The Energy Equation
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:
P1/ γ+ Z1 + V1 2/2g + hp = P2/ γ+ Z2 + V2 2/2g + hL
The components of the energy equation can be combined to express two useful quantities, which are the hydraulic grade and the energy grade.
Hydraulic Grade
The hydraulic grade is the sum of the pressure head (p/g) and elevation head (z). The hydraulic head represents the height to which a water column would rise in a piezometer. The plot of the hydraulic grade in a profile is often referred to as the hydraulic grade line, or HGL.
Energy Grade
The energy grade is the sum of the hydraulic grade and the velocity head (V2/2g). This is the height to which a column of water would rise in a pitot tube. The plot of the hydraulic grade in a profile is often referred to as the energy grade line, or EGL. At a lake or reservoir, where the velocity is essentially zero, the EGL is equal to the HGL.
HGL Convergence Test
In full network calculation, this value is taken as the maximum absolute change between two successive solves of hydraulic grade at any junction or inlet in the system. This test is used to optimize the performance of system solutions. It minimizes the number and extent of hydraulic grade line computations in the upstream direction. For a given discharge, the upstream propagation of headlosses through pipes will continue until two successive calculations change by an absolute difference of less than this test value.
The HGL Convergence Test value is also used in the standard step gradually varied flow profiling algorithm. If two successive depth iterations are within this absolute test value, the step is solved.