We present a fully parametrized bead-spring chain model for stained lambda-phage DNA. The model accounts for the finite extensibility of the molecule, excluded volume effects, and fluctuating hydrodynamic interactions (HI). Parameters are determined from equilibrium experimental data for 21 mum stained lambda-phage DNA, and are shown to quantitatively predict the non-equilibrium behavior of the molecule. The model is then used to predict the equilibrium and nonequilibrium behavior of DNA molecules up to 126 mum. In particular, the HI model gives results that are in quantitative agreement with experimental diffusivity data over a wide range of molecular weights. When the bead friction coefficient is fit to the experimental relaxation time at a particular molecular weight, the stretch in shear and extensional flows is adequately predicted by either a free-draining or HI model at that molecular weight, although the fitted bead friction coefficients for the two models differ significantly. In shear flow, we find two regimes at high shear rate (gamma) that follow different scaling behavior. In the first, the viscosity and first normal stress coefficient scale roughly as gamma(-6/11) and gamma(-14/11), respectively. At higher shear rates, these become gamma(-2/3) and gamma(-4/3). These regimes are found for both free-draining and HI models and can be understood based on scaling arguments for the diffusion of chain ends.