Probe selection for tube examination is a compromise between coupling and clearance, and fill factor is how it is expressed. Fill factor is the square of the diameter ratio, eta = (d_probe / D_id)^2, so the probe diameter that achieves a required fill factor is d_probe = D_id x sqrt(eta). Working the relationship in this direction is what a technician actually needs: the tube dimensions are given, and the question is which probe out of the kit to fit.

Too small a probe loses signal to the annular gap and, worse, loses noise margin. Wobble becomes a larger fraction of the clearance, small OD-initiated indications sink into the noise, and the phase readings that carry depth information get noisier along with everything else. Too large a probe gives excellent coupling right up to the moment it jams in a dent, an ovalised span, a deposit or a U-bend – and retrieving a stuck probe from an in-service heat exchanger costs far more than the few percent of amplitude that a smaller probe would have given away.

Common practice settles at 85 to 90 % fill for bobbin probes in straight tubing, and lower – often 75 to 80 % – for U-bend and severely fouled tubes where passage matters more than sensitivity. Note that fill factor changes far more slowly than diameter: over the whole 85 to 90 % band the probe diameter only moves about 3 %, so a kit with a sensible diameter increment covers a wide range of tube sizes.

Whatever probe is selected, sensitivity has to be proved and not assumed: the calibration standard is examined with that same probe, at the same frequencies, and the response from the calibration reflectors is what sets the gain. A probe change mid-job is a re-calibration, not an adjustment.

Worked example

Tube outside diameter	19.05 mm
Tube wall thickness	1.24 mm
Minimum target fill factor	85 %
Maximum target fill factor	90 %
Tube inside diameter	16.57 mm
Smallest acceptable probe	15.28 mm
Recommended probe diameter	15.5 mm
Largest acceptable probe	15.72 mm
Radial clearance at largest probe	0.425 mm
Radial clearance at smallest probe	0.647 mm
Fill factor at recommended diameter	87.5 %

19.05 mm OD x 1.24 mm wall (3/4 in x 0.049 in) stainless exchanger tube. Bore = 19.05 - 2 x 1.24 = 16.57 mm. For 85 % fill, d = 16.57 x sqrt(0.85) = 16.57 x 0.92195 = 15.28 mm; for 90 %, d = 16.57 x sqrt(0.90) = 16.57 x 0.94868 = 15.72 mm; mid-band 87.5 % gives 16.57 x sqrt(0.875) = 16.57 x 0.93541 = 15.50 mm, which is a standard probe size. Clearances: (16.57 - 15.720)/2 = 0.425 mm at the largest probe and (16.57 - 15.277)/2 = 0.647 mm at the smallest, both worked from the unrounded diameters. Checking the recommendation, (15.50/16.57)^2 = 87.50 % fill.

Use at your own risk — verify before you act

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