In addition to pressure head, elevation head, and velocity head, there may also be head added to the system, by a pump for instance, and head removed from the system due to friction. These changes in head are referred to as head gains and headlosses, respectively. Balancing the energy across two points in the system, you then obtain the energy equation:

Where:

p = Pressure (N/m2, lb./ft.2)

= Specific weight (N/m3, lb./ft.3)

z = Elevation at the centroid (m, ft.)

V = Velocity (m/s, ft./sec.)

g = Gravitational acceleration constant (m/s2, ft./sec.2)

hp = Head gain from a pump (m, ft.)

hL = Combined headloss (m, ft.)

The components of the energy equation can be combined to express two useful quantities, which are the hydraulic grade and the energy grade.