How Pressure and Flow Relate in a Real System
Why this matters
A pressure reading taken with nothing running and a pressure reading taken with the building in use are two different facts about two different situations, and techs report both as "the pressure." That is how a system with a good static reading gets signed off and then starves every time two fixtures run, and how a genuinely weak supply gets blamed on a fixture. Pressure and flow are not two independent properties you can measure separately. They are one point, and it moves.
Before you put a gauge on anything
Stored pressure hurts people who assume a system is dead because it is off.
Do not remove a gauge, plug, or fitting from a pressurized line. Isolate, open a drain or a fixture at a low point to relieve, and confirm zero on a gauge that is still installed before a wrench touches anything. A closed system that has been heated holds pressure that did not come from the supply and will not disappear when you shut the supply valve.
Do not open a hot fluid path with your body in front of it. Hot water and hot glycol scald on contact and travel further than people expect out of a partly loosened fitting; let the system cool, and crack fittings with the opening pointed away from you and away from anyone else.
Never dead-head a positive displacement pump to see what it will make. It does not stall at a comfortable number; it keeps building pressure until the weakest component in the path gives up. The control for that is a properly set relief device in the discharge path, not attention.
An accumulator, expansion tank or pressure vessel is stored energy in the sense of 29 CFR 1910.147, and its isolation and bleed-down belong in the isolation sequence rather than being assumed to follow the line.
Match the gauge to the expected reading. A gauge whose full scale sits far above the value you are measuring will be reading in the bottom of its range, where its accuracy is worst; put the expected value somewhere in the middle third of the scale.
One point, two curves
Every system has a resistance curve: the pressure it consumes to push a given flow through it. Push more flow and the resistance rises steeply, because friction loss goes with roughly the square of velocity. That curve belongs to the piping, the fittings, the valves, the filters and the fixtures.
Every source has a capability curve: the pressure it can deliver at a given flow. Draw more flow and the available pressure falls. That is true for a pump, for a well, for a booster and for a municipal main; the main is just a much stiffer curve than the others.
Where the two cross is the operating point, and it is the only place the system can actually sit. Both the flow and the pressure you measure are outputs of that intersection. Change either curve and both numbers move.
This is why the two most common field statements are both incomplete. "The pressure is fine" describes a point on the source curve at zero flow. "It flows fine" describes one point, usually the easiest one. Neither tells you where the system lands when the building asks for something.
Static, residual, and the reading that is not a reading
Three quantities, and the difference between them is the whole diagnosis.
Static pressure is what the gauge reads with nothing flowing. It is a property of the source, not the system, because with no flow there is no friction loss to consume any of it.
Residual pressure is what the gauge reads at the same point while a stated flow is running. It is static minus everything the path consumed getting that flow to where it went.
Pressure drop is the difference, and it is the only one of the three that describes the piping.
A residual pressure recorded without the flow that produced it is not a measurement. Two techs can write 28 psi on a ticket, one of them at 6 gallons per minute and one at 20, and those tickets describe systems that are not remotely alike.
The record, and its fields
| Field | What goes in it |
|---|---|
| Gauge location | Where on the system, precisely enough to return to |
| Static pressure | With everything closed, after it has settled |
| Flow point 1 | Flow in gpm, residual psi, computed drop |
| Flow point 2 | A materially higher flow, residual psi, computed drop |
| Computed exponent | How steeply drop rose with flow between the two points |
| Predicted drop at target flow | The extrapolation the card exists to produce |
| Static recovery | How fast and how fully static returned after the flow stopped |
| What was open | Which outlets were running for each point, on the plan |
Two flow points are the minimum, because one point plus a static gives you a single drop with no slope, and a slope is what lets you predict anything.
The filled-in card
A residential supply with a complaint that the second-floor fixtures die when the laundry runs. Flow measured by filling a marked 5 gallon container and timing it, which is accurate enough for this and needs nothing you do not already carry.
| Field | Entry |
|---|---|
| Gauge location | Hose bibb at the front of the house, downstream of the meter and main valve |
| Static pressure | 62 psi, settled, all outlets closed |
| Flow point 1 | 5 gal in 150 s = 2.0 gpm; residual 58 psi; drop 4.0 psi |
| Flow point 2 | 5 gal in 50 s = 6.0 gpm; residual 28 psi; drop 34.0 psi |
| Computed exponent | 1.95 |
| Predicted drop at 8.0 gpm | 59.7 psi, leaving about 2.3 psi residual |
| Static recovery | Back to 62 psi within a few seconds of closing |
| What was open | Point 1, one hose bibb throttled; point 2, hose bibb wide plus laundry valve |
The exponent, worked: flow went up by a factor of 6.0 / 2.0 = 3.0, and drop went up by a factor of 34.0 / 4.0 = 8.5. The exponent n that satisfies 3.0 to the power n equals 8.5 is ln(8.5) / ln(3.0) = 2.140 / 1.099 = 1.95.
The prediction, worked: at 8.0 gpm the flow ratio against point 1 is 8.0 / 2.0 = 4.0, so predicted drop is 4.0 psi x 4.0 to the power 1.95, which is 4.0 x 14.93 = 59.7 psi. Against a 62 psi static that leaves about 2.3 psi at the hose bibb, which is nothing.
So this system does not have a fixture problem. It has a ceiling somewhere between 6 and 8 gpm, and the laundry plus a shower is on the wrong side of it. That conclusion came from two timed bucket fills and a gauge.
Reading the exponent
The exponent is the most diagnostic number on the card and almost nobody computes it.
Around 1.8 to 2.0 is what distributed pipe friction produces. Loss is spread along the run and rises with roughly the square of velocity. A system reading in this band is behaving like piping, and the problem is length, diameter, or the flow being asked for. The 1.95 above sits squarely here.
Near 1.0 means the loss is not behaving like pipe friction. Look for a source whose delivered pressure is falling roughly in proportion to draw, or check your own work: two flow measurements too close together produce a meaningless slope, and a gauge that lags will flatten it.
Well above about 2.5 means something in the path is getting worse as flow increases, which pipe does not do. Candidates: a flexible connector or liner collapsing inward under flow, a pressure regulator that cannot keep up and is closing down, a check valve or screen fluttering into the stream, or a source running out of curve, which is what a drawing-down well or a pump approaching the end of its curve looks like from this end.
State the flow band with the exponent, always. An exponent computed between 2 and 6 gpm describes that band. It does not promise the same behavior at 15.
The other half: what static recovery tells you
Static recovery separates a source problem from a path problem, and it costs nothing to observe.
Fast, full recovery to the original static, as above, says the source has plenty of head available and the losses are downstream of the gauge, in the path you can work on.
Slow recovery, or recovery to a lower static than before, points upstream: a well drawing down and refilling, a booster on a duty cycle, a partially closed or partly obstructed service, a meter or backflow device that has lost capacity. On that system, replacing downstream piping improves nothing, because the source curve is what you are running out of.
Take static at the start and at the end of the visit. Two statics an hour apart that differ on a system nobody touched is a source that varies, and that alone explains a fault that comes and goes.
Moving the curves on purpose
Every fix is a move on one curve or the other, and knowing which one keeps you from selling the wrong thing.
Lowering the resistance curve means less loss at the same flow: larger effective diameter, shorter or straighter path, fewer or better fittings, a cleaned strainer, a valve fully open rather than partly. The sibling article on friction loss over a long run works the diameter and length arithmetic.
Raising the source curve means a pump, a booster, a larger service, or a regulator adjusted upward where the system's rating allows it. This adds energy rather than removing waste, so it is the answer when the source genuinely is the constraint and the expensive answer when it is not.
The throttling paradox is worth having in your head for the moment a customer or another trade says something backwards. Closing a valve partway raises the pressure you read upstream of it and lowers the flow through it. Nothing was added to the system. You steepened the resistance curve, which slid the operating point up the source curve to a lower flow and a higher pressure. The pressure went up because less is flowing. Read a rising gauge and a falling flow together as one event, not as two contradictory ones.
Variable-speed sources move their own curve, and the relationships are steep. For a centrifugal machine, flow varies roughly with speed, head with the square of speed, and shaft power with the cube. Dropping speed to 80 percent gives roughly 80 percent of the flow, about 64 percent of the head, and around half the power, subject to the system curve the machine is working against, which is why these relationships are a guide to expected behavior rather than a substitute for the curve.
The prediction that tests the card
The card earns trust by predicting a point it was not built from.
From the filled-in example, predicted drop at 4.0 gpm is 4.0 psi x (4.0 / 2.0) to the power 1.95, which is 4.0 x 3.86 = 15.5 psi, leaving a predicted residual of 62 - 15.5 = 46.5 psi.
Go measure it. Landing within a couple of psi says the two-point model describes this system across that band and the extrapolation to 8 gpm is worth acting on. Landing materially worse than predicted says something between those flows is behaving nonlinearly, and the useful next step is to move the gauge, not to argue with the arithmetic: measure at a point closer to the source and repeat, and whichever segment shows the disproportionate loss is the one holding the system back.
Landing materially better than predicted usually means one of the original two points was contaminated, most often by another outlet being open during a test or by a gauge that had not settled. Re-run the point rather than averaging it in.
References
- Hydraulic Institute standards and pump manufacturer curve documentation for source capability curves and affinity relationships
- Model plumbing code fixture unit and demand tables for the flow a system will actually be asked to deliver
- 29 CFR 1910.147 for isolation of stored energy, including pressurized vessels and accumulators
- See related: What Friction Loss Does Over a Long Run; Reading a Pressure Gauge: What Normal Looks Like