CHAPTER 7  WEIRS
6. Partially and Fully Contracted Rectangular Weirs
Kindsvater and Carter (1959) developed an improved method for calibration rating of rectangular thinplate weirs. The method applies to both fully and partially contracted rectangular weirs. The method also rates the equivalent of a suppressed weir. The capability of rating partially contracted weirs provides design versatility, especially in selection of low crest heights to reduce head drop and side contraction needed to measure flow. Thus, these weirs can reduce head loss and conserve delivery head. These weirs have coefficients that vary with measuring head as well as geometry. The resulting calibrations are at least as accurate as the equations and tables for "standard" fully contracted weirs. Weir use and dimension limits are defined by the curves for determining the calibration ratings.
The basic equation for the KindsvaterCarter method is:
(71)
where:
Q = discharge, cubic feet per second (ft^{3}/s)
e = a subscript denoting "effective"
C_{e} = effective coefficient of discharge, ft^{1/2}/s
L_{e} = L + k_{b}
h_{1e} = h_{1} + k_{h}
In these relationships:
k_{b} = a correction factor to obtain effective weir
length
L = measured length of weir crest
B = average width of approach channel, ft
h_{1} = head measured above the weir crest, ft
k_{h} = a correction factor with a value of 0.003 ft
The factor k_{b} changes with different ratios of crest length, L, to average width of approach channel, B. Values of k_{b} for ratios of L/B from 0 to 1 are given on figure 74. The factor k_{h} is a constant value equal to 0.003 ft.

The effective coefficient of discharge, C_{e}, includes effects of relative depth and relative width of the approach channel. Thus, C_{e} is a function of h_{1}/p and L/B, and values of C_{e} may be obtained from the family of curves presented on figure 75. p is the vertical distance from the weir crest to the approach pool invert.

The straight lines on figure 75 have the equation form:
(72)
where:
C_{e} = effective coefficient of discharge
C_{1} = equation coefficient
h_{1} = head on the weir (ft)
p = height of crest above approach invert (ft)
C_{2} = equation constant
For convenience, the coefficients and constants for straight lines of each L/B on figure 75 are given in the following tabulation for interpolation:
Table 71. Coefficient and constants used in determining the effective coefficient of discharge for the KindsvaterCarter method 

L/B 
C_{1} 
C_{2} 
0.2 
0.0087 
3.152 
The straightforward, comprehensive, and accurate KindsvaterCarter method of determining discharges for rectangular weirs is well suited for discharge rating use. It is particularly useful for installations where full crest contractions or full end contractions are difficult to achieve.
Traditional rectangular weirs that do not meet crest height limits or that are using the older methods of correcting for velocity of approach should be recalibrated using the KindsvaterCarter method. Weirs that fall out of the limits of the KindsvaterCarter rating curves need replacement or field calibration by thorough current metering.
Limits on usage and dimensions are: