How Much Power Does a 30m Diameter Windmill Generate?

[desi01]

Homework Statement

In this era of high energy prices, there is a focus on renewable sources of energy such as wind energy. Consider a large windmill 30m in diameter. On a windy day, suppose that the windmill entrains a stream of air 25 m in diameter at a speed of 14 m/s. Downstream of the windmill, the entrained stream exits over a large diameter at a speed of 5 m/s. The pressure equals atmospheric pressure at both inlet and outlet. Density of air: ρ = 1.2 kg/m3

Find the power (in megawatts) generated by the windmill.

Homework Equations

1/2 Δ(v^2) + gΔz + (ΔPressure)/density + lost work + shaft work/mass flow rate = 0

The Attempt at a Solution

So I know that that is no change in Pressure and no lost work so those go to 0. I don't think that you would need the gΔz part either?? So basically I'm thinking plug in the velocities given and that would only leave shaft work which I'm solving for and mass flow rate. Now I don't know what velocity and area I would use for that either so that's where I'm stuck?? Am I headed in the right direction?
Thanks.

 

[Redbelly98]

Welcome to Physics Forums. You're correct that gΔz is not needed (it is zero).

You can use the initial velocity and area, and density, to get the mass flow rate.

Also, note that "shaft work" would actually be power here.