Fig. 1: Uniform Flow through a Channel

Specific Energy is normally used for open channels. For uniform flow, the specific energy of a channel will be constant when the depth and width of the channel remain constant (y and v will then be constant). Notice the similarities between specific energy for open channels and the Bernoulli Equation.

#### Specific Energy Equation

E = E_P + E_V = y + \frac{V^2}{2g}

where

• EP = Energy due to pressure
• EV = Energy Due to velocity
• E = energy per unit weight with elevation datum taken as the bottom of channel
• y = water depth (ft)
• V = velocity (ft/sec)
• g = gravity

Since V = Q/A, the Specific Energy Equation can also be written as:

E = y + \frac{Q^2}{2gA^2}

Lastly since the area of a rectangular channel can be taken as b*h you can...

E = y + \frac{Q^2}{2g(bh)^2} \quad \text{ [Rectangular Channels]}

where

• b = the base of the rectangular channel (ft)
• h = the height of the rectangular channel (ft)

## References:

1. H. Chanson, "The Hydraulics of Open Chanel Flow: An Introduction (2nd Edition)", 2004

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