We study experimentally
the influence of dissipation on stationary capillary wave
turbulence on the surface of a liquid by changing its viscosity.
We observe that the frequency power-law scaling of the capillary
spectrum departs significantly from its theoretical value when
the dissipation is increased. The energy dissipated by capillary
waves is also measured and found to increase nonlinearly with
the mean power injected within the liquid. Here we propose an
experimental estimation of the energy flux at every scale of the
capillary cascade. The latter is found to be nonconstant through
the scales. For fluids of low enough viscosity, we found that
both capillary spectrum scalings with the frequency and the
newly defined mean energy flux are in good agreement with wave
turbulence theory. The Kolmogorov-Zakharov constant is then
experimentally estimated and compared to its theoretical value.