The hydraulic grade and the energy line are graphical presentations of the Bernoulli equation
The Bernoulli Equation
For steady, inviscid (having zero viscosity), 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) (Pa, N/m2)
ρ = density (kg/m3)
γ = specific weight (N/m3)
v = flow velocity (m/s)
g = acceleration of gravity (9.81 m/s2)
h = elevation height (m)
Each term of this equation has the dimension force per unit area - N/m2 or psi, lb/ft2 in Imperial units.
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 (m)
Each term of this equation has the dimension length - m or ft in Imperial units.
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 (m)
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 (m)
The hydraulic grade line lies one velocity head below the the energy line.
- en: energy line hydraulic grade line
- es: rasante hidráulica línea de energía
- de: Energieleitung hydraulische Drucklinie