We present the results of nonequilibrium molecular dynamics simulations of a model decane fluid performed at constant pressure and compare them with results previously obtained from simulations performed at constant volume. The strain rate dependence of the viscosity at constant pressure is found to differ from that obtained previously at constant volume. The shear thickening at high strain rates observed in constant volume simulations vanishes when the simulations are performed at constant pressure. We also investigate the question of how our low strain rate data for decane can be accurately extrapolated to zero strain rate. We find a well defined first Newtonian region in which the viscosity is independent of strain rate to within errors. The value of the viscosity that we obtain in this region agrees well with the zero strain rate viscosity calculated from the Green-Kubo formula at equilibrium.