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 (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.

energy line hydraulic grade line

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)


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 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)


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.

Related Topics

  • Fluid Mechanics - The study of fluids - liquids and gases. Involves velocity, pressure, density and temperature as functions of space and time

Related Documents

  • Energy - Energy is the capacity to do work
  • Major loss in Ducts, Tubes and Pipes - Major loss - head loss or pressure loss - due to friction in ducts, pipes and tubes
  • Bernoulli Equation - Conservation of energy - non-viscous, incompressible fluid in steady flow
  • Pitot Tubes - Pitot tubes can be used to indicate fluid flow velocities by measuring the difference between the static and the dynamic pressures in fluids
  • U-Tube Manometer - The inclined and vertical u-tube manometers are inexpensive and common in the differential pressure measurement with flow meters like pitot tubes, orifices and nozzles
  • Pressure Gradient Diagrams - A pressure gradient diagram is a graphical presentation of the static pressure throughout a fluid flow system

Tag Search

  • en: energy line hydraulic grade line
  • es: rasante hidráulica línea de energía
  • de: Energieleitung hydraulische Drucklinie

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