  We derive here, from first principles, the energy-momentum densities of a
perfect fluid, in the form of an ideal molecular gas, in an inertial frame
where the fluid possesses a bulk motion. We begin from the simple expressions
for the energy density and pressure of a perfect fluid in the rest frame of the
fluid, where the fluid constituents (gas molecules) may possess a random
motion, but no bulk motion. From a Lorentz transformation of the velocity
vectors of molecules, moving along different directions in the rest frame of
the fluid, we compute their energy-momentum vectors and number densities in an
inertial frame moving with respect to the rest frame of the liquid. From that
we arrive at the energy-momentum density of the fluid in a frame where it has a
bulk motion. This way we explicitly demonstrate how a couple of curious
pressure-dependent terms make appearance in the energy-momentum density of a
perfect fluid having a bulk motion. In addition to an ideal molecular gas, we
compute the energy-momentum density for a photon gas also, which of course
matches with the energy-momentum density expression obtained for a molecular
gas having ultra-relativistic random motion.
