The hydraulic grade and the energy line are graphical presentations of the Bernoulli equation
The Bernoulli Equation
For steady, inviscid, incompressible flow the total energy remains constant along a stream line as expressed through the Bernoulli Equation:
p + 1/2 ρ v2 + γ h = constant along a streamline (1)
p = static pressure (relative to the moving fluid)
ρ = density
γ = specific weight
v = flow velocity
h = elevation height
Each term of this equation has the dimension force per unit area - psi, lb/ft2 or N/m2.
By dividing each term with the specific weight - γ = ρ g - equation (1) can be transformed to express the "head":
p / γ + v2 / 2 g + h = constant along a streamline = H (2)
H = the total head
Each term of this equation has the dimension length - ft, m.
The Total Head
(2) states that the sum of
- pressure head - p / γ
- velocity head - v2 / 2 g
- elevation head - h
is constant along a stream line. This constant can be called the total head - H.
The Piezometric Head
The sum of pressure head - p / γ - and elevation head - h - is called the piezometric head. The piezometric head in a flow can be measured through an flat opening parallel to the flow.
The Energy Line
The Energy Line is a line that represent the total head available to the fluid and can be expressed as:
EL = H = p / γ + v2 / 2 g + h = constant along a streamline (3)
EL = Energy Line
For a fluid flow without any losses due to friction (major losses) or components (minor losses) - the energy line would be at a constant level. In a practical world the energy line decreases along the flow due to losses.
A turbine in the flow reduces the energy line and a pump or fan in the line increases the energy line.
The Hydraulic Grade Line
The Hydraulic Grade Line is a line representing the total head available to the fluid - minus the velocity head and can be expressed as:
HGL = p / γ + h (4)
HGL = Hydraulic Grade Line
The hydraulic grade line lies one velocity head below the the energy line.
- en: energy line hydraulic grade line