Uniform flow

Water flowing in an open channel typically gains kinetic energy as it flows from a higher elevation to a lower elevation. It loses energy with friction and obstructions. Uniform flow occurs when the gravitational forces that are pushing the flow along the channel are in balance with the frictional forces exerted by the wetted perimeter that are retarding the flow. For uniform flow to exist:

• Mean velocity is constant from section to section.
• Depth of flow is constant from section to section.
• Area of flow is constant from section to section.

Therefore, uniform flow can only truly occur in very long, straight, prismatic channels where the terminal velocity of the flow is achieved. In many cases, the flow only approaches uniform flow.

Since uniform flow occurs when the gravitational forces are exactly offset by the resistance forces, a resistance equation can be used to calculate a velocity. The most commonly used resistance equation is Manning’s equation (eq. 19).

given

then

where:
A = flow area (ft²)
R = hydraulic radius (ft)
S = channel profile slope (ft/ft)
n = roughness coefficient

The 1.486 exponent is replaced by 1.0 if SI units are used. The flow area (A) and the hydraulic radius (R) relate how the flow interacts with the boundary.

A rough estimate of the flow capacity or average velocity at a natural cross section may be determined with Manning’s equation. A designer may assume a roughly trapezoidal cross section, estimating bottom width, side slopes, and profile slope from topographic maps. The roughness coefficient is a significant factor, and its determination is described in NEH654.0609(c).