The method by which this error has to be combined with other sources of error is I

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1 The error in the discharge coefficient (including C,) of a triangular broad-crested (truncated) eir, hich has been constructed ith reasonable care and skill, may be deduced form the equation X, = f (3 H,/L (4-7) + 4) per cent The method by hich this error has to be combined ith other sources of error is shon in Annex Modular limit a. Less-than-full case The modular limit, or that submergence ratio HJH, hich produces a 1 YO reduction in the equivalent modular discharge, depends on a number of factors, such as the value of the ratio H,/Hb and the slope of the donstream eir face. Results of various tests by the Hydraulic Laboratory, Agricultural niversity, Wageningen, , and by Smith & Liang (1969), shoed that for the less-than-full type eir (H,/Hb d 1.25) the droned flo reduction factor (0(i.e. the factor hereby the equivalent modular discharge is decreased due to submergence), varies ith H,/H,, as shon in Figure The modular limit for eirs ith a vertical back-face equals H,/H, = This modular limit may be improved by constructing the donstream eir face under a slope of -to-6 (see also Figure 4.2) or by decreasing p2. b. Over-full case No curve is available to evaluate the modular limit of over-full type eirs. t may be expected, hoever, that the modular limit ill change gradually to that of a broadcrested eir as described in Section if the ratio H,/Hb increases significantly above A more accurate estimate of the modular limit can be made by use of Section SBMERGENCE RATO Hsl H o DROWNED FLOW REDCTON FACTOR f Figure 4. 1 Droned flo reduction factor as a function of H,/H, 142

2 4.3.4 Limits of application The limits of application of the triangular broad-crested eir and truncated eir for reasonable accuracy are: - The practical loer limit of h, is related to the magnitude of the influence of fluid properties, boundary roughness, and the accuracy ith hich h, can be determined. The recommended loer limit is 0.06 m or 0.07 times L, hichever is greater; - The eir notch angle 8 should not be less than 30"; - The recommended upper limit of the ratio H,/p, = 3.0, hile p, should not be less than O. 15 m. - The limitation on H,/L arises from the necessity of ensuring a sensible hydrostatic pressure distribution at the control section. Values of the ratio H,/L should therefore not exceed 0.50 (0.70 if sufficient head is available); - The breadth B, of a truncated triangular broad-crested eir should not be less than L/ Broad-crested rectangular profile eir Description From a constructional point of vie the broad-crested rectangular profile eir is a rather simple measuring device. The eir block shon in Figure 4.12 has a truly flat and horizontal crest. Both the upstream and donstream eir faces should be smooth vertical planes. The eir block should be placed in a rectangular approach channel perpendicular to the direction of flo. Special care should be taken that the crest Figure 4.12 Broad-crested rectangular profile eir (after BS 1969) 143

3 surface makes a straight and sharp 90-degree intersection ith the upstream eir face. The upstream head over the eir crest should be measured in a rectangular approach channel as shon in Figure The head measurement station should be located at a distance of beteen to and three times Hlmax upstream from the eir face. Depending on the value of the ratio HJL, four different flo regimes over the eir may be distinguished: a) H,/L < 0.08 The depth of flo over the eir crest is such that sub-critical flo occurs above the crest. The control section is situated near the donstream edge of the eir crest and the discharge coefficient is determined by the resistance characteristics of the crest surface. Over this range the eir cannot be used as a measuring device. b) 0.08 < HJL < 0.33 At these values of HJL a region of parallel flo ill occur somehere miday above the crest. The ater surface slopes donard at the beginning of the crest and again near the end of the crest. From a hydraulic point of vie the eir may be described as broad-crested over this range of HJL only. The control section is located at the end of the section here parallel flo occurs. Provided that the approach velocity has no significant influence on the shape of the separation bubble (see Figure 4.13) the discharge coefficient has a constant value over this HJL-range. c) 0.33 < H,/L < about 1.5 to 1.8 n this range of H,/L values the to donard slopes of the ater surface ill merge and parallel flo ill not occur above the crest. Streamline curvature at the control has a significant positive effect on the discharge, resulting in higher C,-values. n fact the eir cannot be termed broad-crested over this range but should be classified as short-crested. The control section lies at station A above the separation bubble shon in Figure d) H,/L > about 1.5 Here the ratio H/L has such a high value that the nappe may separate completely OH1 Re= b :0.109 Hl Figure 4.13 Assumed structure of entry-edge separation bubble as a function of H and the Reynolds number (Hall 1962) 144

4 from the crest and the eir in fact acts as a sharp-crested eir. f Hl/L becomes larger than about 1.5 the flo pattern becomes unstable and is very sensitive to the sharpness of the upstream eir edge. For H,/L values greater than 3.0 the flo pattern becomes stable again and similar to that over a sharp-crested measuring eir (see Chapter 5). To prevent underpressures beneath the overfloing nappe from influencing the headdischarge relationship, the air pocket beneath the nappe should be fully aerated henever H,/L exceeds Dimensions of the aeration duct should be determined as shon in Section The modular limit, or that submergence ratio H,/H, hich produces a 1 YO reduction from the equivalent modular discharge, depends on the ratio H,/L. f 0.08 Q HJL Q 0.33, the modular limit may be expected to be f H,/L = 1.5, hoever, the modular limit is about 0.38 and over the range 0.33 < H,/L < 1.5 the modular limit may be obtained by linear interpolation beteen the given values. Provided that the ratio h,/(h, + p,) d 0.35, Figure 4.18, too, can be used to obtain information on the reduction of modular flo due to submergence Evaluation of discharge The basic head-discharge equation derived in Section can be used to evaluate the flo over the eir. This equation reads (4-8) here the approach velocity coefficient C, may be read from Figure 1.12 as a function of the dimensionless ratio CdA*/Al = Cdhl/(hl + p,). Experimental results have shon that under normal field conditions the discharge coefficient is a function of the to ratios h,/l and h,/(h, + p,). As mentioned in the previous section, the discharge coefficient remains constant if there is parallel flo at the control section and if the approach velocity does not influence the shape of the separation pocket. Hence Cd remains fairly constant if both 0.08 < h,/l Q 0.33 and h,/(h, + P) Q 0.35 The average value of Cd ithin these limits is and is referred to as the basic discharge coefficient. f one of the limits is not fulfilled the basic Coefficient should be multiplied by a coefficient correction factor F hich is alays greater than unity since both streamline curvature at the control section and. a depression of the separation bubble have a positive influence on eir flo. Values of F as a function of h,/l and h,/(h, + p) can be read from Figure There are not enough experimental data available to give the relation beteen c d and the ratios h,/l and h,/(h, + p,) ith satisfactory accuracy over the entire range. f, hoever, the influence of the approach velocity on Cd is negligible, (i.e. if h,/(h, + p) < 0.35), C,-values can be read as a function of h,/l from Figure

5 LL LL z 1.0s o 1.OE a g z 106 p 1.05 h. W o o0 RATO hlll Figure 4.14 Coefficient correction factor F as a function of hl/l and hl(hl + pi) (adapted from Singer 1964) O4 1.o2 u = J i 0.92 Q e Q RATO hqll _. Figure 4.15 Cd-values and F-values as a function of hl/l, provided that hl!(hl + p) <