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

Purpose: A single cross-section function table is computed in the MULCON command to represent the hydraulic characteristics of one or more conduits. The conduits may be circular, rectangular, true elliptical, nominal elliptical, reinforced-concrete arch pipe, or corrugated-metal arch. For two or more conduits, the hydraulic characteristics at a given water-surface elevation are aggregated in MULCON. Only a cross-section table for the barrels of a culvert or for a storm sewer are computed. No culvert losses are computed. Computation of culvert losses is done in the CULVERT command with the cross-section function table developed in MULCON 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 the table number as positive, 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 now 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 1Variable: TAB, CIN

Format: 7X, I5, A50

Example: TABLE

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. |

Variable: WSLOT

Format: 6X, F10.0

Example: WSLOT

Explanation:

WSLOT is the width of the hypothetical slot used to maintain a free surface in the conduit. This width is used for each conduit and the final slot for the table is the sum of the slot widths. The final width should be made 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 conduits involved. |

Variable: HSLOT

Format: 6X, F10.0

Example: HSLOT

Explanation:

HSLOT is the height of the hypothetical slot above the invert of the conduit, which has the minimum elevation. HSLOT is overridden on output so that any value greater than the vertical distance from invert to top of the conduit is acceptable. |

Variable: NPIPES, ZEPS

Format: 7X, I5, F10.0

Example: NPIPES

Explanation:

NPIPES is the number of conduits present. Valid range is 1 NPIPES 96. ZEPS is the difference in elevation across a mud line, if one is present, in the conduit. The default value of ZEPS is 0.02 ft. |

Variables: TYPE(i)

Format: 5X, 6A10,/,(5X, 6A10)

Example: TYPE

Explanation:

TYPE specifies the type of conduit. Valid types are given in table 6. The nominal-elliptical conduit is called nominal because it is elliptical in name only as it is composed of four circular arcs that approximate an elliptical shape. The difference between a nominal-elliptical conduit and a true-elliptical conduit is only at most a few percent. |

Variables: SPAN(

Format: 5X, 6F10.0,/,(5X, 6F10.0)

Example: SPAN

Explanation:

SPAN is the maximum horizontal dimension of the opening for each of the conduits. |

Variables: RISE(

Format: 5X, 6F10.0,/,(5X, 6F10.0)

Example: RISE

Explanation:

RISE is the maximum vertical dimension of the opening for each conduit. The combination of SPAN and RISE defines the size of the conduit. The required information depends on the TYPE of the conduit. If TYPE is CIRC, then SPAN defines the diameter and RISE is ignored. If TYPE is NHE, either RISE or SPAN, or both, may be given. The equivalent-diameter circular pipe from the RISE or SPAN, or from both if both are given, is computed in FEQUTL. If only one of the two values is given, then that value defines the equivalent diameter. If both values are given, then the RISE is taken as the defining value, and a warning message is issued if the equivalent diameter computed from the SPAN differs from the equivalent diameter computed from the RISE by more than 3 percent. If TYPE is NVE, the same rules as for NHE apply. If TYPE is TE, then both the SPAN and the RISE must be given because there is no standard shape for a true elliptical pipe. Finally, if TYPE is any of the arch shapes, then either RISE or SPAN, or both, may be given. If RISE or both are given, the SPAN is computed from the RISE and, if the SPAN is given, a warning message is issued if the SPAN computed from the RISE differs by more than 2 percent from the SPAN as given. If only the SPAN is given, then the RISE is computed from the SPAN. The priority given to the value of RISE is based on the belief that this dimension usually is easier to measure in the field than is the SPAN. For arch shapes, only certain standard sizes are available, and these sizes do not have a constant-scale relation. Thus, any given size cannot be scaled to represent a larger or smaller size. However, linear interpolation between the standard sizes is applied for the dimensions so that nonstandard sizes can be approximated. The true-elliptical shape is provided so that nonstandard elliptical pipe can be represented in a cross-section table.
In MULCON as in MULPIPES, each pipe is considered a different
subsection of a cross section. Thus, the values of ALPHA and
BETA computed in FEQUTL may differ from 1.0 even if USGSBETA
The number of sides of the polygon used to approximate the multiple conduits is fixed at 40 by MULCON. Furthermore, the datum point for the cross-section description is the invert of the conduit with the minimum invert elevation. The polygon is adjusted so that the full-flow area is matched. As a result, the invert of the polygon will be slightly below the invert of the conduit and, thus, the elevation reported for the cross-section table may be a small negative value and the maximum water-surface height before entering the slot will be slightly larger than the RISE of the conduit. These differences are always much smaller than the manufacturing tolerances allowed for the conduit. |

Variables: BOTTOM(

Example: BOTT

Explanation:

BOTTOM is the height of the invert of each conduit above the invert of the conduit with the smallest invert elevation. In the example, the invert of two conduits is 0.5 ft above the invert of the remaining conduit. |

Variables: ROUGH(

Format: 5X, 6F10.0,/,(5X, 6F10.0)

Example: ROUG

Explanation:

ROUGH is the Manning's |

The following two lines are optional. They are used 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 by ZEPS in Line 4. 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 will be issued and one end of the mud line will be incremented by 0.053 ft to force the relation between top width and depth to be one to one.

LINE 10

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 zero. |

Variables: ROUGH(

Format: 5X, 6F10.0,/,(5X, 6F10.0)

Example: ROUG= 0.035 0.055 0.02

Explanation:

ROUGH is the Manning's |

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