Magnetic flux leakage only works when the wall is driven into magnetic saturation. Below saturation the steel is still able to carry more flux, so a wall-loss feature simply diverts flux within the metal instead of forcing it out into the air where the sensors sit, and the leakage signal collapses. Required levels are high — typically around 1.5 T for tank-floor and plate scanners and 1.6 T or more in pipeline in-line inspection — and reaching them is the whole design problem of the magnetiser.

Moving the magnetiser makes it harder. A conductive wall moving through a magnetic field has eddy currents induced in it, and those currents oppose the change, dragging flux backwards relative to the tool and reducing the flux density actually established in the wall under the sensors. The governing group is the magnetic Reynolds number Rm = µ₀·µr·σ·v·t: velocity effects are negligible when it is well below about 0.1, measurable around 0.1 to 1, and severe above 1. Setting Rm = 1 gives a speed limit v = 1/(µ₀·µr·σ·t) which, for carbon steel of 5 MS/m at 8 mm wall and a differential permeability of 5 in saturation, lands near 4 m/s — the same order as the run-speed limits real in-line inspection tools are specified to.

The permeability to use is the differential permeability at the working point, dB/dH, not the ratio B/(µ₀H). Deep in saturation the differential value falls to single figures, which is why saturation both improves the leakage signal and, helpfully, reduces the velocity effect. Below the knee, where the differential permeability is in the hundreds, velocity effects are severe at walking pace.

The effective flux density here is estimated with a first-order lag, B = B₀/(1 + Rm). Treat it as a screening estimate only: real magnetiser design needs finite-element modelling, and the tool vendor’s qualified speed range and the qualification report are what govern acceptance. Use this calculation to sanity-check a proposed scanning speed and to understand why a thick wall or a fast run degrades sizing — not to certify a tool.

Worked example

Application	tank_floor
Wall thickness	8 mm
Scanning speed	1 m/s
Differential relative permeability	5
Electrical conductivity	5 MS/m
Static flux density achieved	2 T
Magnetic Reynolds number criterion	1
Required flux density	1.5 T
Speed at the Rm criterion	3.98 m/s
Magnetic Reynolds number at this speed	0.251
Estimated flux density at this speed	1.598 T
Margin on required flux density	0.098 T
Speed at which saturation is just lost	1.33 m/s
Saturation maintained	1

µ0·µr·σ·t = 1.2566e-6 x 5 x 5e6 x 0.008 = 0.25133 s/m, so Rm = 1 at v = 3.98 m/s. At 1 m/s, Rm = 0.251 and the first-order estimate gives B = 2.0/1.251 = 1.598 T, which is 0.098 T above the 1.5 T needed. Saturation is lost when B0/(1+Rm) = 1.5, i.e. Rm = 2.0/1.5 − 1 = 0.333, at 0.333 x 3.979 = 1.33 m/s.

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