Flow, Velocity and Sizing a Duct or Pipe

The equation is the easy part

Volumetric flow across any section equals the mean velocity of the fluid multiplied by the area it is crossing. Nothing in that sentence is particular to air, water or gas, and nothing in it was fitted to data: it is conservation of mass written for a fluid whose density does not change along the run.

A dozen or so pages on this site are that one line rearranged. A duct velocity check divides one way; a duct sizing page divides the other way and then takes a square root; a gas capacity page multiplies. What separates them is packaging, not method.

Most of the apparent difficulty is unit bookkeeping. The North American duct trade divides cubic feet per minute by square feet and reads feet per minute straight off, with no factor at all. Metric is not so tidy: litres per second over square metres is millimetres per second, so a thousand has to be divided out before the answer is in metres per second. The 144s and 60s and 60,000s scattered through trade shortcuts are those conversions wearing the costume of physics. Each compute function here converts at its own boundary so the relation itself stays legible.

Velocity is the variable you actually choose

Of the three quantities, the flow is not yours to pick. It arrives from elsewhere — a room-by-room cooling load, a fixture unit count run through a diversity curve, a pump curve read at the real head, a rainfall intensity. By the time anyone is sizing the conduit, Q has been settled by another calculation.

The area is not a choice either; it is the answer. That leaves velocity as the single free variable, and sizing collapses into three moves: settle on a velocity you can live with, divide, then turn the area into a diameter or a pair of sides.

Which is why the sizing pages here take target velocity as a visible input instead of hiding a default inside the arithmetic. That figure is the design decision. A page that quietly makes it on your behalf has made the only judgement in the whole exercise and then presented the result as a measurement.

One practical wrinkle: the diameter that falls out is never a size anyone stocks. Moving up to the next standard size drops the velocity below the target, which is the safe direction. Moving down raises it above — and the target was chosen precisely to avoid that.

What caps the velocity from above

Noise comes first in air. Every damper blade, turning vane and grille core regenerates sound as air passes it, and the acoustic power grows with a steep power of velocity — steep enough that the gap between a branch at 4 m/s and the same branch at 6 m/s is not a marginal difference. Nobody reports it as an undersized duct. They report a bedroom that hisses, and that is the complaint that gets a finished installation opened up again.

In water the cap is wear. Copper suffers erosion-corrosion: fast flow strips the protective oxide film mechanically, and the film re-forms by consuming fresh metal. The process is temperature-sensitive, so the recommended velocity ceiling for hot water in copper sits below the cold-water figure. Suspended grit pushes it lower still, which is one reason a system refilled carelessly after alteration is abrasive for weeks afterwards.

Then there is the cost of pushing. Within a fixed pipe, friction loss climbs roughly with the square of velocity and the power to sustain it with the cube. Read the other way — flow fixed, pipe varying — halving a diameter quadruples the velocity and multiplies the friction loss by something near thirty. Undersizing to save on materials is paid for by the pump or the fan, every hour, for the life of the building.

Velocity is also the quantity a closing valve has to arrest. Surge pressure on sudden closure scales with the change in velocity rather than with the working pressure, so a fast line hammers hard whatever the static pressure reads. Generous sizing is the cheapest surge control on the market.

The floor, and the components that want to be slow

A conduit can be too generous as well as too mean. Gravity drainage shows this plainly: a sewer or storm drain depends on its own flow to carry solids along, and below a self-cleansing velocity those solids come to rest and stay there. An oversized drain laid at a flat grade silts steadily and fails months later as a blockage rather than immediately as a flood. Grade and velocity are therefore designed together, and capacity alone is the wrong question.

Some components invert the argument entirely. A hydronic air and dirt separator earns its keep by being slow — entrained bubbles need residence time to rise and particulates need it to fall out of the stream — so its connection is sized at a small fraction of the velocity the mains carry. The consequence surprises people on site: the separator's connection frequently comes out larger than the pipe it interrupts. A fitter who reduces it back to line size has converted a separator into a length of pipe.

Return air grilles trade in both directions at once. Push the face velocity up and the core whistles; drop it too far and the result is a large, costly plate of metal in a wall. The free-area fraction complicates the sum, because blades occupy part of the face: the gross size must exceed the bare flow area by the reciprocal of that fraction. Sizing a grille on its gross dimensions at duct velocity is a reliable way to build in noise.

So there is no single acceptable band. There is a band per component, and a well-behaved system deliberately runs at different speeds in different places.

Where the arithmetic stops being the answer

Dividing Q by A returns a mean. The actual distribution across a duct or pipe is nowhere near flat — zero at the wall, peaking near the centreline, and in fully turbulent pipe flow the centre moves appreciably faster than the average. Checking a computed velocity against a manufacturer's rated maximum compares one average with a limit that was itself derived from averages. That is legitimate, and it is not the same as knowing what the fastest fluid in the section is doing.

The frequent mistake, though, is not the division. It is A. Nominal pipe size is not bore, and which way it errs depends on the material: metric copper is labelled by its outside diameter and carries less than the number implies, while Schedule 40 steel and PVC in the common sizes bore out slightly larger than their nominal designation. Neither is safe to assume. The other three errors lean one way only. A lined duct loses the liner thickness on every side. Push-fit plastic fittings restrict at every joint. A grille's gross face is not its opening. Wherever the true area is smaller than the assumed one, the true velocity exceeds the reported one, and the page looks conservative while the installation is not.

Constant density is assumed throughout. That holds for water and for air at the pressures building ductwork sees. It stops holding for compressible gas at pressure, where a given mass occupies less volume upstream than down — which is why the fuel gas page here is described as a velocity screen and why fuel gas codes size the pipe from pressure-drop tables rather than from this relation.

Most importantly, velocity sizing answers half a question. It yields a conduit that will pass the required flow at a tolerable speed provided something drives it. Whether the fan or pump can drive it is a separate problem in static pressure and friction across the entire system — every fitting, filter, elbow and metre of run — and no amount of care with the continuity equation stands in for that calculation.