Wind Machine [P_e]

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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 amount of energy harnessed from energy sources, such as wind, hydro, or geothermal power, converted into usable electricity.
Power Coefficient of Wind Machine - Power Coefficient of Wind Machine is a measure of the efficiency of a wind turbine in converting wind energy into mechanical energy.
Density of Air - (Measured in Kilogram per Cubic Meter) - Density of Air is the mass of air per unit volume, typically measured in kilograms per cubic meter.
Rotor Radius - (Measured in Meter) - Rotor Radius is the distance from the axis of rotation to the tip of the blade in a rotor.
Free Stream Wind Speed - (Measured in Meter per Second) - Free Stream Wind Speed is the speed of wind that occurs naturally in the atmosphere, unaffected by any obstacles or wind turbines.

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: 0.168173 Meter per Second --> 0.168173 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)*0.168173^3)

Evaluating ... ...

P_e = 0.189340398949541

STEP 3: Convert Result to Output's Unit

0.189340398949541 Watt -->0.000189340398949541 Kilowatt (Check conversion here)

FINAL ANSWER

0.000189340398949541 ≈ 0.000189 Kilowatt <-- Power Extracted by Rotor

(Calculation completed in 00.004 seconds)

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< Other Renewable Energy Sources Calculators

Power Extracted by Rotor given Power Coefficient of Wind Machine

LaTeX 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

LaTeX 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

LaTeX 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

LaTeX 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

Power Extracted by Rotor given Power Coefficient of Wind Machine Formula

LaTeX Go

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)

What is Power Coefficient of Wind Machine?

The Power Coefficient (Cp) of a wind machine measures how effectively a wind turbine converts wind energy into usable mechanical power. It is calculated as the ratio of the turbine’s actual power output to the total available wind power at a given wind speed. A higher Cp indicates greater efficiency, though the theoretical limit, known as the Betz limit, caps Cp at 0.59 or 59%, meaning a turbine can capture at most 59% of the wind's kinetic energy due to aerodynamic limitations.

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 -> 1.9E-7 = 0.4*(0.5*1.293*pi*(7^2)*0.168173^3).

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 a measure of the efficiency of a wind turbine in converting wind energy into mechanical energy, Density of Air is the mass of air per unit volume, typically measured in kilograms per cubic meter, Rotor Radius is the distance from the axis of rotation to the tip of the blade in a rotor & Free Stream Wind Speed is the speed of wind that occurs naturally in the atmosphere, unaffected by any obstacles or wind turbines.

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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