Full Equations Utilities (FEQUTL) Model for the Approximation
of Hydraulic Characteristics of Open Channels and Control
Structures During Unsteady Flow
A free surface is maintained at all times in this hypothetical slot. Consequently, the governing equations for unsteady flow can remain the same as for flow in a branch. Furthermore, the small width of the slot causes the wave celerity to increase to a large value. For rigorous analysis the slot could be sized to approximate the speed of an abrupt pressure wave in the conduit. However, this is rarely needed; in any case, the estimation of the speed of a water-hammer wave in a storm sewer is difficult. The width should be made small so that the area of flow is not greatly increased for the expected surcharge levels. High levels of surcharge in small conduits should be avoided. The approximations inherent in this approach to flow in closed conduits are not meant for the pressures encountered in a typical water-distribution network. However, substantial levels of surcharge can probably be represented for large storm sewers.
Details of the hydraulic characteristics of a closed conduit are not directly utilized in FEQ simulation because only cross-section function tables are required in FEQ simulation. Therefore, three commands for computing cross-section function tables representing closed conduits are provided in FEQUTL. In the simplest command, SEWER (section 5.19), a cross-section function table is computed for a single circular pipe. In the next most simple command, MULPIPES (section 5.17), a cross-section function table is computed for one or more circular conduits. Finally, in the most general command, MULCON (section 5.16), a cross-section function table is computed for one or more circular, elliptical, pipe-arch, or box-shaped conduits. For two or more conduits, the hydraulic characteristics at a given water-surface elevation are aggregated in MULPIPES and MULCON.
In the commands for computing cross-section function tables for closed conduits, the basic definition of the shape is utilized to compute a polygonal approximation to that shape. In the SEWER and MULPIPES commands, the user specifies the number of sides utilized in the polygon. The number of sides in the polygonal approximations in MULCON is fixed in FEQUTL. The polygon is computed such that the full flow area of the shape is matched. The polygonal description then becomes the same in form as that used in the commands FEQX or FEQXEXT described in section 3. The internally generated description is then processed in the same way as a polygonal description given by the user. A polygon of 20 or more sides approximates the shape of the conduit more precisely than the manufacturing tolerances allowed for the shape. Therefore, the use of a polygonal approximation introduces no additional errors.
The combination of conduits or culvert barrels of different shapes and sizes into a single cross-section function table should be done with care. If the sizes differ too much or if the invert elevations are significantly different, then the conduits should not be combined into one function table. Two or more flow paths should be utilized to represent the flow in such a conduit system. Each flow path would then consist of a set of conduits comparable in size and invert elevation. If this is not done, a major distortion of the flow in the conduit system may result.
The commands for computing cross-section function tables for closed conduits are applied to compute the descriptions of culvert barrels as well as for storm sewers. Relatively large amounts of sediment may accumulate in the bottom of a culvert barrel. In some cases, this sediment remains even during floodflows. Therefore, an optional specification of a mud line in a conduit is provided in FEQUTL. This mud line can have a roughness value that differs from the wall of the conduit. A wetted-perimeter averaged roughness is computed for each conduit. For multiple conduits, the conveyance for each conduit is computed separately and then the total conveyance corresponding to a given water-surface elevation is summed for all conduits.