Hydraulic Efficiency of Grate and Curb Inlets - Urban Drainage and ...

2.3 Manning’s Equation
Uniform flow is a state of open-channel flow that occurs when accelerating and
decelerating forces acting on the flow are equal (Chaudhry, 2008). In this state, the channel
itself exerts hydraulic control over the flow. Often, uniform flow occurs in long and straight
prismatic channels that do not vary in bottom slope or cross-sectional character with distance.
Flow depth corresponding to uniform flow is called normal depth. The numerical relationship of
Manning’s equation commonly used to describe uniform flow is provided as Equation 2-15.
Known channel geometry, flow depth, roughness, and bottom slope can be used in Manning’s
equation to solve for flow velocity. Alternatively, surface roughness can be solved for. The
friction slope (S f ) term in Manning’s equation represents the rate of energy dissipation caused by
frictional forces acting along the channel perimeter. When a state of uniform flow exists, the
friction slope is equal to the bottom slope of the channel (S o ). Manning’s equation is then
simplified by assuming that S f is equal to S o . Conversely, Manning’s equation can provide an
explicit solution for the friction slope when uniform flow does not exist:
Φ 2 1
3 2
V = R S f
Equation 2-15
n
where:
V = cross-sectional averaged flow velocity (ft/s);
Φ = unit conversion constant, equal to 1.49 for U. S. Customary and 1.00 for SI;
R = hydraulic radius (ft), which is a function on depth;
S f = friction slope; and
n = Manning’s roughness coefficient.
2.4 Froude Number
In open-channel flow, where gravity is the driving force, the Froude number represents
the ratio of inertial to gravity forces (Chaudhry, 2008). Stated another way, it is the ratio of bulk
flow velocity to elementary gravity wave celerity. The Froude number (Fr) is defined as
Equation 2-16:
V
Fr = Equation 2-16
gD
15