For an 8x4 to 5x7 transition duct with a 3" take-off toward the 5x7 side, what is the slope of the bottom?

To determine the slope of the bottom of a transition duct designed to change from an 8x4 dimension to a 5x7 dimension with a 3" take-off, it is essential to visualize the duct and how the dimensions change.

In this case, the transition occurs over a certain length. The width of the duct increases from 4 inches to 7 inches, creating a total increase of 3 inches in width. Additionally, the duct also goes from a height of 8 inches to a height of 5 inches. The take-off is occurring towards the larger side (5x7), which is vital for determining airflow dynamics.

To ensure smooth airflow and maintain proper function, the transition should be conducted at an angle that allows for a gradual change in dimensions. When calculating the slope in this setup, one needs to consider the difference in width along with the corresponding height.

Since the duct is wider on one end and adjusting for the take-off, the slope must rise at the correct angle to facilitate airflow. The answer of 6 inches implies that for every width increase, there is a proportionate height decrease to maintain optimal airflow characteristics. This choice represents a gradual transition that avoids sharp angles, which can cause turbulence and inefficiencies