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Abstract A unified one-dimensional (1D), steady-state flow and heat transfer model is presented for the pipeline transport of fluids at high pressures, including the supercritical (SC) conditions. The model includes a generalized temperature equation, presented here for the first time, and accounts for all of the important effects, including the property variation, viscous dissipation, Joule-Thomson (J-T) cooling, and heat exchange with the surrounding. With appropriate approximations, this model can yield all isothermal and nonisothermal pipe flow solutions reported thus far. A generalized multizone integral method is developed which solves the two resulting algebraic equations for pressure and temperature in conjunction with a property database, such as the National Institute of Standard and Technology (NIST) reference fluid thermodynamic and transport properties (REFPROP). With appropriately selected number and size of the zones and using property values at the mean temperature and pressure within each zone, this integral method can accurately predict the complex effects of the governing parameters, such as the pipe diameter and length, inlet and exit pressures, mass flowrate, J-T cooling, and inlet and surrounding temperatures. Its accuracy for small-to-large diameter pipes has been ascertained by a comparison with the numerical solutions of the differential form of governing equations that requires a large number of small grids along the pipe and the values of mean properties within each grid. Indeed, this integral model can be used for the pipeline transport at both subcritical and supercritical pressures as long as the fluid does not encounter its anomalous states and the phase-change.