Design an EPG loop: medium, drive, transit, pickup and the energy accounting

Can this medium, pumped at this speed past this drive coil, induce anything in a pickup coil downstream — how much, into what load, and at what cost?

ε = Np \cdot \mu_0 \cdot Ma \cdot A \cdot \frac{v}{\max(\ell_c,\, w)}

Method

1. The medium first: its density and viscosity from the recipe, its susceptibility and saturation from the particulate and loading, its remanence and coercivity from the particulate's hysteresis, its holding time from particle size against the carrier's viscosity, and how fast it settles.
2. The loop: the pressure drop and hydraulic power at this speed through this bore.
3. The drive: the pulse's on-time, how much current the coil's L/R lets through in that time (or the supply's limit), the field that puts in the tube, and the slug length and pitch it writes at this speed.
4. The transit: how far the flow smears the slug's front over the distance to the pickup, and how much of the remanence the particles keep for that long.
5. The pickup: what the arriving magnetisation induces, against the ceiling a saturated sharp slug would; then into the load through the coil's own resistance and inductance.
6. The accounting: drive copper loss at this duty plus the pump against the mean power into the load.
7. Every step is its own calculation with its own page; every formula is shown below with these numbers in it.

Assumptions

• Every assumption of every constituent applies: dilute rigid spheres, a straight smooth tube, a finite solenoid's on-axis field, single-time-constant relaxation, a bipolar pulse whose fundamental the load sees.
• One drive coil and one pickup, the pickup downstream and outside the drive's field. The transformer coupling between the two — the drive's own field through the pickup, which has nothing to do with the fluid — is not in this chain; the studio computes it beside the transported signal, and the "fluid stopped" trace there is the experiment that separates them.
• The drive is a pulse train. A capacitor dump and a sequenced row of coils have their own calculations and are modelled in the studio.
• The slug arrives at the mean velocity; in laminar flow parts of it arrive early and late, which the smearing step covers.
• Nothing here is Meyer's except the speed and the pump the EPG #1 holding gives. The recipe, the coils and the coercivities are engineering choices, and the page says so on every step.