### Wind Turbine Power and Efficiency Calculation**Problem Statement:**5) Calculate the power generated by a wind turbine with 32-meter diameter blades given a wind speed of 15 m/s. Assume the air density is \(1.42 \, \text{kg/m}^3\).b) Determine the efficiency (in %) of the above wind turbine system if the maximum power generated was measured to be \(0.35 \times 10^6\) watts.**Explanation:**To solve these problems, we use the following formulas:1. **Power Generation Formula:** \[ P = \frac{1}{2} \cdot \rho \cdot A \cdot v^3 \] Where: - \( P \) is the power in watts. - \( \rho \) is the air density (\(1.42 \, \text{kg/m}^3\)). - \( A \) is the rotor swept area in square meters, calculated as \( \pi \cdot \left(\frac{D}{2}\right)^2 \) for diameter \( D = 32 \) meters. - \( v \) is the wind speed (\(15 \, \text{m/s}\)).2. **Efficiency Calculation:** \[ \eta = \left( \frac{P_{\text{measured}}}{P_{\text{calculated}}} \right) \times 100\% \] Where: - \( \eta \) is the efficiency in percentage. - \( P_{\text{measured}} = 0.35 \times 10^6 \) watts.Plugging in these values will provide answers for calculating both power and efficiency.

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5)How much power a Wind Turbine with 32 meter Diameter blades can generate with a wind speed of 15 m/s. Assume Air density is 1.42 kg m3 b)What is the efficiency(in %) of the above Wind Turbine system if the max power generated was measured to be 0.35*106 Watts

5)How much power a Wind Turbine with 32 meter Diameter blades can generate with a wind speed of 15 m/s. Assume Air density is 1.42 kg m3 b)What is the efficiency(in %) of the above Wind Turbine system if the max power generated was measured to be 0.35*106 Watts

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Question

### Wind Turbine Power and Efficiency Calculation

**Problem Statement:**

5) Calculate the power generated by a wind turbine with 32-meter diameter blades given a wind speed of 15 m/s. Assume the air density is \(1.42 \, \text{kg/m}^3\).

b) Determine the efficiency (in %) of the above wind turbine system if the maximum power generated was measured to be \(0.35 \times 10^6\) watts.

**Explanation:**

To solve these problems, we use the following formulas:

1. **Power Generation Formula:**

\[
P = \frac{1}{2} \cdot \rho \cdot A \cdot v^3
\]

Where:
- \( P \) is the power in watts.
- \( \rho \) is the air density (\(1.42 \, \text{kg/m}^3\)).
- \( A \) is the rotor swept area in square meters, calculated as \( \pi \cdot \left(\frac{D}{2}\right)^2 \) for diameter \( D = 32 \) meters.
- \( v \) is the wind speed (\(15 \, \text{m/s}\)).

2. **Efficiency Calculation:**

\[
\eta = \left( \frac{P_{\text{measured}}}{P_{\text{calculated}}} \right) \times 100\%
\]

Where:
- \( \eta \) is the efficiency in percentage.
- \( P_{\text{measured}} = 0.35 \times 10^6 \) watts.

Plugging in these values will provide answers for calculating both power and efficiency.

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