Full Equations Utilities (FEQUTL) Model for the Approximation of Hydraulic Characteristics of Open Channels and Control Structures During Unsteady Flow
Purpose: The Hulsing (1967) procedure for flow over embankmentshaped weirs is implemented as outlined in section 4.3. Flow over a variety of weirs can be computed if the appropriate tables are provided.
Notes: A warning message has been added to EMBANKQ to alert the user
to potentially unrealistic results for flow over the embankment when the
height of the embankment above the approach section becomes small relative
to the head on the embankment. If the ratio of piezometric head to the
weir height becomes much greater than 4 or 5, the coefficients used for
flow over the weir are inaccurate. The depth at which the weirflow coefficients
become inaccurate is not known. However, if the head to height ratio goes
above 7, the weirflow coefficients are certainly inaccurate. The message
is only a warning, and the flow will be computed in FEQUTL for whatever
ratio is present. The user must decide if the result is reasonable. The
flow at each point along the crest of the embankment is limited to be no
more than the critical flow rate in the approach section. Therefore, when
weir subsections with small heights are present in the stream system, the
critical flow in the approach section is applied. However, no warning is
issued when this is done. The best method to apply for weir subsections
with small heights is to divide the embankment into subsections and apply
CHANRAT (section 5.3) for those sections
with crest elevations very close to the approach section elevation.
LINE 1
Variable: TABLE, TYPE, HLCRIT, HLMAX
Format: 7X, I5, A5, A5
Example: TABLE #= 9900
Explanation:
TABLE is table number for the table to be computed in FEQUTL.
TYPE is the table type and can be either 6 or 13 with 13 applied by default if TYPE is omitted. HLCRIT is the critical ratio between approach head and embankment width that distinguishes between highhead and lowhead flow. Ratios at or greater than HLCRIT correspond to highhead flow and ratios less than HLCRIT correspond to lowhead flow. The default value is 0.15 based on Hulsing (1967) and Kindsvater (1964). HLMAX is the maximum ratio of approach head to embankment width that can be applied without generating a warning message in EMBANKQ. This warning message alerts the user to the possibility that the weir coefficients may no longer be valid at head ratios greater than HLMAX. The approximate upper limit of the headtowidth ratio in the experiments defining the weir coefficients is represented in HLMAX. HLMAX defaults to 0.32 based on Hulsing (1967) and Kindsvater (1964). 
TAB(1) is the table number for the function table listing the lowhead 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(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 the 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.
If PSUBTB and GSUBTB are given as zero, then no submergence computations are done and the resulting function table will be type 2. If they are nonzero, then submergence computations are done and the resulting function table will be type 13. 
LABEL is a usersupplied label that will be output as part of the heading for the table produced in FEQUTL computations. 
HEAD gives a heading for subsequent columns of input. 
The values given on this line define, in a subsectionbysubsection
approach, the geometry of the crest of the embankmentshaped weir applied
in computation of the flow over the embankment.
OFF is the horizontal offset. 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 in the computations, then an approach elevation that is much lower than the crest elevation should be specified so that the velocity head computed will be small. SURF is 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 weircrest specification gives the type of surface as GRAVEL and the second line of the weircrest specification gives the type of surface as PAVED, then the weir 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 giving END for the type of surface. Thus, if the third line of the input in this example had 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. 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. The surface value also propagates so that for constant surface type, only the first line must have PAVED or GRAVEL. END is specified for the final line to indicate the end of geometric input.
LINE 11
Variable: HEAD
Format: A80
Example: UPSTREAM HEADS TO USE IN COMPUTING THE TABLE
Explanation:
HEAD gives the heading for subsequent column of input. 
The following two lines (11a and 11b) are optional. However, if one is applied, the other also must be applied. If they are omitted, NFRAC defaults to 21 and POWER defaults to 2.
LINE 11a
Variable: CHAR5, NFRAC
Format: A5, 1X, I5
Example: NFRAC = 11
Explanation:
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 embankment simulated. Generally, the spacing should be small for the low heads and larger for the high heads. 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. 