Calculate the power required to move air in a duct of 1.4*1.4m with a speed of 10.5m/s and pressure of 5220Pa

To calculate the power required to move air in a duct, we can use the following formula:

\[
\text{Power} = \text{Pressure} \times \text{Flow Rate}
\]

Where:
- **Pressure** is given as \( 5220 \, \text{Pa} \).
- **Flow Rate (Q)** is calculated as the product of the cross-sectional area of the duct and the velocity of the air.

### Step 1: Calculate the Cross-Sectional Area of the Duct

The duct has dimensions of \( 1.4 \times 1.4 \, \text{m} \).

\[
\text{Area} = 1.4 \times 1.4 = 1.96 \, \text{m}^2
\]

### Step 2: Calculate the Flow Rate

The flow rate is calculated using the velocity of the air:

\[
Q = \text{Area} \times \text{Velocity} = 1.96 \, \text{m}^2 \times 10.5 \, \text{m/s} = 20.58 \, \text{m}^3/\text{s}
\]

### Step 3: Calculate the Power

Now, using the formula for power:

\[
\text{Power} = \text{Pressure} \times \text{Flow Rate} = 5220 \, \text{Pa} \times 20.58 \, \text{m}^3/\text{s} = 107,421.6 \, \text{W}
\]

\[
\text{Power} = 107.42 \, \text{kW}
\]

### Final Answer:
The power required to move air in the duct is **107.42 kW**.

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Would you like more details or have any further questions? Here are some related questions:

1. How does duct size affect the power required for air movement?
2. What factors influence the pressure in a duct system?
3. How can you reduce the energy consumption of air handling systems?
4. What is the relationship between air velocity and pressure drop in ducts?
5. How do you calculate the power required for different duct shapes?

**Tip:** Always ensure that the duct system is properly sealed to avoid unnecessary energy losses due to leaks.

Learn how to calculate the power required to move air in a duct with dimensions 1.4m × 1.4m, air velocity of 10.5 m/s, and pressure of 5220 Pa. Follow a detailed step-by-step solution using fluid dynamics principles. Suitable for advanced learners and professionals.

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