As we continue our study of indoor air quality and filtration, we now come back to duct design. Today’s lesson is on an interesting bit of physics that applies to anything that flows. It could be heat or particles or electromagnetic energy. In our case, it’s air — a fluid — and the physics we’re looking at is called the continuity equation.
It’s basically a conservation law, similar to conservation of energy. I’ll use diagrams to tell the story.
First, we have a duct. Air enters the duct from the left. As the air moves through the duct, it encounters a reducer and then a smaller duct.
What do we know about the flow here? Thinking about conservation laws, we can safely assume that all of the air that enters the duct on the left has to come out of the duct somewhere. We’ll take the case of the perfectly sealed duct — so no air leaks out along the way.
But we can strengthen our statement from just the amount of air to the rate of flow. Using “those annoying imperial units,” we can say that for each cubic foot per minute (cfm) of air entering the duct on the left, a matching cfm of air leaves the duct on the right. We represent flow here by the symbol q.
So, we have conservation of air — no air is created or destroyed in the duct — and we have conservation of the flow rate. The rate of flow entering equals the rate of flow leaving. But to make this second claim we’ve had to make an assumption.
We know the number of air molecules has to be the same no matter what, but to say the volume of air is the same means that the density…