Energy-Depth Relationships

Bernoulli's equation can be applied to a flow through an open channel. In the case of flow through an open channel, the stream lines are straight and parallel or a little curved. As per Bernoulli's equation, total energy per unit weight,
 Constant along a stream line.
In the case of an open channel flow height of free surface represents potential head + pressure head, as shown in the figure.

So Bernoulli's equation for an open channel flow is simplified as,
Height of liquid surface above datum + (v²/2g) = Constant (neglecting the frictional losses)
If frictional losses are considered, the Bernoulli's equation for an open channel can be written as,
Where, h_f = frictional loss, V₁ and V₂ are average flow velocities, h₁ and h₂ are depth of flow and Z₁ and Z₂ are channel bed heights at two section 1 and 2 as shown in the figure.

To account for non-uniformity of velocity over a crosssection, the equation can be modified as,