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