Full Equations Utilities (FEQUTL) Model for the Approximation of Hydraulic Characteristics of Open Channels and Control Structures During Unsteady Flow

# 5.17 MULPIPES Command

Purpose: A single cross-section function table is computed in the MULPIPES command to represent the hydraulic characteristics of one or more circular conduits. For two or more conduits, the hydraulic characteristics at a given water-surface elevation are aggregated. The same values are computed in the MULCON and MULPIPES commands. However, the MULCON command was added at a later time so that MULPIPES is retained for support of older FEQUTL input files. A cross-section table is computed in MULPIPES only for the barrels of a culvert or for a storm sewer. No culvert losses are computed. Computation of culvert losses is done in the CULVERT command (section 5.5) using the cross-section function table developed in MULPIPES and entered on Line 14 of the input to the CULVERT command as part of the description of the culvert.

Notes: In closed conduits, the conveyance will decrease with depth as the conduit approaches the full-flow condition. Two options are allowed in FEQUTL. The first option, selected by giving a positive table number, is to propagate the conveyance of the full conduit to smaller depths where the conveyance may actually be higher than the full-flow conveyance, so that the maximum conveyance in the conduit is the full-flow conveyance. This means that the maximum conveyance in the conduit that usually results at depths close to the crown of the pipe is overridden. This is done because the point of maximum conveyance is often close enough to the crown of the conduit such that attainment of the maximum conveyance is unlikely. As the water surface approaches the crown of the conduit, the flow can easily oscillate between full flow and part-full flow as the air cavity is removed. This results because the normal undulations in the water surface have great effects in that the pipe is filled momentarily. Also, the normal variation in water-surface height in the pipe will often contribute to the instability close to the crown. In the second option, selected by giving a negative table number, warning messages for decreasing conveyance are issued, but the decreasing conveyance is retained for further computations. The conveyance in the hypothetical slot is forced to be a constant with the value given by the full-flow conveyance in both options.
LINE 1
Variable: TAB, CIN
Format: 7X, I5, A50
Example: TABLE #= 9 OUT
Explanation:
 TAB is the table number of the cross-section table computed in FEQUTL. CIN are user-specified options for cross-section table computations. The user may specify the same options after the table number as in FEQX (section 5.8). If the table number is positive, the conveyance is not permitted to be larger than the full-flow conveyance at any water level. If the table number is negative, the conveyance is computed with no modifications.
LINE 2
Variable: NSIDES
Format: 7X, I5
Example: NSIDES = 30
Explanation:
 NSIDES is the number of sides in the polygon used to approximate the multiple pipes. The polygon is sized so that the area of the polygon and the pipes are the same when the pipes are flowing full. A hypothetical slot is added to the top of each pipe and the aggregated slot is included in the cross-section table to maintain a free surface at all stage levels. The minimum permitted value for NSIDES is 10. Values of 20 to 30 represent the pipes to a precision higher than applied in the manufacturing processes used to make the pipes.
LINE 3
Variable: WSLOT
Format: 6X, F10.0
Example: WSLOT = 0.01
Explanation:
 WSLOT is the width of the hypothetical slot used to maintain a free surface in the pipe. This width is used for each pipe, and the final slot for the table is the sum of the slot widths. The width should be small so that the area of flow is not greatly increased for the expected surcharge levels. The final slot width is NPIPESxWSLOT where NPIPES is the number of pipes.
LINE 4
Variable: HSLOT
Format: 6X, F10.0
Example: HSLOT = 50.0
Explanation:
 HSLOT is the height of the slot above the invert of the conduit with the lowest invert elevation. HSLOT is overridden on output so that any value greater than the top of the largest conduit is acceptable.
LINE 5
Variable: NPIPES, ZEPS
Format: 7X, I5, F10.0
Example: NPIPES = 3 0.05
Explanation:
 NPIPES is the number of conduits. The valid range is 1 NPIPES 96. ZEPS is the difference in elevation across a mud line, if one is present, in the pipe. The default value of ZEPS is 0.02 ft.
LINE 6
Variables: DIAM( i )
Format: 5X, 6F10.0,/,(5X, 6F10.0)
Example: DIAM = 4.0 4.5 4.0
Explanation:
 DIAM is the diameter of each of the pipes in feet or meters.

LINE 7
Variables: BOTTOM( i )
Format: 5X, 6F10.0,/,(5X, 6F10.0)
Example: BOTT = 0.5 0.0 0.5
Explanation:
 BOTTOM is the height of the invert of each pipe above the invert of the pipe with the smallest invert elevation. In the example, the invert of two pipes is 0.5 ft above the invert of the remaining pipe.
LINE 8
Variables: ROUGH( i )
Format: 5X, 6F10.0,/,(5X, 6F10.0)
Example: ROUG = 0.02 0.03 0.02
Explanation:
 ROUGH is the Manning's n for each of the pipes.

The following two lines are optional. The lines are utilized to specify a mud line in the conduit to represent the accumulation of sediment in the conduit. The mud line is assumed to be essentially horizontal with the difference in elevation across it given in ZEPS in Line 5. If all the mud lines are at the minimum elevation in the cross section, then ZEPS may be 0. If ZEPS is 0 and a mud line is not at the minimum elevation in the cross section, a warning message is issued in FEQUTL computations, and one end of the mud line is incremented by 0.053 ft to force the relation between top width and depth to be one to one.

LINE 9
Variables: ZMUD( i )
Format: 5X, 6F10.0,/,(5X, 6F10.0)
Example: MUDL= 0.55 0.6 1.0
Explanation:
 ZMUD is the thickness of the sediment measured from the invert of each conduit. The part of the conduit boundary that is below the sediment line is truncated in FEQUTL computations. If a conduit has no sediment, the thickness value is 0.
LINE 10
Variables: ROUGH( i )
Format: 5X, 6F10.0,/,(5X, 6F10.0)
Example: ROUG= 0.035 0.055 0.02
Explanation:
 ROUGH is the Manning's n for the sediment in the conduit. A perimeter-weighted composite Manning's n for the conduit is computed in MULPIPES if a mud line is present.