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


5.9 FEQXEXT Command

Purpose: Hydraulic characteristics of a cross section are computed and a cross-section function table is output with the FEQXEXT command. Frictionless line segments and roughness values that vary with water level are included in FEQXEXT, and these features represent an extension of the FEQX command.

Notes: A more flexible input for the cross-section boundary points is available in FEQXEXT than in FEQX. In the FEQX command, it is required that the line of information for each boundary point (that is the line giving the offset, the elevation, and the subsection number) be in a fixed order (offset first, elevation second, and subsection number last) and in fixed columns (1-10 for offset, 11-20 for the elevation, and 21-25 for the subsection number).

A free format of boundary-point input is allowed in FEQXEXT, but the fixed order is retained. A more complex description of the variation of roughness on the channel boundary also is permitted in FEQXEXT. Application of this more complex description will add one or more values to each line of information for a point on the cross-section boundary. To distinguish the end of one value and the beginning of another value, a delimiter is required in FEQXEXT. The delimiters permitted are one or more spaces or a comma. All of the values for a point must appear on a single line of the input.

Default values are available for much of the information in FEQXEXT. For example, the default value for the subsection number for all but the first point on the boundary is the number for the preceding point on the boundary. The subsection number needs to be given only for the first point in each subsection.

The roughness for each line segment on the boundary may be specified in FEQXEXT, not just each subsection as in FEQX. This value appears after the subsection number in the input. If the default value for the subsection number is to be used by omitting the number for a boundary point, then an asterisk must be used to request the default value, or two consecutive commas must be used to indicate the place that the subsection number would have occupied had it been given. If this is not done, the line-segment roughness value will be taken as being a subsection number because it is the third value seen on the line of input. The third value is always the subsection number. The asterisk or the dual commas indicate that the third value and the line-segment roughness value are given the proper input order.

In general, any value that has a default that is skipped over in a line must have its place shown by either an asterisk or by a pair of commas. If this is not done, the results of the command will be in error and an error message may be issued.

Variable: TAB, CIN
Format: 7X, I5, A50
Example: TABLE #= 00025 MONOTONE SAVE22

TAB is the table number that identifies the cross-section function table computed from the cross-section boundary description specified in the subsequent lines.

CIN is an alphanumeric field in which the user may specify several options after the table number. The options are as follows.

EXTEND: A vertical, frictionless extension is added to the first or last point of the cross section, as needed, to match the point of maximum elevation in the cross section.

MONOTONE: The offsets for the cross section are examined to ensure that they are increasing. This is useful in preliminary checking of cross sections for natural streams.

NEWBETA: The momentum-flux correction coefficient, This is the Greek letter Beta, and the kinetic-energy-flux correction coefficient, This is the Greek letter Alpha, are computed by application of a method suggested by Schönfeld (1951) and discussed in section 3.1.2. The geometric mean of the critical flows estimated with the momentum and energy principles are tabulated in this option.

NEWBETAE: Same as NEWBETA except that the critical flow tabulated is based on the energy principle.

NEWBETAM: Same as NEWBETA except that the critical flow tabulated is based on the momentum principle.

NEWBETA, NEWBETAM, and NEWBETAE can only be used for cross sections that do not have converging boundaries. Thus, these options imply checking for monotonicity.

OLDBETA: The coefficients This is the Greek letter Alpha and This is the Greek letter Beta for the cross section are computed from equations 7 and 8 in section 3.1.1. The velocity-distribution coefficients, This is the Greek letter Alpha i and This is the Greek letter Beta i in each subsection of the cross section in these equations are taken to be 1.0 if USGSBETA = NO in the Standard Header Block (section 5.1). If USGSBETA=YES, then these coefficients are estimated as described following equation 8 in section 3.1.1. In either case, the critical flow in the cross section is estimated as if the velocity distribution coefficients are both 1. Thus, critical flow is computed ignoring the effect of velocity distribution.

SAVEnn: A copy of the resulting table is saved internally in the FEQUTL computations in type nn format, where nn gives the two-digit table type with the valid range from 20 through 25.

SAVE: Same as SAVE21.

NOSAVE: A copy of the table is not saved internally in the FEQUTL computations. This is the default action if none of the save options are given.

OUTnn: A copy of the table is output to the standard function-table file in the Type nn format. If no output option is given, a cross-section function table of type 21 is output to the standard-function table file.

NOOUT: Output of the table to the standard function-table file is suppressed.

Variables: STAT, LEFT, RIGHT
Format: 8X, F10.0, 6X, F10.0, 7X, F10.0
Example: STATION = 8.256 LEFT = 100.0 RIGHT = 967.

STAT is the station of the cross section.

LEFT is the offset on the left side of the cross section where a vertical frictionless wall is added in computation of the cross section.

RIGHT is the offset on the right side of the cross section where a vertical frictionless wall is added in computation of the cross section.

Thus, encroachments on the cross section can be indicated without changing the cross section. If LEFT RIGHT, then the encroachments are not calculated. LEFT is set equal to RIGHT by default if the input is omitted.

Format: 5X, A4, 7X, F10.0, 7X, F10.0
Example: VARN = NCON SCALE = 1.0 SHIFT = 0.2

VARN specifies the variation of Manning's n . Three options are available for VARN:

NCON-constant n; HYDY- n varies with hydraulic depth in each subsection; MAXY- n varies with maximum water-surface height in each subsection. HYDY is the default option for VARN.

SCALE is multiplied with the offsets and can be used to adjust for scaled measurements from a map. The default value is 1.

SHIFT is added to elevation of each point on the boundary of the cross section. The default value is 0.

Variables: NSUB, N(1),...,N(NSUB)
Format: 4X, I5, 6F10.0,/,(9X, 6F10.0)
Example: NSUB 3 0.03 0.02 0.04

NSUB is the number of subsections. The valid range for NSUB is from 1 to 96.

N( i ) is Manning's n for each subsection for the cross section.

The divisions between subsections are defined by frictionless, vertical lines.

Variable: HEAD
Format: A80
Example: OFFSET ELEVATION SUB N0 Y1 N1 Y2 N2 Y3 N3 Y4 N4

HEAD is a user-defined heading to describe the information on subsequent lines. No fixed columns are given for subsequent input, only a fixed order. Therefore, the headings can be spaced for user convenience.

LINE 6 (Repeated for each point on the boundary.)
Variables: X( i ), Z( i ), SB( i ), N0( i ), (YATN, NATY)(*, i )
Example 1: -20.0 675.0 1 0.032
Example 2: -20.0 600.0 * 0.050 20.0 0.035

X( i ) is the offset of the coordinate point i on the boundary of the cross section.

Z( i ) is the elevation of the coordinate point i on the boundary of the cross section.

SB( i ) is the subsection number for the coordinate point i on the boundary of the cross section.

N0( i ), YATN, NATY are parameters used to describe the variability of Manning's n with respect to water-surface height and position in the cross section. The definition of these variables changes depending on the specification of VARN on Line 3 as described in the following discussion.


N0 is the value of Manning's n at a zero value of water-surface height in a subsection. YATN is the value of hydraulic depth (HYDY) or maximum water-surface height (MAXY) at which a value of the variable Manning's n is specified.

In this case, N0 as well as YATN and NATY can only be given at the first point of each subsection. The variation of Manning's n is specified by five points: one at zero water-surface height and four others at user-defined levels in each cross section. Linear variation of the n value with water-surface height (hydraulic or maximum) is assumed in each subsection. The values of water-surface height given for the variation of Manning's n in each subsection must be increasing. If VARN = HYDY or VARN = MAXY, but N0 is not given, then the value of N0 from the subsection n value is utilized in FEQXEXT. Moreover, if N0, YATN, and NATY are omitted, the roughness is assumed to be constant for all subsections at the value given for the subsection in the FEQXEXT computations.

If VARN = NCON or if no data are given for vertical variation of roughness,

a wetted-perimeter weighted composite roughness value in each subsection is computed in FEQXEXT. If N0 = 0 for a line segment, that line segment is treated as frictionless in the computation of the composite roughness value.
It is possible to have four different modes of variation of roughness in a cross section. The first is no variation. The second is variation with the hydraulic depth in the subsection. The third is variation with the maximum water-surface height in the cross section. The fourth and last variation is in the composite value of n as the water level in the subsection changes. Not all combinations can result in a cross section simultaneously. However, three of the four combinations can be used simultaneously in a single cross section, if necessary.

The last point on the cross-section boundary is indicated by a subsection number of -1. This convention means that the subsection number for a point applies to the line segment connecting the point to the subsequent point. Thus, a subsection assignment is not required for the last point because no line segment is present between it and a subsequent point. Therefore, the subsection for the last point is used in FEQUTL as a flag to signal the end of the cross-section specification.

The minimum data for the first point of a cross-section boundary are the offset, elevation, and subsection number. The minimum information for all subsequent points is offset and elevation. If more than one subsection is required to describe the cross-section boundary, then a subsection number must be added at the first point in each of the subsections after the first.

A conduit-closed section can be specified by defining the offsets and elevations of points around the perimeter of the section. The description should begin at the high point of the section and should not close completely so that a free surface remains. The closed-conduit section should be traversed in a counterclockwise direction when defining points on the boundary.

Some users have used the columns after the subsection number for a boundary point in the command FEQX for comments about the source of the data for that point. These could include the state plane coordinates of that point, the nature of the point, and related information. The line is not read beyond the subsection number columns in FEQX. However, the entire line is read in FEQXEXT. In order to support these comments, the remainder of a line after the single quote character (') is not read in FEQXEXT. Thus, it becomes possible, where needed, to utilize FEQXEXT and still maintain the unsupported comments on the line.

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