What is the required steel duct diameter for a system set at 700 feet per minute velocity with a design friction loss of 0.08 inches water column and 380 CFM airflow?

To determine the required steel duct diameter, we need to apply the principles of airflow in ducts, particularly the relationships governed by velocity, airflow, and friction loss.

First, we know that the airflow (measured in cubic feet per minute, or CFM) and velocity (measured in feet per minute, or FPM) are related through the cross-sectional area of the duct. The duct's area can be calculated using the formula:

[ \text{Area} = \frac{\text{CFM}}{\text{Velocity}} ]

In this case, with a known airflow of 380 CFM and a velocity of 700 FPM, we can calculate the required duct area:

[ \text{Area} = \frac{380 , \text{CFM}}{700 , \text{FPM}} \approx 0.543 , \text{square feet} ]

Next, to find the diameter of the duct, we can use the formula for the area of a circle:

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

We can rearrange this to solve for the diameter:

[ d = 2 \times \sqrt