Head Loss, Falls and Surge: Resistance in Pipes, Ducts and Drains

The exponent on diameter is the whole subject

Friction loss along a pipe or duct rises with roughly the SQUARE of velocity and falls with roughly the FIFTH power of diameter at a fixed flow rate. Those two exponents, and not the choice of formula, are what make or break a distribution system.

Work the second one through and it stops being abstract. Increasing a diameter by a quarter — one nominal size, in most tables — divides the friction loss by about three at the same flow. Halving the flow through an unchanged pipe divides the loss by about four. No other adjustment available to a designer moves the number that far, which is why oversizing the index run is the standard answer to a pump that will not deliver and why undersizing to save material is a decision that gets paid for continuously in fan and pump energy.

It is also why velocity, not flow, is the quantity to hold in mind. Two systems carrying entirely different flows behave similarly if their velocities match, and the conventional limits — for noise, for erosion, for pressure loss — are all velocity limits.

Which formula, and where each one stops being true

Darcy-Weisbach is derived and general: it works for any Newtonian fluid at any temperature, in any flow regime, provided the friction factor is right. Getting that factor right is the catch, because the standard expression for it is IMPLICIT — the friction factor appears on both sides — and has to be solved iteratively or read from a chart.

Hazen-Williams avoids that by being an empirical fit, and it is excellent inside the range it was fitted to: water, at ordinary temperatures, in turbulent flow, in pipes above about 50 mm. Outside that range it drifts, and the drift is invisible because the formula still returns a plausible number. Hot water, glycol mixes, very small bores and laminar flow are all cases where it should not be the method and frequently is.

The C coefficient carries the same warning. It is not a measured roughness; it is a calibration constant for a material AND ITS CONDITION, and published values for the same pipe span a wide band because a tuberculated fifty-year-old main and a new one are not the same hydraulic object. Designing a long-life system on a new-pipe C and no allowance for ageing is a known route to a system that meets its duty on the day it is commissioned and not afterwards.

Air is different again. Duct charts are built on the same physics but presented as loss per unit length at a stated air density, so the published figure needs correcting for altitude and for temperature — and a duct system designed at sea level and built at height moves less air than its drawings claim.

Minor losses are not minor, and flex duct is the extreme case

Fittings, bends, tees, dampers, valves and transitions are called minor losses, which is a naming accident. In a compact plant room or a short residential duct run, the fittings routinely account for MORE of the total resistance than all the straight pipe combined, and a calculation that omits them is not conservative in any direction — it is simply wrong.

They are handled either as an equivalent length of straight pipe or as a multiple of the velocity head, and the second form makes the dependence obvious: a fitting's loss also goes with the square of velocity, so the fittings on the fastest section of a system dominate the fittings elsewhere.

Flexible duct is where this reaches its worst. A flex duct's published resistance assumes it is pulled taut. Left compressed, the interior becomes a corrugated helix rather than a smooth bore, and the measured loss at a modest degree of compression can be several times the rated figure — a factor of four at around thirty per cent compression is a commonly reported result. Nothing in the calculation shows this: the length is right, the diameter is right, and the system is starved. It is an installation variable that swamps every design variable on the same run, which is why the pages here state the taut assumption rather than leaving it implied.

Filters belong in the same paragraph for the opposite reason: their resistance is not constant. A filter's pressure drop RISES as it loads, so the system's operating point moves throughout the filter's life, and the design has to carry the dirty-filter figure rather than the clean one.

The operating point is an intersection, not a nameplate

A pump or fan does not deliver its nameplate flow. It delivers whatever flow satisfies both its own curve — pressure it can produce against flow — and the system's curve, which is resistance rising with roughly the square of flow. The delivered duty is where those two cross, and it moves whenever either curve moves.

This explains several things that look like faults. A system built with more fittings than designed rides up its own curve and delivers less flow at a higher pressure. Closing a balancing valve steepens the system curve and reduces flow rather than merely redirecting it. Two identical pumps in parallel do not double the flow, because doubling the flow quadruples the resistance they have to work against; parallel pumps add flow at the same head and series pumps add head at the same flow, and choosing the wrong arrangement is a common way to spend money for nothing.

For a circulator, the head that matters is only the friction loss around the circuit. Static lift does NOT appear in a closed loop, because the column of fluid coming down balances the column going up — a fact that regularly leads to grossly oversized circulators in tall buildings when a designer adds the building height to the friction. An open system, such as a sump or a water feature, is the opposite case: there the static lift is real and usually dominates.

A residential duct design runs the arithmetic backwards from the fan. The blower's external static pressure at the design airflow, less what the coil, the filter, the outlets and the grilles take, is all the ducts may spend; spread over the total effective length of the longest supply and return runs — measured duct plus the equivalent length of every fitting — it is the friction rate ACCA Manual D sizes each duct at, in inches of water per hundred feet or pascals per metre.

Gravity drainage: a fall can be too steep

Flow in a part-full drain is a different problem with a different equation — Manning's, in which the driving force is the slope rather than a pump. And unlike a pressurised pipe, the governing criterion is usually not capacity at all.

What governs is SELF-CLEANSING VELOCITY, conventionally around 0.6 to 0.75 metres per second, below which solids settle out and build up. That sets a MINIMUM gradient, and it is why the familiar falls for waste pipework are quoted as ratios like one in forty or one in eighty rather than derived from the flow they carry.

There is also a maximum, which surprises people. A drain laid too steeply runs shallow and fast: the liquid outruns the solids and leaves them behind, and the pipe blocks for the opposite reason to a flat one. Steeper is not safer in drainage, and the codes that give a minimum fall frequently give a maximum alongside it.

Falls on surfaces work the same way and fail differently. A roof falls to its drains so that water leaves before it can pond, and a road is cambered so that it sheds sideways rather than sheeting along the wheel path. In both, the risk of getting the gradient wrong is not blockage but standing water, which on a roof adds load in a feedback loop and on a road causes aquaplaning.

Overflows: capacity goes with head, steeply

A scupper, a weir or an overflow is not sized like a pipe. Flow over a weir grows with the head above its sill raised to the power of one and a half, and flow through a submerged orifice with the square root of the head — so the capacity of an opening depends critically on how much water is allowed to stand behind it.

That head is not a free choice. On a roof it is limited by the structure's tolerance for ponding and by the height of the upstand or the door threshold, so a scupper is usually sized from a head of a few tens of millimetres. Within that range the exponent works against the designer: allowing a little less head costs a disproportionate amount of capacity.

The design case is also not the ordinary storm. Secondary drainage exists for the condition where the primary system is blocked, so it is sized on the full design rainfall with no credit for the primary drains — and its outlet is deliberately made visible, so that water discharging from a scupper is the signal that the primary drains need clearing.

Surge: the pressure a pump could never produce

Stopping a moving column of water quickly converts its momentum into pressure, and the rise does not depend on the pump, the static head or the length of the pipe. It depends on the CHANGE IN VELOCITY and on the speed at which the pressure wave travels — around a kilometre per second in rigid pipe, considerably slower in plastic.

The magnitude routinely exceeds the working pressure by several times. A common rule of thumb puts the surge at roughly a hundred metres of head for each metre per second of velocity destroyed, which means a system running at a perfectly ordinary two metres per second can see a transient far above anything its pump is capable of. This is why pipework fails at a fitting on the day a quick-acting solenoid valve is installed and not before.

Two things follow. First, the mitigation is TIME: a valve that closes slower than the wave's round trip along the pipe never develops the full surge, which is why slow-closing valves and soft-stop pump controls are the primary control and arrestors the secondary one. Second, a long pipe is not safer — length changes how long the transient lasts, not how high it is.

Leakage, balancing, and what has to be measured

A duct system's leakage is quoted as a flow per unit of surface area at a reference pressure, and it scales with pressure raised to about 0.65 — so a system operating above its test pressure leaks more than its class implies. Leakage is also proportional to surface AREA rather than to length, which means a large low-velocity duct leaks more than a small one of the same run at the same class.

The reason it matters is that leaked air is paid for twice: the fan moves it and the plant conditions it, and it is delivered to a ceiling void rather than to a room. A system that leaks badly cannot be balanced into compliance, because there is no damper position that returns the lost air.

Which is the honest limit of everything on this page. Friction factors, fitting coefficients, roughness, leakage class and flex-duct condition are all assumptions about how a system was built. The calculators here size and check a design; the evidence about an installed system comes from a pressure test, a flow hood and a balancing report, and every result here is a prediction until one of those exists.