Full Equations Utilities (FEQUTL) Model for the Approximation
of Hydraulic Characteristics of Open Channels and Control
Structures During Unsteady Flow
Flow at a bridge or a culvert often involves multiple flow paths when the water levels are high enough to overflow the bridge. Water may flow through the structure, over the structure, and (or) around the structure in the flood plain of the stream. If the flood plain is crossed by an embankment leading to a road crossing of the stream (culvert of bridge), then this embankment serves as a broad-crested weir. The flow over the road can be included in the flow table, but if the flow in the flood plain is large, multiple flow paths should be simulated. Studies of friction losses for flow through bridges and culverts have shown that an important factor is the degree of contraction that results for the water flowing through the structure opening. This may be only a small part of the water in the stream at flood stage. Therefore, careful division of the flow into (1) the flow through and directly over the structure and (2) the flow around the structure through the flood plain increases the reliability of the estimates of friction losses resulting at the structure.
The FEQUTL command, EMBANKQ (section 5.6), may be applied to compute the flow over a roadway or an embankment. This is discussed in section 4.3. In some cases, however, the approaches to the road crossing are essentially at the same level as the surrounding terrain. This often is true in parks and golf courses. The roadway then does not form a meaningful weir. In this case, the flow in the flood plain is flow in a wide open channel with the roadway constituting part of the boundary roughness, and the slope of this channel is typically mild, zero, or adverse. If the slope of the short bypass channel was steep, then the roadway could be simulated as an embankment weir. The CHANRAT command (section 5.3) in FEQUTL is designed to compute a flow relation for application in FEQ in this case. A 2-D table of type 13 is computed in CHANRAT for the flow in a short, prismatic channel with a mild, zero, or adverse slope. The rating for the flow through the channel, as a function of the upstream water-surface elevation and the difference in water-surface elevation, is given in this type 13 table. The flow is assumed to be subcritical at all levels. Furthermore, the table is only computed for one flow direction. If bidirectional flow might result, then two separate CHANRAT commands are needed to compute the two tables required to represent the bidirectional flows.
(81)
where F is the Froude number and S 0 is the slope of the bottom with a drop in the x -direction taken as positive.
where y n is the normal depth (water-surface height) for the given flow, and the plus sign is applied if the current profile is above normal depth, and the minus sign is applied if the current profile is below normal depth.
The flow will be computed as normal flow if the computed profile length between the water-surface height at the downstream end and the stopping water-surface height when the flow is normal is less than the length of the channel. This can result for small upstream heads. These complications are not considered if normal depth cannot result. Thus, the computations proceed more rapidly if the bottom slope is zero or adverse and normal depth cannot result.