🔍 What’s the Continuity Equation?

Mass can’t just vanish or appear from nowhere. So, for steady flow of (mostly) incompressible fluids like air in typical HVAC ducts, the flow rate must be the same everywhere along the path.

In one line: A₁·V₁ = A₂·V₂ — If a duct gets narrower, velocity increases so the same amount of air per second still gets through.

Good to know: The “incompressible” assumption is fine for air when the speed is below about Mach 0.3 (≈ 100 m/s at sea level). Above that, compressibility needs attention.

📘 A Quick Example

You have a section of duct with area 0.5 m² and velocity 4 m/s. Downstream it narrows to 0.25 m². What’s the new velocity?

0.5×4 = 0.25×V₂ → V₂ = 2 / 0.25 = 8 m/s

Just like putting your thumb on a hose, smaller opening → faster jet.

🧮 Continuity Solver

Give any three of A₁, V₁, A₂, V₂ and I’ll solve the fourth. Areas in m², velocities in m/s.

🔁 L/s ↔ CFM Converter

Formula: Q = A · V. Keep Q the same and area shrinks → velocity rises.

🚀 Duct “Squeeze” Demo

Slide the area ratio and watch velocity change. We keep the upstream flow rate constant.

📏 Quick Area Helper (Round Duct)

Enter diameter and get area. Handy for plugging numbers into the solver.

Formula: A = π·D² / 4

1) Duct Sizing & Air Velocity

High airspeed ⇒ noise + pressure loss. Low airspeed ⇒ poor throw. Control velocity by choosing the right cross‑sectional area for a known flow (A = Q / V).

2) Diffuser & Grille Sizing

Outlets should not whoosh like a jet nor whisper too little. Size the free area so discharge velocity sits in the comfort zone — continuity makes the math trivial.

3) Fan Selection & System Balancing

Fans deliver a volume (Q). Ensure the sum of branch flows equals the fan flow; check each branch velocity via area to avoid noisy hotspots.

4) Energy Efficiency & Pressure Drops

Too‑tight ducts spike velocity → friction and fittings losses rise → fans work harder. Right‑size areas to reduce resistance and save power.