The quantity of air to be delivered out of a diffuser is 2000 cfm at a velocity of 1000 fpm. What diameter of round pipe is required?

To determine the diameter of the round pipe required to deliver 2000 cubic feet per minute (cfm) of air at a velocity of 1000 feet per minute (fpm), it's essential to understand the relationship between flow rate, velocity, and cross-sectional area.

The flow rate (Q) can be expressed as the product of the cross-sectional area (A) of the pipe and the velocity (V) of the air, represented by the equation:

[ Q = A \times V ]

To use this equation, first, we need to calculate the required cross-sectional area in square feet:

1. Rearranging the equation gives:

[ A = \frac{Q}{V} ]

Substituting the values:

[ A = \frac{2000 , \text{cfm}}{1000 , \text{fpm}} = 2 , \text{ft}^2 ]

2. The area of a round pipe is calculated using the formula for the area of a circle:

[ A = \pi \left(\frac{d}{2}\right)^2 ]

Where d is the diameter of the pipe.

3. Setting the area equal to 2 ft²,