How to Estimate Flow Without a Flow Meter

Why this matters

Almost no residential or light commercial system has a flow meter, and almost every real diagnosis needs flow. So you substitute something you can measure for the thing you cannot, and every one of those substitutions carries an error band. The band, not the arithmetic, is what decides whether your number can settle the question you are being paid to settle. A tech who reports "37 GPM" without knowing whether that is 37 plus or minus 1 or 37 plus or minus 4 has produced a number that cannot be argued with and cannot be relied on either. The fix is to choose the method from the size of the difference you must detect, before you take a reading.

Before you catch, probe or clamp

Each method in this article carries its own hazard, and they are not the same hazard.

• Catching and timing hot water: discharge into a container rated for the temperature, positioned so you never carry it while full, at a valve you can shut with one hand from outside the splash line. Face shield and heat-rated gloves. Shut the heat source and let the line drop below 120 F where the job allows it.
• Catching from an open cooling tower or an evaporative basin: basin water aerosolizes, and inhaled aerosol from a poorly controlled basin is a bacterial exposure route, not a splash problem. Stand out of the drift, shut the fan before you sample, and wear a fitted respirator selected under a program meeting 29 CFR 1910.134. Gloves do not address this route.
• Clamping a meter on motor conductors: if the conductors are accessible outside the enclosure, clamp them there. If the work requires opening an energized enclosure, that is electrical work under 29 CFR 1910.333(b)(2), and the instrument must be proved on a known live source before and after per NFPA 70E-2021, 120.5.
• Probing a duct or a pitot traverse near a running blower: lock the disconnect open before any part of you or the probe passes the cabinet opening (29 CFR 1910.147), and see the static and velocity pressure card for the drilling hazards.
• Opening a thermometer well on a live system: it is a port on a pressurized line. Isolate and confirm zero on a gauge before you break it, or use an insulated surface probe instead and accept the extra uncertainty rather than cutting into a live pipe.

The sheet you are filling in

Every estimate is these eight fields. Fill them in order; the order is what stops you from picking a method because it is the tool already in your hand.

Field 2 sets field 3, and here is the arithmetic that links them

Commit to this default: pick a method whose uncertainty is no more than about a third of the difference you must detect, then tune it to how much argument your shop is willing to have with a customer. A band half as wide as the gap you are testing leaves you unable to call it either way, which is the outcome that costs a second trip.

The methods, and what actually drives each one's band:

The two entries worth memorizing are the second and third, because they are the counterintuitive ones. A pump curve is a good flow meter only where it is steep. In a flat region a 1 ft head uncertainty can be 5 GPM. And heat-balance accuracy is set by the temperature difference you happen to have, not by how good your thermometers are. Buying better probes does not rescue a 6 F difference.

Field 5: the corrections that must happen before the arithmetic

• Elevation, on any pressure pair whose taps are at different heights: 1 psi is 2.31 ft of water, and that column is in your raw difference whether anything is flowing or not.
• Glycol, both ways and in opposite directions. On the heat-balance side, the 500 constant in Btu/h = 500 x GPM x temperature difference is water at ordinary service temperature: it is 60 minutes per hour times about 8.33 pounds per gallon times a specific heat of 1.0. A glycol mix is denser and has a lower specific heat, so substitute the mix's actual density and specific heat at the operating temperature from the fluid manufacturer's property table; for common propylene glycol mixes the constant comes down noticeably (a 30 percent mix near 100 F is around 470), and because the constant sits in the DENOMINATOR, using 500 anyway understates flow, about 6 percent low on that mix. On the pressure-drop side the correction runs the other way: a glycol mix is more viscous and produces more drop at the same flow, so reading a glycol system against a water-based component curve overstates flow again.
• Air density, on anything derived from velocity pressure. The 4005 constant assumes standard air. See the static, velocity and total pressure card for the density-general form.

The filled-in sheet

Field 1. A chilled water coil, design 45 GPM, clean-condition drop 11 ft of water at that flow. Below 85 percent of design flow the shop cleans the coil; above 95 percent it does not; between the two it re-checks next visit.

Field 2. The narrowest gap between two different actions is 10 percentage points of design, which is 4.5 GPM. A third of that is about 1.5 GPM, so the method needs to be good to roughly 3 percent of design.

Field 3. Component drop against the published curve. The pump curve is flat in this region and the load is not independently known, so those two methods are out on resolution before any reading is taken.

Field 4. Coil drop measured at 7.6 ft of water. Two runs, one with a pair of ordinary gauges and one with a differential gauge, to show what field 3 is actually buying.

Field 5. Both coil taps are at the same elevation, so no column correction. Straight water, no glycol.

Field 6. Flow scales with the square root of drop:

flow = 45 x square root of (7.6 / 11) = 45 x 0.831 = 37.4 GPM

That is 83 percent of the 45 GPM design.

Field 7. Propagate the instrument accuracy, remembering the square root halves proportional error:

• Two separate gauges, each contributing about 0.5 ft: 1.0 ft on a 7.6 ft reading is 13.2 percent of the drop, so about 6.6 percent on flow, which is plus or minus 2.5 GPM. Band 34.9 to 39.9 GPM.
• One differential gauge, about 0.25 ft: 3.3 percent of the drop, about 1.6 percent on flow, plus or minus 0.6 GPM. Band 36.8 to 38.0 GPM.

Field 8. The threshold is 0.85 x 45 = 38.25 GPM.

The two-gauge band runs to 39.9 GPM, which is above the threshold, so that reading cannot tell you whether to clean the coil. Same tech, same coil, same afternoon, and the trip produced nothing. The differential-gauge band tops out at 38.0 GPM, entirely below 38.25, so it settles the question: flow is below 85 percent, clean the coil.

One more line belongs in field 8, and leaving it out is the most common way this method misleads. The drop method assumes the component is at its published resistance. If this coil is fouled, its resistance is higher and the same 7.6 ft is being produced by less flow than the clean-coil arithmetic reports. So 37.4 GPM is an upper bound on the true flow, never a lower one. Here that only strengthens the verdict. On a job where the drop method had landed just above a threshold, the bound direction would have made the reading useless in the other direction, and that is worth saying out loud rather than discovering later.

What a second method buys you, and what it does not

Run a heat balance on the same coil as a cross-check. Air-side load, taken independently, is 269,000 Btu/h. Water temperature difference across the coil is 14.4 F.

flow = 269,000 / (500 x 14.4) = 37.4 GPM

Two methods, same answer to the tenth of a gallon per minute. That feels like a tight result and it is not one. Propagate this method's band: two probes contributing 0.5 F each on a 14.4 F difference is about 6.9 percent, which is plus or minus 2.6 GPM before you account for any uncertainty in the 269,000 Btu/h itself.

Agreement between a tight method and a loose one does not narrow the band. The band is still plus or minus 0.6 GPM, set by the differential gauge. What the second method bought is different and still worth the ten minutes: it rules out a gross error. A mis-selected component curve, a tap on the wrong side of a tee, or a decimal in the wrong place would have shown up as a disagreement of tens of percent, not tenths. Use a cross-check to catch blunders, and use instrument selection to set precision. They are different jobs and only one of them is on the sheet twice.

References

• Manufacturer submittal data for component pressure drop at rated flow, and fluid manufacturer property tables for glycol density and specific heat at operating temperature
• ASHRAE Handbook, Fundamentals, for the sensible heat relationships used in heat-balance flow estimates
• OSHA 29 CFR 1910.134, respiratory protection where open-basin water is aerosolized; 29 CFR 1910.147 for blower and pump isolation; 29 CFR 1910.333(b)(2) with NFPA 70E-2021, 120.5 for instrument work inside an energized enclosure
• See related: Measuring Flow: Generic Methods (the method catalogue); How to Read a Pressure Drop Across a Component; Static, Velocity and Total Pressure