The Measurement That Changes What It Measures

Why this matters

Connect an instrument to something and you have joined it to the system. From that moment the instrument is part of the thing you are measuring, and the number on the display describes the combined arrangement, not the machine as it ran before you arrived. Most of the time the disturbance is too small to care about. The trouble is that techs learn "too small to care about" as a general fact rather than as a condition, so the one time the instrument is a serious fraction of the system, the reading is treated exactly like all the others. That is how a shop replaces a mixing valve that was set correctly, and how a sealed system gets condemned on a pressure that the gauge itself pulled down.

Every instrument takes something from what it measures

The currency is different by trade, the arithmetic is the same. A temperature probe takes heat, because it arrives at a different temperature than the thing it touches and both end up somewhere in between. A pressure gauge takes volume, because its bourdon tube, its port and the hose in front of it have to be filled. A pitot or a thermal anemometer takes flow area, because it stands in the stream. A gas-sampling probe takes sample, because a pump has to pull it out of the flue and into the analyzer. An electrical instrument takes current or imposes burden voltage, which is its own article and is not re-derived here (see References).

In every one of those, the size of the disturbance is a ratio: what the instrument takes, divided by what the system has. That is the only quantity worth estimating, and you can usually estimate it to within a factor of two in your head, which is enough to tell you whether to think harder.

Before you break into a system to fit one

Some of these instruments connect without touching the process. Some require you to open it, and opening it is the dangerous act, not the reading.

• Fitting a gauge to a pressurized line. Relieve the pressure and verify the gauge you are relieving against reads zero before a joint is broken. Stored pressure energy is 29 CFR 1910.147 territory: isolate, block the isolation valve, release the stored energy and lock the isolation before a wrench goes on a fitting. A closed valve is not an isolation until it is locked and the downstream side has been proven at zero.
• Any refrigerant-bearing line. Recover rather than vent; knowingly venting most refrigerants during maintenance, service or repair is prohibited under the EPA's Section 608 rules at 40 CFR Part 82 Subpart F, and the certification requirement runs to the technician personally.
• Drilling a test port in a duct or plenum. De-energize and lock out the air handler before drilling or before a hand goes near an opening, under 29 CFR 1910.147 for the rotating fan, and confirm what is behind the sheet metal before the bit touches it. Line sets, control wiring and branch conductors share chases with ductwork, and a blind drill finds them.
• Sampling flue gas. Wear a personal carbon monoxide monitor in the occupied space before the appliance fires. If ambient carbon monoxide climbs toward the 50 ppm eight-hour time-weighted average in 29 CFR 1910.1000 Table Z-1, everyone leaves immediately, no switch is touched on the way out, and the space is ventilated from outside before anyone re-enters. Flue probes come out hot enough to burn; handle by the grip and set them on a non-combustible surface.
• Sampling hot water. At the delivery temperatures a service water heater runs, a splash is a scald exposure and the time to a serious burn falls steeply across the range between a comfortable shower and a storage setpoint. Wear liquid-resistant gloves and eye protection, set the container down on a stable surface and throttle the flow into it. Never hold a container in the stream.

The thermal rule, and the condition it holds under

Put a probe at one temperature into a sample at another and both end up at a single mixed temperature, weighted by how much heat each can hold. Write the probe's capacity as its water-equivalent mass: its physical mass multiplied by the ratio of its specific heat to the liquid's. Stainless steel holds roughly 0.12 the heat per unit mass that water does, so a stainless stem weighs far more than it counts.

Let r be the probe's water-equivalent mass divided by the sample's mass. Then:

Error = r / (1 + r) x (sample temperature minus probe temperature), and the reading lands that far below the true sample temperature when the probe starts colder.

That relationship is derived for a closed, well-stirred mix with no heat leaving to the surroundings, a single liquid phase, and both parts ending at one temperature. It is a bound on the error, not a prediction: real containers also lose heat outward, which pushes the reading further from the truth in the same direction.

This is a different error from a reading taken before the probe has settled, and the two have opposite fixes. Waiting longer cures a settling error and does nothing for a mixing error, because the mix is already at one temperature and that temperature is genuinely wrong. A sibling article owns settling (see References).

Pressure, flow and sampling: the same ratio in three other currencies

Pressure. A gauge and its hose have internal volume that has to be filled from the system. On a sealed gas volume with no source to make it up, adding dead volume equal to a tenth of the system volume drops it from a 30 psig reading to about 27 psig, isothermally, once you work in absolute pressure and account for the dead volume arriving at atmospheric. On a liquid-full sealed system the same added volume can collapse the reading almost to nothing, because a liquid has almost no compressed volume to give back. And on any system with a source that keeps up, a compressor, a pump, a regulator, the disturbance disappears entirely because the source refills what the gauge took.

Flow. A probe standing in a duct blocks part of the area, and the air that used to go through that area goes around it, faster. The probe reports the accelerated local stream, so it reads high on a disturbance it created. This is negligible when the probe's frontal area is a small fraction of the duct area and becomes the dominant error in small ducts and small pipes.

Sampling. A sample pump pulls gas out of the flue at a point that may be at, near, or below room pressure. If the probe hole around the stem leaks, part of what reaches the analyzer is room air. Oxygen reads high, and everything computed from oxygen, excess air and combustion efficiency, moves with it. Seal the port around the probe rather than assuming the flue is positive enough to push air out past it.

The case: a 23 degree error that was not in the thermometer

A tech is sent on a complaint that hot water at a fixture is not hot enough. Standard method at that shop: run the tap, fill a cup, dip the stem thermometer, write down the number. The tech reads 116.7 F and the setpoint is well above it, so the mixing valve gets blamed and quoted.

Work the ratio. The stem thermometer is stainless, call it 170 g of metal, which at 0.12 the specific heat of water is about 20 g water-equivalent. The cup was sitting in the van at room temperature and is worth roughly another 30 g water-equivalent. The sample is about 100 g. So the foreign mass is 50 g against 100 g of sample, and r is 0.5.

Water arriving from the line is at 140 F. The cup and probe start at about 70 F, so the difference is 70 F. Error is 0.5 / 1.5 x 70 F, which is 23.3 F, and the mixed temperature is 116.7 F. That is exactly what the tech read, to the tenth, and none of it came from the water heater.

Run it again with the probe alone, no cup, held in the flowing stream. Now the foreign mass is the probe's 20 g against a stream that keeps replacing itself, so r is effectively zero and the reading approaches 140 F. That is the number the setpoint should be judged against.

What flips this. Nothing about the thermometer's accuracy. The mass ratio. Fill the same cup a second and third time from the same running tap and the cup and probe come up to temperature, so the third fill reads within a degree or two of the truth. The shop's method was not wrong in principle; it was wrong on the first fill and right on the third, and nobody had written down which fill to read.

The failure mode. A correctly-set mixing valve gets replaced, the complaint does not change, and the tech goes back a second time and now suspects the heater. Two parts, two visits, and the instrument was in tolerance the whole way through. The tell that should have caught it: a 23 F error is enormous, and an error that large almost never comes from an instrument's calibration. When a number is far off, suspect the coupling before the calibration.

When the disturbance is small enough to ignore

State it as a ratio and most of the time you can stop thinking about it in one step.

• The system replenishes what you took. A running pump, a firing burner, a flowing stream. The instrument takes from a source, not from a fixed stock.
• The instrument's share is under a few percent of the system's. A small bead probe in a large tank, a gauge on a large receiver, a small pitot in a large duct.
• You are looking for a change rather than a value. If the same instrument is connected the same way each time, the disturbance is common to both readings and largely cancels out of the difference. This is why trending survives disturbances that would ruin an absolute number.

Where none of those hold, the honest move is to say the reading is of the disturbed system and either recompute the true value from the ratio, as the case above does, or change the method so the ratio collapses.

How to verify you got this right

• Take the reading twice with the instrument already conditioned. If the second reading differs materially from the first, the first one was measuring the instrument's arrival, not the system.
• Estimate the ratio out loud before you accept a surprising number. Instrument capacity over system capacity, to a factor of two. If it is over about a twentieth, name it on the ticket.
• Check the direction. A colder probe reads low, a warmer probe reads high, a gauge that adds volume reads low on a sealed system, a probe blocking flow reads high. If your explanation has the sign backwards, the mechanism you named is not the one operating.

References

• 29 CFR 1910.147 - control of hazardous energy for stored pressure and rotating equipment, isolation locked before a joint or an access panel is opened
• 40 CFR Part 82 Subpart F - EPA Section 608 recovery and technician certification requirements for refrigerant-bearing systems
• 29 CFR 1910.1000 Table Z-1 - the carbon monoxide permissible exposure limit used as the evacuation trigger during flue sampling
• See related: What Loading Does When You Connect an Instrument; What Response Time Does to a Reading You Took Too Soon; Why Where You Put the Probe Decides the Answer