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Some explanation
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)
Après avoir regardé la publi indiquée par Laurent, il semble que l'hypothèse que l'énergie soit relative à la distance est juste
Wheis, 1978
Work for constant speed energy
Thrust equal to hydrodynamic resistance R
R=a/2*Af*Cd*V²
a density of the water
With Af=frontal area
Cd=drag coefficient
V relative velocity between the water and the fish
Total work=R*D where D is the distance covered
The total energy requirement inclusdes in addition to the energy expenditure the maintenance of bodily functions
=standard resting metabolic rate
Esm=M*t
where M is the standard resting metabolic rate and t is time
total work=propulsive eneregy + standard metabolic rate energy=
Epe+ Esm=
R*D +Mt=R*D+M*D/V
=a/2*Af*Cd*V²*D+M*D/V
on retrouve bien pour une vitesse relative constante une grandeur relative à la distance parcourue
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)
