Energy and Hydraulic Grade Line
The hydraulic grade and the energy line are graphical forms of the Bernoulli equation
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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)
where
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.
The Head
By dividing each term with the specific weight - γ = ρ g - (1) can be transformed to express the "head":
p / γ + v2 / 2 g + h = constant along a streamline = H (2)
where
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 - and elevation head - h - is constant along the stream line. This constant can be called the total head - H -.
The total head in a flow can be measured by the stagnation pressure using a pitot tube.
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)
where
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 the practical world the energy line decreases along the flow due to the losses.
A turbine in the flow will reduce the energy line and a pump or fan will increase the energy line.
The Hydraulic Grade Line
The Hydraulic Grade Line is a line that represent the total head available to the fluid minus the velocity head and can be expressed as:
HGL = p / γ + h (4)
where
HGL = Hydraulic Grade Line
The hydraulic grade line lies one velocity head below the the energy line.
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