Full Equations Utilities (FEQUTL) Model for the Approximation of Hydraulic Characteristics of Open Channels and Control Structures During Unsteady Flow
LINE 1
Variable: TABLE
Format: 7X, I5
Example: TABLE #= 9900
Explanation:
TABLE gives table number of the 2D function table computed for the flows through the culvert. 
CHAR4 must be TYPE.
TABTYP specifies the table type. Types 6 and 13 are currently supported in the FEQ model. Both table types contain the same information, but type 13 is more compact, takes less tablestorage space, and is easier to read. Type 13 should be used unless type 6 is more appropriate for a specific application. 
CHAR6 must be LABEL.
LABEL gives a userdefined label that will appear in the table for identification purposes. 
HEAD gives a subheading to break the input into logical components. The subheading may be any text, but should describe the data that follow. 
CHAR6 must be APPTAB.
APPTAB gives the table number for the crosssection table of the approach section for the culvert. This table must have been input with the FTABIN command (section 5.13) or have been computed with the SAVE option in the FEQX, FEQXEXT, or FEQXLST commands (sections 5.85.10). Furthermore, the approach crosssection table must be of type 22 or 25 because values of critical flow are required in the CULVERT command. 
CHAR6 must be APPELV.
APPELV supplies the elevation of the minimum point of the cross section specified in APPTAB. This elevation should match the bottomprofile elevation at the downstream end of the branch upstream from the culvert in the FEQ input. 
CHAR6 must be APPLEN.
APPLEN gives the distance between the approach cross section and the entrance to the culvert. This distance should be about the same as the opening width of the culvert or the sum of the opening widths of multiple culverts. This value must be > 0. 
CHAR6 must be APPLOS.
APPLOS gives the hydraulicenergy loss resulting from special approach conditions in terms of the fraction of the velocity head in the approach cross section. Normally this loss is 0, but it can be used to approximate the losses resulting from trash racks, rightangle bends upstream from the culvert entrance, and other entrance conditions. This value should be between 0 and 1. 
CHAR 6 must be APPEXP.
APPEXP gives a coefficient to be applied to the difference between the approachvelocity head and the velocity head in the culvert entrance if the culvert is an expansion in flow area instead of a contraction in flow area. The discharge coefficient for the entrance loss for the culvert is set to the maximum value for no contraction of 0.98 (Bodhaine, 1968) if the flow is expanding instead of contracting. This value should be between 0 and 1. 
HEAD provides a subheading for the culvert cross section, elevation, and length description. 
CHAR 6 must be NODEID.
NODEID indicates whether an identifying string for each node along the culvert is included in the input. If NODEID is YES, then identifying strings are present; otherwise, they are omitted. At a minimum, each culvert will have two nodes: the entrance and the exit of the culvert. More nodes may be needed, however, if the shape or slope of the culvert is changed. Also, additional nodes may be needed to compute the flow through the culvert. 
CHAR4 must be SFAC.
SFAC gives the multiplying factor that converts the stations in the input to distances required in FEQUTL. The required distances are in feet for the ENGLISH unit option and in meters for the METRIC units option. 
HEAD gives userdefined heading that describes the information on subsequent lines. 
Variables: NODE, XTAB, X, Z, KA, KD
Format: 2I5, 2F10.0, 2F5.0 
Variables: NODE, NAME, XTAB, X, Z, KA, KD
Format: I5, 1X, A8, 1X, I5, 2F10.0, 2F5.0 
NODE is the node number on the current culvert. The end of a culvertbarrel
description is indicated by a negative value of the NODE entry. The remainder
of the line containing the terminating node number may be blank. The number
for the first node on each branch must be given. The NODE
column may be left blank for the other nodes and the node number will be computed in FEQUTL. If node numbers are given, they must be consecutive and increasing. The entrance to the culvert is the first node in the table. NAME is the identification string for the node. XTAB is the number of the crosssection table computed with the SEWER
(section 5.19), MULPIPES (section
5.17), or MULCON (section 5.16)
command.
Z is the elevation of the minimum point in the stream at the node. KA is the loss coefficient to apply to the difference in velocity head when the velocity is increasing in the direction of flowthat is, when the flow is accelerating. KD is the loss coefficient to apply to the difference in velocity head when the velocity is decreasing in the direction of flowthat is, when the flow is decelerating. 
A culvert may be too long to compute a steadyflow profile by use of cross sections at its entrance and exit only. Thus, additional nodes and cross sections must be added. This will be done in FEQUTL computations, overriding user data if there are at most two crosssection tables specified to describe the culvert barrel and if only two elevations are specified to define the slope of the invert. This means that only two nodes are needed for culvert computations. Only the initial node and the final node on the culvert barrel are needed in FEQUTL computations. Values of KA and KD specified on the line for the final node are used for all other nodes added to the barrel. Internal criteria are used in FEQUTL to define the node spacing so that the steadyflow profile computations will not result in convergence problems.
If the culvertbarrel size and shape change in a manner that cannot be described with just two cross sections, then the user must assign the intermediate nodes. Two methods are available for adding intermediate cross sections. The first method is simple propagation of the last known cross section at equal station intervals and with linear interpolation for the profile elevation. This method is selected by one or more blank lines in the input. A line of complete crosssectional information above the blank lines and a line of complete crosssectional information below the blank lines must be specified. The upstream table number is assigned to each blank line, and the stations and elevations are distributed uniformly between the two lines of known values. Linear interpolation of crosssection characteristics between two known cross sections is utilized in the second method. This method is selected by assigning a negative table number for the crosssection table or, more conveniently, by merely assigning a minus sign in the rightmost column of the field for the table number. An available table number is then supplied at the proper time in the FEQUTL computations. This prevents the problem of the user having to remember which table numbers are available for interpolated cross sections. If the station and elevation values are given, they will be utilized in the interpolation. If they are omitted, the station values will be distributed uniformly and the elevation will be linearly interpolated. The first method should only be applied if the conduit is prismatic over the interval of additional cross sections. The second method should be applied when the conduit characteristics vary over the interval between the known cross sections.
All cross sections given in the culvertbarrel description must be of table type 22 or 25 and must have a vertical slot so that a hypothetical free surface can be computed. The intermediate nodes close to the entrance and the exit should have small spacing less than one inlet maximum vertical dimension between them. Conditions change rapidly near these points, and the distance increment for profile computation should be relatively small.
To compute type 5 flow, there must be one node that is three times the
inlet maximum vertical dimension from the inlet and one node that is six
times the inlet maximum vertical dimension from the inlet. These locations
are needed because the flow contracts to a minimum area (vena contracta)
at a length of about three times the maximum vertical culvert dimension
from the entrance, and in FEQUTL it is assumed that most of the expansion
losses result within a distance of three times the maximum vertical culvert
dimension downstream from the vena contracta (section
4.2.3).
LINE 15
Variable: CHAR6, CULCLS
Format: A6, 1X, A8
Example: CULCLS = BOX
Explanation:
CHAR6 must be CULCLS.
CULCLS gives the general class of the culvert for selection of the discharge coefficient. The culvert class does not determine the shape of the culvert. Thus, if an irregularshaped culvert is judged to be best described as a box culvert for determination of the hydraulic characteristics, then the culvert class should be specified as BOX even though the culvert is not strictly a box culvert. The available options are: BOXbox culverts, PIPEcircular, elliptical, and arch pipes; MITERmitered entrance for pipe culverts, RCPTGreinforcedconcrete pipe with machine tongueandgroove construction and also pipes with commercially flared entrances. 
HEAD gives a subheading for the departure section data that follow. 
CHAR6 must be DEPTAB.
DEPTAB gives the table number of the crosssection table of the departure section for the culvert. This section represents the stream cross section where the flow concentration caused by the culvert in the downstream flow has essentially dissipated. BEGTAB specifies an optional table number for the crosssection table describing the departure reach at the exit from the culvert. RMFFAC is an optional entry that specifies a multiplying factor on the estimated momentum flux over the roadway. If RMFFAC is omitted, the default value is 1. This value must be > 0 and 1. 
CHAR6 must be DEPELV.
DEPELV gives the elevation of the bottom of the departure section. This elevation should match the elevation of the bottom profile of the upstream end of the branch downstream from the culvert in the FEQ input. BEGELV is the elevation of the bottom of the beginning cross section for the departure reach. The beginning elevation, if omitted, is set as follows. If DEPELV is greater than the culvertexit invert elevation, then BEGELV is set to the culvertexit invert elevation; otherwise, BEGELV is set to the same elevation as DEPELV. DSFFAC is reserved for potential future expansion of FEQUTL and is not used. The default value for DSFFAC is 0. WIDFAC is a width factor for checking the beginning cross section of the departure reach. The default value for WIDFAC is 1.02. 
The validity of BEGTAB may be checked with WIDFAC. BEGTAB represents the cross section of the departure reach at the culvert exit and must always be at least WIDFAC wider than the culvert exit. This width increase is checked at each tabulated watersurface height in the crosssection table for the culvert barrel, and if the test fails at any tabulated watersurface height, the cross section in BEGTAB is rejected. A heightbyheight report on the widths of the two cross sections is output in FEQUTL computations. A cross section for BEGTAB must be input that will not obstruct any part of the exit cross section for the culvert barrel. If the obstruction is present and not just an artifact of the manner in which BEGTAB was defined, then the cross section of the culvert barrel at the exit should be modified to reflect the obstruction.
LINE 19
Variable: CHAR6, LOSOPT
Format: A6, 1X, A8, F10.0
Example: LOSOPT = MOMENTUM
Explanation:
CHAR6 must be LOSOPT.
LOSOPT gives the loss option for the expansion of the flow into the departure reach. The procedure for culvert flow in Bodhaine (1968)includes losses resulting from contraction at the culvert entrance and subsequent expansion in the culvert barrel. The loss caused by the expansion of the flow in the departure reach must be computed separately. One loss option, denoted by MOMENTUM, is available in the CULVERT command. A simple momentum balance in the departure reach is applied to estimate the losses in the expanding flow in this option. Complete details are given in section 4.2.5 
Line 20 is not currently used in FEQUTL, but it is reserved for future expansion of the loss options in the departure reach. This line is retained to maintain the line number sequence. 
HEAD gives the subheading for dischargecoefficient information. 
The selection of the discharge coefficient involves several factors. Some of these factors are purely geometric and are not changed by the depth or flow of water in the culvert. Some of the factors are hydraulic and depend on the depth or flow of water. Consequently, some discharge coefficients are determined by geometric factors alone, and some are determined by a combination of geometric and hydraulic factors. In order to allow for the greatest flexibility in model simulation and to simplify the input for the CULVERT command, the discharge coefficients dependent on hydraulic factors are determined internally in FEQUTL computations. Discharge factors and adjustment factors that depend on geometry only must be supplied in the input. However, the values defined by geometry only may be determined by table look up in FEQUTL computations if requested by the user. Determination of the values by table look up is the preferred method. However, the ability to provide explicit values is retained to maintain maximum flexibility. The values that may be determined by table look up are: the multiplying factor to adjust the basedischarge coefficient for flow types 1, 2, and 3 for the effect of rounding or beveling of the entrance to the culvert, KRB; the adjustment factor for the effect of wingwalls on the discharge coefficient for flow types 1, 2, and 3 when the wingwalls are present for box culverts, KWING; the adjustment factor for the effect for projecting entrances for flow types 1, 2, and 3, KPROJ; and the discharge coefficient for type 4 and 6 flow, C46. To request look up, these four variables are given the value of 0.0 (in Lines 2225, respectively). If a nonzero value for these variables is specified, that value will be applied, and no look up will be done. The special file TYPE5.TAB (which may be retrieved electronically as described in section 5.1) must be input using FTABIN (section 5.13) if look up is requested. This file contains both flowtype 5 related tables and tables defining KRB, KWING, KPROJ, and C46. If look up is requested for any one of these values, the optional input for the flowtype 5 parameters, Line 251, must be given. The input for flowtype 5 parameters has been expanded to include the geometric variables required to define KRB, KWING, KPROJ, and C46.
LINE 22
Variable: CHAR3, KRB
Format: A3, 1X, F10.0
Example: KRB = 1.05
Explanation:
CHAR3 must be KRB.
KRB gives the multiplying factor to adjust the base discharge coefficient for flow types 1, 2, and 3 for the effect of rounding or beveling of the entrance to the culvert. The value should be between 1 and 1.5. The base coefficient is selected on the basis of the culvert class. Bodhaine (1968) presented a series of figures that may be used to estimate the multiplying factor for culverts corresponding to the PIPE and BOX input descriptions. For sharpedged entrance conditions, figure 20 in Bodhaine should be used with the PIPE designation and figure 23 should be used with the BOX designation. For culverts with rounded entrances, the value determined from figure 20 or 23 should be multiplied by the value determined from figure 21. For culverts with beveled entrances, the value determined from figure 20 or 23 should be multiplied by the value determined from figure 22. 
CHAR5 must be KWING.
KWING gives the adjustment factor for the effect of wingwalls on the discharge coefficient for flow types 1, 2, and 3 when wingwalls are present for box culverts. Values are given in figure 24 of Bodhaine (1968). The value should be between 1 and 1.25. Wingwalls do not change the discharge coefficient for a pipe culvert set flush with a vertical headwall. 
CHAR5 must be KPROJ.
KPROJ is the adjustment factor for the effect for projecting entrances for flow types 1, 2, and 3 (Bodhaine, 1968, p. 4142). KPROJ is a function of the length of projection as detailed by Bodhaine (1968, p. 42). The value should be between 0.9 and 1. 
CHAR3 must be C46.
C46 is the discharge coefficient for culvertflow types 4 and 6. This coefficient is purely a function of geometry and must therefore contain all the adjustments for wingwalls, projecting entrance, rounding, beveling, and other conditions discussed in Bodhaine (1968, p. 4243). This value should be between 0.6 and 1. 
HEAD gives heading information for the input of optional type 5 flow parameters and parameters to define the look up of discharge coefficients for other flow types. The first six characters of the heading line must be TYPE 5 or Type 5. The remainder of the line can be any suitable title. Input of parameters for type 5 flow is optional. However, the file TYPE5.TAB (retrieved electronically as described in (section 5.1) must be included in an FTABIN (section 5.13) command to provide a variety of tables that define the boundary between type 5 and type 6 flow and the discharge coefficients for type 5 flow. If the type 5 parameters are omitted, the default values are: RBVALUE = 0.0, WWANGLE = 0.0, and TYPE5SBF = 0.75 (see Lines 252, 253, and 254). 
RBVALUE is the relative rounding/beveling for the culvert entrance. This value is used to define the discharge coefficient for type 5 flow. It also is used to define KRB if table look up is requested by the user. RBVALUE should be 0 and 0.14. The default value of RBVALUE is 0.0. 
BVANGLE is the angle in degrees of the bevel if the entrance to the culvert is beveled. If the entrance is rounded or sharpedged, this value is 0.0. A nonzero value for BVANGLE indicates that the RBVALUE is utilized for beveling and not rounding. BVANGLE must be 0 and 90 degrees. RBVALUE and BVANGLE are used to define KRB if table look up is requested by the user. 
WWANGLE is the wingwall angle in degrees. A value of 0 means that the plane of the wingwall is perpendicular to the culvert barrel. A value of 90 means that the plane of the wingwall is parallel with the barrel. The default value of WWANGLE is 0.0. 
LPOVERD is the average projection length of the culvert barrel relative to the culvert maximum inside vertical dimension. LPOVERD must be 0. This value defines KPROJ when table look up is requested by the user. 
TYPE5SBF is the value of relative watersurface height in the barrel or the barrel exit that will result in full flow in the culvert barrel. The relative watersurface height is expressed in relation to the maximum vertical dimension of the culvert barrel. Thus, a value of 0.75 specifies that water in the culvert barrel must be flowing at a watersurface height equal to or greater than 0.75 (the default value determined from engineering judgment) of the maximum vertical dimension at the exit before full flow in the culvert will result. TYPE5SBF must be 0 and1. For type 5 flow, submergence and full flow are considered to have identical flow and hydraulic characteristics. No effort is made to distinguish between full flow and submergence because no data on which to base such a distinction are available. 
HEAD gives a heading for optional input specifying the table numbers for type 5 flow. These tables provide information of the boundary between type 5 and type 6 flows, and discharge coefficients for type 5 flow. The first five characters of the heading must be TABLE or Table. The remainder of the line can be any suitable heading. The type 5 parameters and table numbers are specified, and then the type 5 parameter input must be specified before the table numbers. 
Table numbers for tables of information used in computing type 5 flows
are specified in this line. All the tables refer to Bodhaine
(1968). If this information is omitted, the default table numbers are
given in the current example. The default function tables are stored in
a file, TYPE5.TAB, which is available by electronic retrieval as described
in section 5.1. These numbers should
be supplied only if there is some conflict between the default table numbers
and a planned or previously used tablenumbering scheme.
TB6ADR is the 2D table of type 10 representing table 6 in Bodhaine (1968)"Discharge coefficients for box or pipe culverts set flush in a vertical headwall with variation of head and entrance rounding or beveling, type 5 flow." TB7ADR gives the 2D table of type 10 representing table 7 in Bodhaine (1968)"Discharge coefficients for box culverts with wingwalls with variation of head and wingwall angle,, type 5 flow." TB8ADR gives a 1D table of type 2 representing the discharge coefficients
for flared pipeend
TB15ADR gives a 2D table of type 10 representing the data presented in figure 13. TB16ADR(1) through TB16ADR(4) give the table numbers for 2D tables of type 10 for the four parts of figure 14. 
HEAD gives a heading for the optional parameters for type 1 flow. These optional parameters relate to the limits for type 1 flow. The first six characters of the line must be either TYPE 1 or Type 1. Type 1 parameters must be specified after the Type 5 parameters if both are specified. The following defaults are used if this input is omitted: TY1YTD = 0.95 and TY1HTD = 1.4. 
TY1YTD is the relative watersurface height in the culvertbarrel entrance for the upper limit of type 1 flow. TY1YTD specifies the upper limit for the type 1 flow rate because the flow rate is determined from critical depth at the entrance of the culvert barrel. The relative watersurface height is relative to the maximum vertical dimension of the culvert barrel. For example, a value of 0.95 indicates the watersurface height in the barrel entrance will be at 0.95 of the maximum vertical dimension at the maximum type 1 flow. This limit is needed because critical flow increases without bound as the watersurface height of the flow approaches the soffit of a closed conduit with converging walls. TY1YTD must be 0.5 and < 1. 
TY1HTD is the maximum relative head permitted for type 1 or type 2 flow at their upper limits. Experiments and field observations indicate that full flow in culverts will result if the approach head measured relative to the invert of the culvert inlet is 1.5 or greater. Full flow may result at a lower approach head, and for type 2 flow, full flow may begin for a relative head as small as 1.2. The specification of the relative watersurface height using TY1YTD may, for culverts other than box culverts, result in a relativehead ratio that is greater than 1.5. If the ratio is greater than 1.5, this result is ignored and the relativehead ratio is set to the value given by TY1HTD in CULVERT command computations. The type 1 flow conditions at that limit are then computed for the maximum type 1 flow. The limit is not set at 1.5 to permit computation of a transition zone between the lowhead free flows, types 1 and 2, and the highhead free flows, types 5 and 6. TY1HTD must be 1. 
HEAD gives a subheading for the roadway description. A format similar to that used in the EMBANKQ command is applied here. 
TAB(1) is the table number for the function table listing the lowhead
weir coefficient for a paved surface. The table number in this example
is the default value, and this table may be retrieved
electronically as described in section 5.1. 
TAB(2) is the table number for the function table listing the lowhead weir coefficient for a graveled surface. The table number listed in this example is the default value, and this table may be retrieved electronically as described in section 5.1. 
TAB(3) is the table number for the function table listing the highhead weir coefficient for a paved surface. The table number listed in this example is the default value, and this table may be retrieved electronically as described in section 5.1. 
TAB(4) is the table number for the function table listing the highhead weir coefficient for a graveled surface. The table number listed in this example is the default value, and this table may be retrieved electronically as described in section 5.1. 
TAB(5) is the table number for the function table listing the submergence correction factor for a paved surface. The table number listed in this example is the default value, and this table may be retrieved electronically as described in section 5.1. 
TAB(6) is the table number for the function table listing the submergence correction factor for a graveled surface. The table number listed in this example is the default value, and this table may be retrieved electronically as described in section 5.1. 
HEAD gives a heading for subsequent columns of input. 
LINE 34 (Repeated as necessary to include all offsets describing the
roadway embankment.)
Variables: OFF(I), CREST(I), WIDTH(I), APPROC(I), SURF(I)
Format: 4F10.0, 1X, A8
Explanation: The values given on this line define, subsectionbysubsection,
the geometry of the crest of the roadway applied in computation of flow
over the roadway.
OFF is the horizontal offset for which geometric characteristics are
entered on this line.
CREST is the crest elevation.
WIDTH is the width of the crest in the direction of flow. APPROC is the elevation of the approach channel. If the approach velocity should be ignored, then an approach elevation that is much lower than the crest elevation should be specified so that the computed velocity head will be small. SURF is the the type of surface, and the designation applies to the line segment beginning at the offset for which the surface type is given. For example, if the first line of the roadwaycrest specification gives the type of surface as GRAVEL and the second line of the roadwaycrest specification gives the type of surface as PAVED, then the roadway crest between the first and second offset is taken to be of a roughness similar to a graveled roadway. Two closely spaced points should be placed on the crest at the change in roughness to represent the transition between the two surface conditions. The end of the weir specification is indicated by entering END for the type of surface. Thus, if the third line of the input in this example contained END for the type of surface, then the weir crest between the second and third offset would have a roughness similar to a paved roadway. 
These geometric characteristics are input for the boundaries of the subsections. The crest elevation, crest width, and approachchannel elevation are assumed to change linearly between the given points on the crest as illustrated in figure 18 (in section 5.6). To make input easier, the values for width, approachchannel elevation, and surface type propagate downward into fields left blank. Thus, if the elevation of the approach channel is constant and the width is constant, only the first line of the specification must contain the elevation of the approach channel and the width of the weir crest.
LINE 35
Variable: HEAD
Format: A80
Example: Head sequence definition
Explanation:
HEAD gives the heading for the parameters listing the sequence of upstream heads and the distribution of the partial free drops used to define the downstream heads for the 2D table. 
CHAR5 must be NFRAC.
NFRAC is the number of partial free drops used in computing the table. Complete details on partial free drops are given in the discussion of 2D function tables in section 11.2 of the documentation report for FEQ (Franz and Melching, 1997). 
CHAR6 must be POWER =.
POWER is the power applied to distribute the proportion of free drop from a value of 0 to 1. The proportion of free drop is given by

HUVEC is the upstream head to use in computing the 2D table. The sequence of heads should be positive and strictly increasing. The end of head input is signaled by a negative value for head. The heads specified here will be the values of head that appear in the table. It is the user's responsibility to choose a spacing that is appropriate for head distribution for the culvert and roadway embankment simulated. Generally, the spacing should be small for the low heads and larger for the high heads. The head interval should become small when flow over the roadway, if any, begins. A spacing of 0.1 ft or even 0.01 ft may be needed to define the lowhead range of the table if the range of heads is small. Generally, no more than about 20 subdivisions should be used to represent the range of heads expected. More subdivisions can be used, but this results in larger tables. 