Channel crosssectional parameters
A variety of channel cross-sectional parameters are used in the hydraulic analysis of streams and rivers. It is important to measure and use these parameters consistently and accurately. A generalized cross section is shown in figure 1.
The flow depth is the distance between the channel bottom and the water surface. For rectangular channels, the depth is the same across an entire cross section, but it obviously varies in natural channels. Depth is often measured relative to the channel thalweg (or lowest point). Normal depth is the depth of flow in a uniform channel for which the water surface is normal or parallel to the channel profile and energy slope.
For a cross section aligned so that streamlines of flow are perpendicular, the flow area is the area of the cross section between bed and banks and water surface. For a rectangular channel, flow area is depth multiplied by top width. For a natural channel cross section, the area may be approximated with the sum of trapezoidal areas between cross-sectional points. The top width of a channel cross section at the water surface, typically designated as T, is a factor in the hydraulic depth.
The hydraulic depth is the ratio of the cross-sectional area of flow to the free water surface or top width. The hydraulic depth, d, is generally used either in computing the Froude number or in computing the section factor for critical depth. Since only one critical depth is possible for a given discharge in a channel, the section factor, Z, can be used to easily determine it (Chow 1959).
For a cross section normal to the direction of flow, the wetted perimeter (typically designated P) is the length of cross-sectional boundary between water and bed and banks. The hydraulic radius is the ratio of the cross-sectional area of flow to the wetted perimeter or flow boundary. The hydraulic radius, R= A/P, is used in Manning’s equation for calculation of normal depth discharge, as well as for calculation of shear velocity.
Velocity is a physics term for a change in distance during a time interval. Flow velocity refers to the areal extent of the flow (in a cross section) for which a velocity is specified. For example, an average velocity that applies to an entire cross-sectional area may be determined from V = Q/A or if the discharge is unknown, a uniform flow velocity may be determined from Manning’s equation.
Another useful formulation is critical velocity, which is average flow velocity at critical depth, and is calcu-lated from equation 3:
where:
Vcr = critical velocity
g = gravitational acceleration
dcr = critical depth
Determining the state of flow is a matter of determining whether the velocity is greater than critical velocity Vcr (supercritical flow) or less than critical velocity Vcr (subcritical flow).
Conveyance is a measure of the flow-carrying capacity of a cross section which is directly proportional to discharge. Conveyance, typically designated K, may be expressed from Manning’s equation (without the slope term) as:
where:
A = flow area (ft2)
R = hydraulic radius (ft)
Q = flow rate (ft3/s)
S = slope, dimensionless
In backwater calculations, change in conveyance from cross section to cross section is a useful way to determine the adequacy of section spacing in a stream reach. Within a cross section, conveyance may be used to compare channel and overbank flow carrying capacity.