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Building Science

The Continuity Equation and Air Flow

Filters and ducts can work a lot better if HVAC designers and installers understand this simple physics formula

A lot can happen when air moves through ducts. One of the things that happens is a change in velocity when the duct size changes. The continuity equation relates the velocity change to the cross-sectional area of the duct.

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…

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One Comment

  1. Dennis Miller | | #1

    I don't know about Bohr's alleged comment, but British mathematician Sir Horace Lamb (look him up) actually commented about fluid dynamics in his later years. In a 1932 speech he said "I am an old man now, and when I die and go to heaven, there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic." I would tend to agree. Fluid Mechanics was not my favorite college course, but I do look forward the articles still to come from Dr Bailes.

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