# Energy and Hydraulic Grade Line

## The hydraulic grade and the energy line are graphical presentations of the Bernoulli equation

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### 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 + 1/2ρ v^{2}+ γ h = constant along a streamline(1)

where

p= static pressure (relative to the moving fluid) (Pa, N/m^{2})

ρ= density (kg/m^{3})

γ= specific weight(N/m)^{3}

v= flow velocity (m/s)

g= acceleration of gravity(9.81 m/s^{2})

h= elevation height (m)

Each term of this equation has the dimension *force per unit area* - *N/m ^{2}* or

*psi, lb/ft*in Imperial units.

^{2}### The Head

By dividing each term with the specific weight - *γ = ρ g -* equation *(1)* can be transformed to express the "*head*":

p / γ + v^{2}/ 2 g + h = constant along a streamline=H(2)

where

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**-*v*^{2}/ 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 + v^{2}/ 2 g + h = constant along a streamline(3)

where

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)

where

HGL= Hydraulic Grade Line (m)

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

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