How Much Power Does a 35% Efficient 80m Wind Turbine Generate at 30kph?

[russde]

I have a Thermo I problem:
Given: 80m diameter wind turbine rotating at 20rpm under steady wind conditions at an average wind velocity of 30kph. The eff of the system is 35%.

Need: Power generated

Assumptions (made by me):delta PE ~0; mass=constant; operating at Steady Sate; T~constant

Now, since the eff is = W/Energy and E=delta U +deltaKE +deltaPE this should reduce to:
Eff=W/deltaKE with my assumptions

deltaKE=1/2 m (V2^2 - V1^2)
I know that V2 should be larger than V1 and p2 should be less than p1 but this is where I get stuck, finding V2.
With T~constant specific enthalpy is 0, and entropy will also be 0...
right?
How about a hint to get me on the right path?
Thanks,
R

 

[Delta]

This is less about thermodynamics and more about flow.

Bernoulli's equation gives us the Kinetic Energy per unit volume. From the diameter of the blades we can work out the acceptance area and hence the volume flowing through the turbine per second using the wind velocity.

Then the maximum power can be found.

Don't forget the efficieny!

 

[thepatientmental]

andy

Hello Randy,

To calculate the power generated by a wind turbine, we can use the following formula:

P = 0.5 * ρ * A * v^3 * Cp

Where:
P = power generated (in watts)
ρ = air density (in kg/m^3)
A = swept area of the turbine blades (in m^2)
v = wind velocity (in m/s)
Cp = power coefficient (efficiency of the turbine)

In your given scenario, we have the following values:
ρ = 1.225 kg/m^3 (for standard air density at sea level)
A = π * (80/2)^2 = 5026.55 m^2 (using the diameter of 80m to calculate the swept area)
v = 30 kph = 8.33 m/s (converting from kph to m/s)
Cp = 0.35 (given efficiency of the system)

Plugging in these values, we get:
P = 0.5 * 1.225 * 5026.55 * (8.33)^3 * 0.35 = 1,473,985 watts

So, the power generated by the wind turbine in this scenario is approximately 1.47 MW (megawatts). Keep in mind that this is an ideal calculation and the actual power output may vary depending on factors such as wind speed and turbine efficiency.

I hope this helps you on the right path. Good luck with your Thermo I problem!