A theorem in which the sum of the pressure-volume, potential, and kinetic energies of an incompressible and non-viscous fluid flowing in a pipe with steady flow with no work or heat transfer is the same anywhere within a system. When expressed in head form, the total head is the sum of the pressure, velocity, and static head. It is applicable only for incompressible and non-viscous fluids. That is:
where p is pressure, ρ is density, g is gravitational acceleration, v is velocity, and z is elevation. It is effectively a statement of the law of the conservation of energy. It was formulated and published in 1738 by Daniel Bernoulli (1700–82).