Discharge Control Structures
This is the standard weir formulation. All that is required is the weir elevation and length. The max elevation is required for report printing only. The program will compute the discharge for any elevation greater than the crest elevation.
Figure 7: Broad Crested Weir
The following practical design recommendationsCasey_Ref have been proposed for broad crested weirs.
- h1 >= 0.06 m or >= 0.05L, whichever is greater
- radius of cill nose r=0.2H1max;
- p1 >= 0.15 m or >= 0.67H1, whichever is greater;
- 20H1 >= L >= 2H1, to ensure parallel flow while avoiding undulation over the cill;
- b = 0.3 m or >= H1 or >= L/5, whichever is greater;
- to ensure modular flow conditions, the downstream depth and step height p2 should comply with modular limit values set out in the following table
|Vertical back face||Sloping back face(1:4)|
- h1 is the approach HGL.
- H1 is the approach EGL
- L is the length of the weir
- p1 is the depth from the weir cill to the approach bottom of channel.
- p2 is the depth from the weir cill to the bottom of the departing channel.
The broad crested weir as implemented by this program simplifies the input requirement for the following equation:
Where Q is the discharge in cfs; Cd = 3.216;
L is the weir length;
and H is the stage above the weir.
In the case of roadway overtopping, the coefficient is an overtopping coefficient defined as:
Cd=kt * Cr
Where kt is a submergence factor and Cr is a discharge coefficient. The coefficent differs from a weir with a well rounded upstream edge because the upstream edge is really the roadway sagging curve.
The Federal Highway Administration (1985) characterizes the coefficents in Figure III - Discharge coefficients for roadway overtopping.
The program supports a number of different types of culverts for use as control structures. They include circular concrete, circular cmp, pipe arch, elliptical and box shapes. The procedure for inlet and outlet control computations for all support culverts come from Hydraulic Design of Highway Culverts (HDS-5).
Standard shapes for pipe arch culverts are taken from Modern Sewer Design, American Iron and Steel Institute, Third Edition, 1995. Standard sizes for concrete elliptical shapes are taken from Concrete Pipe Design Manual, American Concrete Pipe Association, November 1992.
Figure 15: Culvert Logic Diagram
The above flow diagram is used to evaluate the flow conditions for each culvert based on the flow to be routed through it. In the case of an M1 or M2 condition, a direct step backwater computation is performed to determine impingement. The methodology for the direct step computation is outlined in Chow, Open Channel Hydraulics, 1959
StormShed3G™ supports three variations of infiltration. The primary variation is simply a constant rate in inches per hour. The rate is applied to the wetted surface area of the storage structure.
The second method based on an average saturated hydraulic conductivity. The methodology is taken from The 2005 Washington State Department of Ecology Stormwater Management Manual, Volume III, Section 3.3.8. Specifically, the saturated hydraulic conductivity that StormShed3G is expecting is described in step 6, page 3-89 of the volume.
The third method is a further implementation of the procedure described in Volume III. It allows users compute the saturated hydraulic conductivity (Ksat) directly from soils logs.
The implementation of Ksat is a entirely based on the procedure described in Volume III and is not repeated here.
Ranges of values for natural materials
Table of saturated hydraulic conductivity (K) values found in nature
Values are for typical fresh groundwater conditions — using standard values of viscosity and specific gravity for water at 20°C and 1 atm.
|Unconsolidated Sand & Gravel||Well Sorted Gravel||Well Sorted Sand or Sand & Gravel||Very Fine Sand, Silt, Loess, Loam|
|Unconsolidated Clay & Organic||Peat||Layered Clay||Fat / Unweathered Clay|
|Consolidated Rocks||Highly Fractured Rocks||Oil Reservoir Rocks||Fresh Sandstone||Fresh Limestone, Dolomite||Fresh Granite|
Source: modified from Bear, 1972
This control is a specialized control that allows for the definition of up to five separate circular orifices at different elevations. The control is characterized by a lowest orifice elevation which is BELOW the outlet elevation. The outlet elevation is considered the elevation of the receiving pipe from the pond. The remaining four orifices are located as a distance from the previous orifice.
Figure 13: Multiple Orifice Structure
Note that the orifice diameters are in inches. This implies that the diameters are supposed to be rather small (no 3 ft diameter orifice). However, the program is not very intelligent and will compute flows through orifice up to 5 ft in diameter.
The program does not consider the occurrence of weir flow through any orifice. All flow through any orifice is assumed to be under submerged orifice flow conditions. Driving heads applied to the orifice are computed to the orifice invert. No adjustment is attempted to correct for flow to the centroid of the orifice.
The lowest orifice is simply a placeholder to identify where it physically is located. For hydraulic computations, the elevation that matters is the outlet elevation. Flows through each orifice are computed relative to the outlet elevation.
This weir type is provided as a convenience. It is a broad crested weir with side slopes applied to each end.
The effect of varying the side slope is to vary the weir coefficient. Flow is computed based on:
|Q||Discharge in cfs|
|L||crest length (ft)|
|H||Stage above crest (ft)|
|tan(theta)||side slope xH:1V|
These weirs have large capacity, but have less sensitivity for flow measurement. The rectangular weir is also known as a notch weir. The weir coefficient is based on ratio between the head on the weir crest and the height above the bottom of the pond. Based on the standard formula, in cases where the length is small and the depth is great, the standard formula can become negative. When the adjusted length is less than 0.2 ft, the program will assume that the weir is operating as an orifice with the opening area defined by the current water surface elevation and the weir length. The orifice formula is applied to the centroid of the weir (stg-crest) divided by 2.
Figure 8: Rectangular Weir
Practical design limits for the rectangular weir are:
- H >= 0.03 meters (about 1.2 inches)
- H/p1 <= 2 and p1 >= 0.1 meters (about 4 inches)
- L >= 0.15 meters (about 6 inches)
- The tail water level should be at least 0.05 meters below the weir crest. (about 2 inches)
- H is the depth of flow above the weir.
- p1 is the height from the weir crest to the bottom of the approach channel
- L is the length of the weir
Discharges are computed based on the following equation:
- Q is the discharge rate in cfs; L is the crest length (ft);
- H is the stage above the crest (ft);
- and c is given by the equation:
Where p is the height of the weir above the bottom.
Note that L is an adjusted length shortened by 0.2H! This means that the length can be adjusted to zero and the Q can be reduced to zero! When the adjusted length is less than 0.2ft, the program computes flow through the weir using the orifice equation. The “head” on the imaginary orifice is the average water surface elevation. The orifice coefficient is assumed to be 0.61. (Practical limits are taken from: T.J. Casey, "Water and Wastewater Engineering Hydraulics", Oxford Science Publications, Oxford University Press, 1992).
In May 2001, Steven Wright and Braden Baldwin published Report UMCEE 01-07 titled Notch Weirs for Use in Stormwater Detention Basin Control Structures It is a report out of:
Department of Civil and Environmental Engineering
The University of Michigan
Ann Arbor, Michigan
In the report, they presented an equation that approximated measured data to within three percent. We simply refer to the equation as the Wright/Baldwin Equation.
Since the report is not well known, the Results section of the report is duplicated here.
Q = (3.27 + 0.4H/P)(L - 0.2H)H^3/2 . . . . . . (1)
For reasons of convention, results are presented in terms of a weir coefficient C defined by:
C = Q/L*Pow(H,3/2) . . . . . . (2)
Note that C is not dimensionless in this representation and values therefore depend on the system of units employed. The values presented in this report utilize the U.S. Customary system of units because of the convention in engineering practice in the U.S. In order to convert to S.I. or other units, one only need recognize that C has units of the square root of gravity. To convert to S.I. units, for example, the C values reported herein must be multiplied by 0.3048^1/2 where 0.3048 represents the conversion from feet to meters.
With the notch weir in the side of a circular pipe, there is a choice on how to represent L. It could be given by the circumferential distance from one side of the weir to the other or it could equally well be given by the straight-line distance. Logically, the first definition may be more valid at very low weir heads in which the flow passing over the pipe circumference determines the nature of the flow. At high weir heads, the straight-line distance is perhaps more appropriate as it defines the area that the approach flow "sees" as it approaches the weir. The King and Kitsap County Surface Water Design Manuals suggest that the circumferential length is the appropriate one to be used in the discharge equation. In the data analysis, both definitions of L were employed and the second definition proved to be more capable of collapsing the data in a non-dimensional sense; i.e. to provide more similar values of C for each weir width. The data for the 12 inch pipe and the various weir widths with each definiton of L are presented in Figures 8 and 9. When the weir width is very short such as 1.5 inches, the differences between the two definitions of L are minimal but become more significant when the weir width is a larger proportion of the pipe circumference. From these two figures, it appears that t he use of the straight line distance provided a more consistent presentation of experimental results. Therefore, this definition of L is utilized in all further results presented herein.
Weirs Without Baffles
The majority of the experiments were performed without the baffle installed since it is intended that the baffle not affect the head-discharge relation for the weir. A typical result for a weir width of 1.5 inches is given in Figure 10. Also included on this figure is data from Carter at a similar weir width (1.42 inches). The two data sets are reasonably consistent in terms of the general magnitude of the weir coefficient. All sets of experiments performed in the current study clearly demonstrated the trend that the weir coefficient decreases with increasing head. This may be due to the issue discussed above where the crest length at low heads may be more appropriately correlated with the circumferential length in the sense that a longer length in Equation (2) would reduce the C value; hence using the straight line distance for L yields too large a weir coefficient. This effect would not occur for a weir in a flat plate and is consistent with the observations for the one experiment performed with a flat plate (and discussed below). Carter's Georgia Tech data were inconsistent in the trends of C vs. H for the various weir configurations, in some cases decreasing and in other, increasing with H. This may be due to other effects not investigated in the current study such as small values of P.
Also include in Figure 10 is the prediction of Equation (1) in the limit with H/P=0; this is considered to be the most appropriate description for the experimental configuration studied. It can clearly be seen that Equation (1) does not capture the trend in the data, supporting the previous conclusion (see Appendix 2) that it is an inappropriate equation for this particular application with relatively large H/L values.
The results for the four different crest widths in the twelve-inch PVC pipe are presented in Figure 8. The concept implied by Equation (1) is that an "effective crest length" is computed by reducing the length of the crest by a function that depends on the weir head. The underlying philosophy is cast into doubt by the results in Figure 11 since the weir coefficient should then decrease with crest length since end effects would be greater for smaller crest lengths and the opposite trend is actually indicated. It should be noted that the Georgia Tech data also supports this conclusion for weirs in flat plates although a bit more ambiguously. In the Handbook of Hydraulics, 7th edition, (E.R. Brater, H.W. King, J.E. Lindell and C.Y. Wei, McGraw Hill) page 5.11, a correction to the weir coefficient to account for end contractions is discussed based in part on the Georgia Tech Data. Figure 5.3 on page 5.14 indicates a positive correction to be made to the actual length over nearly the entire range of flow conditions, consistent with the results presented in Figure 8. Such results call into question the structure of Equation (1), even though it currently is the most commonly used equation for contracted weirs. The experiments with the 8-inch pipe with crest lengths of two, four and six inches were intended to correspond to geometrically similar conditions for the 12-inch pipe (i.e. the 2-inch crest length corresponding to the 3-inch, the 4-inch to the 6, etc.) However if the results for the two different pipes are plotted non-dimensionally in terms of H/D where D is the pipe diameter as in Figure 11, there is no correspondence between the results for the two pipes for equal values of H/D. If, however, the results are plotted simply as a function of head H and crest length L as in Figure 12, then the two sets of results appear to be consistent with each other. This finding led to the additional experiment with the 6-inch weir width on a flat plate as described earlier. Figures 13 and 14 show the results for all three six-inch weirs with the two different definitions of L and again support the conclusions based on the data in Figures 8 and 9. The fact that the data in Figure 13 are reasonably consistent with each other implies that the curvature of the pipe that the weir is installed on is basically irrelevant so long as the crest length is interpreted as the linear distances between the two sides of the weirs. Additional experiments may be in order to verity this conclusion over a wider range of geometries.
Attempts were made to collapse the data in some sort of dimensionless presentation without success. Instead, following the development by Kindsvater and Carter as described in Equation 5-35 of the 7th edition of the Handbook of Hydraulics, the only successful means of collapsing the data was by adding a fixed correction to the length as:
Leff = L + Kl . . . . . (4)
Kindsvater and Carter recommends Kl values on the order of 0.008 ft for their studies while a fixed value of 0.045 ft appears to be adequate for collapsing the data for the present study. The values of Kl can, however, be doubled without a significant change in the standard deviation of the fitted equation (Equation 6 below) and the exact value is subject to some uncertainty. Figure 15 shows the result of this correction to the crest length and the ability to present experimental results for several crest lengths as a unique function of the weir head. The differences between the current study and that by Carter (from which the Kindsvater and Carter's correction was derived) appears to be quite substantial in regard to this correction so there is likely to be a difference mechanism associated with the correction in the two studies. It should be noted that many of Carter's experiments were conducted with fairly small P values (H/P less than one) and this may well have an important and significant difference on the flow downstream of the weir crest.
Kindsvater and Carter also recommends using a weir equation in which the head is corrected in a fashion similare to Equation (4):
Heff = H + Kh . . . . . .(5)
After attempts to nondimensionalize the results were not successful, this approach was ultimately selected for the current study as well. Again, a much larger value of Kh, on the order of 0.018 ft, was required to collapse the data as indicated in Figure 16 than the value of 0.003 ft recommended by Kindsvater and Carter. A portion of the difference between the two studies is believed to be due to the curved nature of the notch weir constructed in the side of a pipe, but the limited data with the flat weir do not indicate that this is the case. It also appears that the conditions downstream from the weir are likely to play a significant role on the pressure distribution at the weir crest and therefore to affect the values of the weir coefficients. A future study to investigate this issue is planned. In any case, a flow equation that is adequate to predict the entire range of experimental data to within an accuracy of about three percent (to cover all the experimental data; the standard deviation is about 1.7%) is:
Q = 3.06(L + 0.045)(H + 0.018)^3/2 . . . . . . . . .(6)
This equation is dependent on the system of units employed and should be applied for Q in cfs and L and H in feet. In the S.I. system of units, a similar equation would be:
Q = 1.69(L + 0.014)(H + 0.0055)^3/2 . . . . . . . . (7)
Sutro weirs consist of a rectangular section joined to a curved portion which provides proportionality for all heads above the rectangular section.
Figure 9 - Symmetrical Sutro Weir
For this type of weir, the curved portion is defined by the equation:
And the head-discharge relationship is:
Values of Cd for both symmetrical and non-symmetrical Sutro Weirs are summarized in the tables below.
|Cd Values, Symmetrical|
|a (ft)||b, (ft)|
|Cd Values, Non-Symmetrical|
|a (ft)||b, (ft)|
Table 14 - Values of Cd for Sutro Weirs
Note that when b > 1.5 or a>0.30 use Cd =0.6.
These weirs have greater control under low flow conditions. This weir is either a sharp or broad crested vee shaped weir. The angle of the vee can vary from greater than zero degrees to 180 degrees. It cannot be zero or 180 degrees.
The following are design limitsCasey_Ref for practical applications of sharp crested V-Notch weirs:
- H/p1 <= 1.2
- H/B <= 0.4 and B >= 0.6m
- 0.60 >= H >= 0.05 m
- p1 >= 0.10 m
- 100 deg >= theta >= 25 deg
- Tail water level >= 0.05 m below the vertex of the V-Notch.
|V-Notch sharp crested weir coefficients|
|Notch angle (degrees)||20||40||60||80||100|
Figure 11: Triangular or Vee Weir
Kindsvater and Carter (1957) proposed that the discharge coefficient is a function of the notch angle and effective head (he) on the weir. The effective head is the head on the weir corrected by a correction factor kh such that he = h1 + Kh
This program uses the simplified formula:
- c is the orifice coefficient
- q is the weir angle
- H is the stage above the crest elevation (ft
Values of c are computed at runtime based on the following graph:
Figure 12: Vee Weir Coefficients
This is a standard orifice defined by area. The orifice can be sharp or rounded, circular, rectangular or any other configuration. It is up to the user to specify the coefficient to apply to the orifice. No provision is made to compute weir flows for the weir at low head conditions. It is assumed that the orifice opening is submerged and that the orifice equation applies. This is typically not a problem for small orifice; there would be a problem for large openings.
Figure 14: Vertical Orifice
For circular sharp edged orifice, the following practical design limitsCasey_Ref are recommended:
- edge distance >= d/2
- upstream channel cross-sectional area >= 10 times orifice area
- upstream submergence of top of orifice >= d
- Dh >= 0.03 m
- Dh is the difference between upstream and downstream water surface elevations
- d is the orifice diameter
Under fully contracted, submerged conditions, the discharge coefficient cd may be taken as 0.61 for rectangular sharp crested orifice shapes.
Uses the orifice formula:
- c is the orifice coefficient
- A is the area of the opening in square feet (sf)
- h is the driving head acting on the orifice
Typically 0.61 for a sharp crested orifice, but can be anything that is reasonable. Some typically coefficients for sharp crested weirs:
|Orifice Diameter (m)||Cd - Free flow||Cd - Submerged Flow|
Table 15: Typical Orifice Coefficients for Sharp Crested Orifice