Fully Contracted Standard 90-Degree V-Notch Weir (سرریز مثلثی 90 درجه مستعرق)

Fully Contracted Standard 90-Degree V-Notch Weir

The triangular or V-notch, thin-plate weir is an accurate flow measuring device particularly suited for small flows.

(a) Traditional Equation for Standard 90-Degree Contracted V-Notch Weirs

The Cone equation is commonly used for 90­degree V-notch weirs. This equation is reliable for small, fully contracted weirs generally encountered in measuring water for irrigation.

The Cone equation is:

Q=2.49h₁^2.48   (7-6)

where:

Q = discharge over weir in ft³/s
h₁ = head on the weir in ft

(b) Discharge of 90-Degree Contracted V-Notch Weirs

Table A7-4 contains discharges in cubic feet per second for the standard 90-degree, fully contracted V-notch weir (figure 7-1) from the Cone equation for a range of heads ordinarily used in measuring small flows. To be fully contracted, all the overflow plate edges and the point of the notch must be located at least a distance of 2h_1max from the approach flow boundaries.

(c) Limits of 90-Degree Contracted V-Notch Weirs

The crest of the weir consists of a thin plate beveled 45 degrees or greater from the vertical to produce an edge no thicker than 0.08 in. If heads will be frequently near the 0.2-ft lower limit, then the bevel-ing should be 60 degrees. This weir operates as a fully contracted weir, and all conditions for accuracy stated for the standard contracted rectangular weir apply. To be fully contracted, all the overflow plate edges and the point of the notch must be located at least a distance of two measuring heads from the approach flow boundaries. The head measuring station is located a distance of at least four measuring heads upstream from the weir crest. This 90­degree V-notch weir should only be used for discharges between 0.05 and 4.25 ft³/s and should not be used consistently near the high end of this range because a 2-ft fully contracted rectangular weir will deliver the same flow at 40 percent less head for the same approach channel width. All the requirements of section 5 apply. All the approach flow conditions in chapter 2 apply.

The use of the Kindsvater-Shen method for rating V-notched weirs can considerably extend the limitations described above.

Partially and Fully Contracted Rectangular Weirs (سرریز مستعرق با فشردگی کناری)

Partially and Fully Contracted Rectangular Weirs

Kindsvater and Carter (1959) developed an improved method for calibration rating of rectangular thin-plate 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 Kindsvater-Carter method is:

     (7-1)

where:

Q = discharge, cubic feet per second (ft³/s)
e = a subscript denoting "effective"
C_e = effective coefficient of discharge, ft^1/2/s
L_e = L + k_b
h_1e = h₁ + 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
h₁ = 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 7-4. The factor k_h is a constant value equal to 0.003 ft.

 

Figure 7-4 -- Value of width-adjustment factor from Georgia Institute of Technology tests (courtesy of American Civil Society of Engineers).

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 h₁/p and L/B, and values of C_e may be obtained from the family of curves presented on figure 7-5. p is the vertical distance from the weir crest to the approach pool invert.

 

Figure 7-5 -- Effective coefficient of discharge, C_e, as a function of L/B and h₁/p, from Georgia Institute of Technology tests (courtesy of American Civil Society of Engineers)..

The straight lines on figure 7-5 have the equation form:

(7-2)

where:

C_e = effective coefficient of discharge
C₁ = equation coefficient
h₁ = head on the weir (ft)
p = height of crest above approach invert (ft)
C₂ = equation constant

For convenience, the coefficients and constants for straight lines of each L/B on figure 7-5 are given in the following tabulation for interpolation:

Table 7-1. Coefficient and constants used in determining the effective coefficient of discharge for the Kindsvater-Carter method
L/B	C1	C2
0.2 0.4 0.5 0.6 0.7 0.8 0.9 1.0	-0.0087 0.0317 0.0612 0.0995 0.1602 0.2376 0.3447 0.4000	3.152 3.164 3.173 3.178 3.182 3.189 3.205 3.220

The straightforward, comprehensive, and accurate Kindsvater-Carter 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 Kindsvater-Carter method. Weirs that fall out of the limits of the Kindsvater-Carter rating curves need replacement or field calibration by thorough current metering.

Limits on usage and dimensions are:

• The calibration relationships were developed with rectangular approach flow and head measurement sections for these weirs. For applications with other flow section shapes, the average width of the flow section for each h₁ is used as B to calculate discharges.
• The crest length, L, should be at least 6 in.
• The crest height, p, should be at least 4 in.
• Like all weirs used for head measurement, h₁ should be at least 0.2 ft .
• Values of h₁/p should be less than 2.4.
• All the requirements in section 5 apply.
• The downstream water surface elevation should be at least 2 in below the crest.
• All the approach flow conditions in chapter 2 apply .