Energy Hydraulic Grade Line

Overview

Engineering reference data for Energy Hydraulic Grade Line in fluid mechanics.

Key Formulas

Reynolds Number

$Re = \frac{\rho v D}{\mu}$

Ratio of inertial to viscous forces — determines flow regime.

Bernoulli's Equation

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$

Conservation of energy for steady, inviscid, incompressible flow.

Continuity Equation

$A_1 v_1 = A_2 v_2$

Conservation of mass for incompressible flow.

Darcy-Weisbach

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Pressure drop due to friction in a pipe.

Variables

Hydraulic Grade Line (HGL)

The Hydraulic Grade Line (HGL) represents the total mechanical energy per unit weight of fluid available at any point in the system, excluding the kinetic energy (velocity head). It is defined as the sum of the pressure head and the elevation head.

$HGL = \frac{p}{\gamma} + h$

Where:

• $HGL$ = Hydraulic Grade Line (m fluid column)
• $p / \gamma$ = pressure head
• $h$ = elevation head

The HGL lies exactly one velocity head ($v^2 / 2g$) below the Energy Line (EL) at any given point. For a system with no friction losses, the HGL would be parallel to the EL.

Energy Line vs. Hydraulic Grade Line

• The Energy Line (EL) represents the total head ($H$) and is the sum of pressure head, velocity head, and elevation head.
• The Hydraulic Grade Line (HGL) is the sum of pressure head and elevation head only.
• The vertical distance between the EL and HGL at any point is equal to the local velocity head: $EL - HGL = \frac{v^2}{2g}$.

Practical Implications

• Losses: In real flows, both the EL and HGL slope downward in the direction of flow due to friction (major losses) and components (minor losses).
• Pumps and Turbines:
  • A pump or fan adds energy to the fluid, causing an upward step jump in both the EL and HGL at its location.
  • A turbine extracts energy, causing a downward step jump in both the EL and HGL.

References

• Original Source