Continuity Equation: HVAC Duct Flow Explained Simply

Understanding the Continuity Equation — in Plain, Easy Language 💡💨

Ever wonder how air knows where to go in a duct system? Or why your airflow speeds up in smaller ducts? It’s not magic — it’s physics! And the star of this story is a super simple yet powerful tool called the Continuity Equation. 🧮🚀

Let’s break it down slowly — together — so you can visualize it, use it, and never forget it.

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🔍 What’s the Continuity Equation, Anyway?

Imagine a long, bendy duct in your HVAC system — air flows through it constantly. Now picture a balloon — if you blow air into it with your mouth, it fills up. But if you keep blowing and don’t let any air escape… 💥 it eventually bursts!

That’s because mass (or volume) can’t just disappear or appear out of nowhere. That’s the law of conservation of mass — and it’s the heart of the continuity equation.

🧠 In simple terms:

“What flows into a pipe must flow out of it — unless you’re storing it or leaking it somewhere (which in HVAC, we try to avoid!)”

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🧮 The Continuity Equation: The Basic Form

For fluids like air or water that don’t compress much under normal HVAC pressures, we use a simplified version of the continuity equation:

A₁V₁=A₂V₂

Let’s decode it:

• AAA is the cross-sectional area of the duct (like how wide it is).
• VVV is the velocity of the air moving through that duct.

And the subscripts 1 and 2 just mean “before” and “after” a change (like a duct narrowing or widening).

💬 In Plain English:

If your duct gets narrower, the air speeds up. If it gets wider, the air slows down. But the amount of air passing per second stays the same.

🎯 Let’s Try a Real Example Together!

Picture this:
You’re designing a duct. At one point, it’s 0.5 square meters wide, and air is flowing through it at 4 meters per second. Then the duct narrows to 0.25 square meters. What’s the new velocity?

Let’s plug into our trusty equation:

💨 So the air doubles its speed when it passes into the narrower duct.

🗣️ This is just like putting your thumb over a hose — the water jets out faster because it’s squeezing through a smaller opening!

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📦 What About Volumetric Flow Rate (Q)? Let’s Talk “CFM” & “L/s”

In HVAC, we often use something called volumetric flow rate, symbolized as QQQ, to express how much air is moving — not just how fast, but how much volume per second.

Formula:

Where:

• Q = volume of air per second (usually in L/s or CFM — cubic feet per minute)
• A = area of duct (m² or ft²)
• V = velocity of the air (m/s or ft/min)

Example:

Let’s say:

• Your duct area is 0.3 m²
• Air is moving at 6 m/s

Then:

Q=0.3⋅6=1.8 m³/s

That’s 1800 liters per second — a lot of air! Perfect for large spaces or commercial HVAC systems.

Takeaway:

If the duct size or the velocity changes, the other must adjust to keep Q constant. That’s the continuity equation in action! 🔄

1. Duct Sizing and Air Velocity

If you want your HVAC system to run efficiently and quietly, you need to control the air velocity.
Why? Because:

• High airspeed = 🔊 noise + 💨 pressure loss
• Low airspeed = 🚫 weak air delivery

Let’s say you know the total flow you want (maybe 500 L/s), and you want to keep the velocity below 4 m/s to avoid turbulence and noise.

Using the formula:

So now you know what duct size to use! Easy peasy. 🧠📐

2. Diffuser & Grille Sizing

When you’re delivering air into a room through a diffuser or grille, you don’t want air whooshing out like a jet engine — or barely trickling in.

✅ The continuity equation helps you size the outlet correctly so it gives even, comfortable airflow.

3. Fan Selection & System Balancing

Every fan you install needs to push a certain volume of air, and it must match the airflow needs throughout the duct system.

✅ Use the continuity equation to ensure the airflow entering the system matches the flow going through each duct branch.

4. Energy Efficiency & Pressure Drops

If air speeds up too much through tight ducts or sharp bends, it causes pressure drops. That means the fan has to work harder, wasting energy 💸⚡.

✅ By applying the continuity equation, you can spot problem areas in your duct layout where redesigning or resizing can reduce resistance and save power.