What actually affects your accuracy
Ranked by how much error each one contributes in practice. The instrument specification is near the bottom of this list, which is the point.
1. Wall thickness entry
The largest single source of error and the easiest to get wrong. The meter subtracts the time it believes the signal spent crossing the pipe wall in order to calculate the fluid path. Enter a wall thickness that is 15% out and everything downstream of that assumption is wrong.
Schedule tables are a starting point, not an answer. Old carbon steel corrodes from the inside, and a Schedule 40 line installed in 1968 is not Schedule 40 today. Both rental meters can gauge wall thickness directly — the ProLite with the optional probe, from 2 to 24 mm. Use it.

2. Straight run
An undeveloped or swirling velocity profile invalidates the profile correction factor the meter applies. Typically a few percent, potentially over ten downstream of a throttled valve. It is systematic, so repeating the reading will not reveal it. Full straight run guidance.
3. Lining, unrecorded
Cement-lined ductile iron is the common case on water mains. The lining is acoustically different from the pipe wall and it reduces the bore. Entering the pipe as unlined shifts both the path calculation and the cross-sectional area. If the records are gone, this is the point at which a clamp-on measurement becomes an estimate.
4. Internal scale and tuberculation
The meter computes volumetric flow from the internal diameter you gave it. It has no way of seeing that an old unlined cast iron main has 12 mm of tuberculation reducing the effective bore. Velocity may be measured correctly and the volume still be substantially wrong.
5. Fluid sound speed
Mostly a glycol problem. A 30% ethylene glycol mix runs around 1560 m/s against water's 1482. Enter it as water and you carry a 5% geometry error into the result. Verify the concentration with a refractometer rather than trusting the system label. Sound speed reference.
6. Low flow velocity
Below roughly 0.1 m/s the transit-time difference becomes small relative to the noise, and accuracy degrades regardless of how good the installation is. This bites on oversized pipe at low demand — a makeup line sized for peak that trickles most of the time.
7. Surface preparation and coupling
Loose rust, thick paint, or insufficient coupling gel weakens the signal. This is usually self-announcing: signal strength drops and the meter tells you. Because it is visible in the diagnostics rather than silent, it causes fewer bad readings than the items above it, which give you a confident number that happens to be wrong.
8. The instrument itself
Last on the list. System accuracy on the Ultra ProLite is better than ±0.5% of measured value; the UF801-P is typically 1 to 2%, improving to around 0.5% with field calibration. On a real installation, everything above contributes more than this does.
A ten-second sanity check
Before trusting any reading, compare the sound speed the meter reports against the expected value for your fluid at your temperature. If it is close, your pipe data is probably right. If it is not, stop and fix the entry rather than recording the flow.