Numerous experimental and computational studies show that continuous hopper flows of granular materials obey the Beverloo equation that relates the volume flow rate Q and the orifice width w: Q ∼ (w/sigma - k)^beta, where sigma is the average particle diameter, k is an offset where Q ∼ 0, the power-law scaling exponent beta = d - 1/2, and d is the spatial dimension. Recent studies of hopper flows of deformable particles in different background fluids suggest that the particle stiffness and dissipation mechanism can also strongly affect the power-law scaling exponent beta. We carry out computational studies of hopper flows of deformable particles with both kinetic friction and background fluid dissipation in two and three dimensions. We show that the exponent beta varies continuously with the ratio of the viscous drag to the kinetic friction coefficient, lambda = zeta/mu. beta = d − 1/2 in the lambda goes to zero imit and d - 3/2 in the lambda goes to infinity limit, with a midpoint lambda_c that depends on the hopper opening angle theta. We also characterize the spatial structure of the flows and associate changes in spatial structure of the hopper flows to changes in the exponent beta. The offset k increases with particle stiffness until k ~ kmax in the hard-particle limit, where kmax ~ 3.5 is larger for lambda goes to infinity compared to that for lambda goes to zero. Finally, we show that the simulations of hopper flows of deformable particles in the lambda goes to infinity limit recapitulate the experimental results for quasi-2D hopper flows of oil droplets in water.