Air balancing
A Socratic walk-through of air balancing — reasoned out one step at a time, not lectured.
The question we started with
THE QUESTION #Why must a newly installed ventilation system be deliberately choked back at the dampers when every duct was sized correctly?
A ventilation system is installed exactly as drawn, every duct sized for the flow that branch is meant to carry. Then a commissioning engineer arrives and closes dampers — making several branches worse on purpose — until the readings come right.
The obvious reading is that somebody sized the ducts wrong and the dampers cover for it. But this happens on well-designed systems, every time, and the engineers doing it are not embarrassed. So what does sizing a duct fail to determine?
Reasoning it through
REASONING #Ask what a duct size actually fixes. Choose a section, and for a given flow you have fixed the velocity through it and the friction loss per metre. That is a statement about one piece of ductwork carrying an assumed flow.
Now the different question: what decides how much air a branch gets? The fan does not deliver flows to branches. It raises a pressure, and the air distributes itself among every available route out. Each route's share depends on its total resistance — length, bends, takeoff, flexible tail, damper, and the grille at the end. Duct sizing never equalises those totals, because it works section by section while paths differ in length and fitting count.
How unequal does that make things? For turbulent flow, pressure drop rises roughly with the square of flow: dp = R Q squared, R being the path's resistance. Parallel branches off a common plenum see the same driving pressure, so Q goes as the square root of dp over R — flow splits with the inverse square root of path resistance.
Work an illustration. Three outlets meant to take a third each of 1000 litres per second, with path resistances in the ratio 1 : 2 : 4 — the near one short and straight, the far one long with more bends. Flows go as 1, 1/root 2 = 0.707 and 1/root 4 = 0.5, summing to 2.207, so the shares are 45%, 32% and 23%: 453, 320 and 227 litres per second against a design 333 each. (The ratios illustrate; the arithmetic from them is exact.)
Sit with that, because it is the answer. Nothing is wrong. No duct is undersized, no fitting missing, the fan delivers its full 1000 — and the far room still gets a third less air than promised while the near room is over-ventilated by a third. Correct sizing does not produce correct distribution, because distribution is a property of whole paths and sizing is a property of sections.
So how would you fix it? You cannot add pressure to the starved branch: there is one fan and everything downstream shares it. The only lever is to increase resistance on the branches taking too much, until every path's resistance is equal at its design flow. You level down to the worst path — the index run — deliberately, which is why the work looks like sabotage.
A further property makes the job tractable. Because every path obeys the same square law, closing a damper upstream of several branches scales them all by nearly the same factor rather than changing their shares. So a balancer works in ratios: from the index terminal, set each branch against its neighbour as a proportion, then set the total at the fan, and the ratios survive. Without that, every change would disturb every previous reading — and that proportional balancing works in the field is itself evidence the network behaves as the square law says.
What does it cost, and who pays? Every closed damper is a device whose entire function is to waste pressure, and the fan runs against the index path's requirement for the life of the building. That permanent energy bill falls on whoever operates the building, not on the designer or installer who saved money by not solving it another way — the arrangement that keeps a mediocre practice alive. Better answers exist: a layout whose path resistances are more nearly equal, static-regain sizing, self-regulating constant-flow terminals. Each moves the cost to the capital bill.
There is an honest defence of the pass itself, too. Installed ductwork is never the drawing: flexible duct gets run long and kinked, extra bends appear around a beam. Balancing is the only occasion anyone measures what was built, so deleting it would not remove the imbalance — only the knowledge of it.
The analogy
THE ANALOGY #Think of one door opened onto a crowd, with three exits beyond it down corridors of different lengths. You cannot make more people leave by the far exit, because there is one crowd and one pressure behind it. All a steward can do is narrow the near exits until the far one gets its share — and everyone then leaves more slowly than the building could manage.
People choose their route and change their minds, whereas air does not choose at all; its split is fixed by physics and calculable in advance, which is why the imbalance can be predicted from a drawing while a crowd's cannot.
Clarifying the model
THE MODEL #The misconception to retire is that a duct's size sets its flow. Size sets a relationship between flow and pressure drop in one section; flow is settled competitively, by every path bidding against every other for a share of one pressure.
Two refinements. The square law makes the imbalance milder than intuition suggests and the remedy harsher: quadrupling a path's resistance only halves its flow, so getting a branch down to its share takes a firm throttle. And "balanced" describes one operating point — change the fan speed, block a filter, open a fire damper, and every share is recomputed by the same physics, which is why balanced constant-volume systems drift and why pressure-independent terminals exist.
The test is whether the split follows path resistance under a square law. If it does, branch flows before balancing should rank inversely with total path resistance rather than with branch size; closing a main damper should scale all downstream branches by a common factor while leaving their ratios intact; and quadrupling one branch's resistance should halve its flow. Find flows that track duct size and ignore path length and fittings, or ratios that shift wildly when the main damper moves, and this account is wrong — and proportional balancing, which depends entirely on that ratio-preserving behaviour, would not work in practice, which it does.
A picture of it
THE PICTURE #How to readOne source, three destinations, each ribbon's width the flow in litres per second computed above for path resistances in the ratio 1 : 2 : 4. Compare each against the design intent of 333 per outlet, which would have drawn three equal ribbons: the near outlet's is a third too wide, the far one's a third too narrow. Nothing has leaked — the three still sum to the fan's full 1000 — so read this as misallocation rather than waste, which is why the cure is subtraction at the wide ribbons rather than addition at the narrow one.
What became clearer
WHAT CLEARED #Sizing a duct and setting a flow are different acts. A fan supplies pressure, not flows, and the air apportions itself among competing paths in inverse proportion to the square root of each path's total resistance — something no section-by-section sizing method controls. The commissioning pass therefore has one lever: add resistance to the favoured branches until every path is as bad as the worst. That is permanently wasteful, and the waste lands on the building's operator rather than whoever chose not to design it out. And the same square law that causes the problem makes the fix converge, by letting a balancer set ratios first and the total afterwards.
Where to go next
ONWARD #- How static regain sizing tries to equalise path pressures at the design stage.
Key terms
TERMS #| Term | What it means |
|---|---|
| Index run | the fan-to-terminal path of highest total resistance, which sets the fan's pressure. |
| Proportional balancing | setting branch flows as ratios first, then fixing the total at the fan. |
| Pressure-independent terminal | a box that measures and holds its own flow. |
Every term the collection defines is gathered in the glossary.