16.7 : Energy Line and Hydraulic Gradient Line

Based on Bernoulli's equation, the energy line (EL) and hydraulic grade line (HGL) provide graphical representations of energy distribution in a fluid flow system. For steady, incompressible, inviscid flows, Bernoulli's equation is expressed as:

Here, H is the total head, p/γ is the pressure head, V²/2g is the velocity head, and z is the elevation head.

The energy line (EL) represents the total head available in the flow. It is located above the datum and includes all three energy components. Under ideal conditions, it remains horizontal, as the total energy does not vary along a streamline. The elevation of the EL can be measured using a Pitot tube, which captures the stagnation pressure and provides the total energy value.

The hydraulic grade line (HGL) depicts the piezometric head (p/γ+ z), which excludes the velocity head. It lies below the EL by a vertical distance, which is equal to the velocity head (V²/2g). The HGL represents pressure variations within the system. In pressurized pipelines, it lies above the pipe, while in open-channel flow, it coincides with the water surface.

If the fluid velocity or pipe diameter changes, the HGL elevation adjusts accordingly. The pressure head is zero at the pipe outlet, making the HGL coincide with the elevation head. For steady, inviscid flow from a tank, the EL and HGL are horizontal, reflecting constant head and atmospheric outlet pressure.

Practical applications often incorporate viscous effects and losses, which distort the EL and HGL. These concepts are crucial for analyzing pressure and energy distributions in fluid systems.