work as Distance*Elevation Crossin et al. 2004 or something more ?

Van Ginneken et al. (2008) estimate a cost of transport (COT)in kj.kg-1.km-1 do the amount of energy will be proportional to the distance covered by silver eel. It makes sense to say that the energy expenditure is relative to the distance covered (E1)

The additional distance linked to altitude (water current) is relative to Vitesse d'écoulement :

vitesse instantanée: u = dx/dt vitesse moyenne : V

Dans un chenal, relation empirique de Chezy: V= C (h S)1/2

C : coefficient de friction de Chezy h : profondeur S : pente

The additional energy (E2)due to slope is related to the current distance additional=v*t ~c(hS)1/2*t ~alpha t (E/D)1/2 with alpha a multiplying coeff depending on depth, C t is proportional to the distance so E2= beta(DE)1/2

Energy=D+sqrt(DE) which is correct for dimensions (m) Energy ~ distance ~ mgh (potential energy)