As long as it's not a transformer or something where the leakage from one coil affects another, it might be as simple as putting a resistor in series because the flux is proportional to the current on the wire, and the flux losses are likely proportional to flux density. So, if you're trying to model the losses due to flux leakage, a resistor in series might be your answer.
Your waterwheel is not a bad analogy. Adding resistance in series will cause losses proportional to current, and current happens to be proportional to flux. I know that flux losses depend on physical shape and there are probably some eccentricities to the way flux is lost, but given that those are unknowns without a deep examination, it should be adequate to use a resistor in series for simulation. If you want you can probably use a single resistor to account for all of your losses, flux loss, coil resistance, ringing if present and eddy current losses.
As far as measurement quantities, there are quite a few with regard to magnetics. The Weber is a unit of flux, and flux density is measured in Teslas, so if you have 1 Weber in a cross section of 1 m^2 you have a density of 1 tesla. Coulombs are measurement of charge. 1 Coulomb is 1 Mol (Avogadro's number) of electrons or holes. A capacitor has capacitance rated in Farads, and a capacitance of 1 Farad means that the capacitor can store 1 coulomb of charge per volt it is charged to. The electric field is measured in volts, as basically all a capacitor does is store voltage (pressure)