Free Stream Wind Speed given Drag Coefficient Solution

STEP 0: Pre-Calculation Summary
Formula Used
Free Stream Wind Speed = sqrt(Drag Force/(0.5*Density of air VC*pi*Rotor Radius^2*Drag Coefficient))
V = sqrt(FD/(0.5*ρvc*pi*R^2*CD))
This formula uses 1 Constants, 1 Functions, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
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.
Drag Force - (Measured in Newton) - Drag Force is the resisting force experienced by an object moving through a fluid.
Density of air VC - (Measured in Kilogram per Cubic Meter) - Density of air VC is air density at normal condition.
Rotor Radius - (Measured in Meter) - Rotor Radius is the radius of rotation of the rotor.
Drag Coefficient - Drag Coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water.
STEP 1: Convert Input(s) to Base Unit
Drag Force: 80 Newton --> 80 Newton No Conversion Required
Density of air VC: 1.225 Kilogram per Cubic Meter --> 1.225 Kilogram per Cubic Meter No Conversion Required
Rotor Radius: 7 Meter --> 7 Meter No Conversion Required
Drag Coefficient: 30 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = sqrt(FD/(0.5*ρvc*pi*R^2*CD)) --> sqrt(80/(0.5*1.225*pi*7^2*30))
Evaluating ... ...
V = 0.168173802241389
STEP 3: Convert Result to Output's Unit
0.168173802241389 Meter per Second --> No Conversion Required
FINAL ANSWER
0.168173802241389 0.168174 Meter per Second <-- Free Stream Wind Speed
(Calculation completed in 00.004 seconds)

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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

Free Stream Wind Speed given Drag Coefficient Formula

Free Stream Wind Speed = sqrt(Drag Force/(0.5*Density of air VC*pi*Rotor Radius^2*Drag Coefficient))
V = sqrt(FD/(0.5*ρvc*pi*R^2*CD))

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A 5° pitch angle is optimum for a wind turbine when the operating velocity is 7 m/s for optimum power generation.

How to Calculate Free Stream Wind Speed given Drag Coefficient?

Free Stream Wind Speed given Drag Coefficient calculator uses Free Stream Wind Speed = sqrt(Drag Force/(0.5*Density of air VC*pi*Rotor Radius^2*Drag Coefficient)) to calculate the Free Stream Wind Speed, The Free Stream Wind Speed given Drag Coefficient 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 is denoted by V symbol.

How to calculate Free Stream Wind Speed given Drag Coefficient using this online calculator? To use this online calculator for Free Stream Wind Speed given Drag Coefficient, enter Drag Force (FD), Density of air VC vc), Rotor Radius (R) & Drag Coefficient (CD) and hit the calculate button. Here is how the Free Stream Wind Speed given Drag Coefficient calculation can be explained with given input values -> 0.168174 = sqrt(80/(0.5*1.225*pi*7^2*30)).

FAQ

What is Free Stream Wind Speed given Drag Coefficient?
The Free Stream Wind Speed given Drag Coefficient 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 and is represented as V = sqrt(FD/(0.5*ρvc*pi*R^2*CD)) or Free Stream Wind Speed = sqrt(Drag Force/(0.5*Density of air VC*pi*Rotor Radius^2*Drag Coefficient)). Drag Force is the resisting force experienced by an object moving through a fluid, Density of air VC is air density at normal condition, Rotor Radius is the radius of rotation of the rotor & Drag Coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water.
How to calculate Free Stream Wind Speed given Drag Coefficient?
The Free Stream Wind Speed given Drag Coefficient 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 is calculated using Free Stream Wind Speed = sqrt(Drag Force/(0.5*Density of air VC*pi*Rotor Radius^2*Drag Coefficient)). To calculate Free Stream Wind Speed given Drag Coefficient, you need Drag Force (FD), Density of air VC vc), Rotor Radius (R) & Drag Coefficient (CD). With our tool, you need to enter the respective value for Drag Force, Density of air VC, Rotor Radius & Drag Coefficient 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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