Bernoullis equation results from the application of the
general energy equation and the first law of
thermodynamics to a steady flow system in which no work is done on or by the
fluid, no heat is transferred to or from the
fluid, and no change occurs in the internal energy (i.e., no temperature
change) of the fluid. Under these conditions, the general energy equation is
simplified to Equation 3-9.

Substituting appropriate expressions for the potential energy
and kinetic energy, Equation 3-9 can be
rewritten as Equation 3-10.

Note:

The factor gc is
only required when the English System of measurement is used and mass is
measured in pound mass. It is essentially a conversion factor needed to allow
the units to come out directly. No factor is
necessary if mass is measured in slugs or if the metric system
of measurement is used.

Each term in Equation 3-10 represents a form of energy possessed
by a moving fluid (potential, kinetic, and
pressure related energies). In essence, the equation physically represents a
balance of the KE, PE, PV energies so that
if one form of energy increases, one or more of the others will
decrease to compensate and vice versa.

Multiplying all terms in Equation 3-10 by the factor gc/mg
results in the form of Bernoullis equation
shown by Equation 3-11.