Based on a more direct analogy between turbulent and molecular transport, a foundation was recently presented for an energy-vorticity turbulence model. The new turbulent-energytransport equation contains two closure coefficients; a viscous-dissipation coefficient and a turbulent-transport coefficient. To help evaluate the closure coefficients and provide insight into the energy-vorticity turbulence variables, fully rough pipe flow is considered. For this fully developed flow, excellent agreement with experimental data for velocity profiles and friction factors is attained over a wide range of closure coefficients, provided that a given relation between the coefficients is maintained.