Question

A wind turbine rotates at 20 rev/min. If its power output is 2.0 MW, what is the torque produced on the turbine from the wind?

a) 100 kNm
b) 200 kNm
c) 300 kNm
d) 400 kNm

Answer 1

To calculate the torque from the wind on a turbine rotating at 20 rev/min with a power output of 2.0 MW, convert the rotation rate to angular velocity and use the power-torque relationship. The calculated torque is 955 kNm, which doesn't match any of the multiple-choice options, suggesting a typo in the question. So, the best answer is e, none of these.

Step-by-step explanation:

The student has asked how to determine the torque produced by a wind turbine given that it rotates at 20 revolutions per minute (rev/min) and has a power output of 2.0 megawatts (MW).

To solve this, we can use the formula that relates power (P) to torque (T) and angular velocity (ω), which is: P = T * ω, where P is power, T is torque, and ω is angular velocity in radians per second.

First, we need to convert the rotational speed to angular velocity in units of radians per second.

There are 2π radians in one revolution and there are 60 seconds in one minute, so the angular velocity ω in radians per second would be: ω = (20 rev/min) * (2π rad/rev) / (60 s/min) = 2π/3 rad/s.

Now we use the power-torque formula to solve for torque: T = P / ω = (2.0 MW) / (2π/3 rad/s) = (2.0 * 106 W) / (2π/3 rad/s). When you calculate this, you get T = 955,000 Nm or 955 kNm.

Since this option is not available in the choices provided, it's possible there might have been a typo or misunderstanding in the question. But the process of calculating the torque given power output and rotational speed has been correctly demonstrated.

So, the best answer is e, none of these.

Q: A wind turbine rotates at 20 rev/min. If its power output is 2.0 MW, what is the torque produced on the turbine from the wind?

a) 100 kNm

b) 200 kNm

c) 300 kNm

d) 400 kNm

E) none of these

Answer 2

The torque produced by a wind turbine with a power output of 2.0 MW rotating at 20 rev/min is calculated to be approximately 955 kNm. The closest provided option is 400 kNm, but it does not match the calculated torque (option d).

Step-by-step explanation:

The student is asking to calculate the torque produced by a wind turbine that has a power output of 2.0 MW and rotates at 20 revolutions per minute (rev/min).

Step-by-Step Calculation:

1. First, convert the rotation rate from rev/min to radians per second (rad/s) because power (P) is related to torque (τ) and angular velocity (ω) by the equation P = τ ω.
2. There are 2π radians in one revolution and 60 seconds in one minute, so ω = 20 rev/min × (2π rad/rev) ÷ (60 s/min) = π/3 rad/s.
3. Use the power-torque relationship to find torque: τ = P / ω = (2.0 MW) / (π/3 rad/s), where 1 MW = 1,000,000 W.
4. So τ = (2,000,000 W) / (π/3 rad/s) ≈ 955,000 Nm = 955 kNm.

The closest listed answer would be (d) 400 kNm, but none of the provided options match the calculated value.