Energy and Hydraulic Grade Line

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)

where

p = static pressure (relative to the moving fluid)

ρ = density

γ = specific weight

v = flow velocity

g = acceleration of gravity

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 - equation (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
• elevation head - h

is constant along a stream line. This constant can be called the total head - H.

The total head in a flow can be determined by measuring 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 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)

where

HGL = Hydraulic Grade Line

The hydraulic grade line lies one velocity head below the the energy line.

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