The coefficient of discharge has been determined for sharp-edged orifices under a great variety of conditions. Its mean value, taking the values of ( and c c given above, is 62. For circular orifices, sharp-edged and with complete and perfect contraction, Weisbach found the following values : Coefficients of Discharge for Sharp-edged Circular Orifices. Diameter of Oiifice Coefficient of Discharge =c. in Indies. Head 2 ft. Head 0-8 ft. 0-4 O G-28 0-637 0-8 621 629 1-2 614 622 1-6 607 614 The following table, compiled by Mr Fanning (Treatise on Water Supply Engineering), gives values for rectangular orifices in vertical plane surfaces, the head being measured, not immediately over the orifice, where the surface is depressed, but to the still-water surface at some distance from the orifice. The values were obtained by graphic interpolation, all the most reliable experiments being plotted and curves drawn so as to average the discrepancies. Coefficients of Discharge for Rectangular Orifices, Sharp-edged, in Vertical Plane Surfaces. Head to Ratio of Height to Width. Centre of Orifice. 4 2 1* i ! 1 i i r a X *" -- a _d Sa .= i. 6flT3 w>3 ~3 Ti2 15 3 5 2 ^ T3 " 2 Feet. 5 . *. 2 . *. P-, > = * ii f . i: ^ 5 *. d Z
- 5<2
t; t;
- i^
ei: 10 e o *-< LT: CN "*- o o o <= 2 6333 3 6293 6334 4 6140 6306 6334 5 6050 6150 6313 6333 6 5984 6063 6156 6317 6332 7 5994 6074 6162 6319 6328 8 6130 6000 6082 6165 6322 6326 9 6134 6006 6086 6168 6323 6324 1-0 6135 6010 6090 6172 6320 6320 1-25 6188 6140 6018 6095 6173 6317 6312 1-50 6187 6144 6026 6100 6172 6313 6303 175 6186 6145 6033 6103 6168 6307 6296 2 6183 6144 6036 6104 6166 6302 6291 2 25 6180 6143 6039 6103 6163 6293 6286 2 50 6290 6176 6139 6043 6102 6157 6282 6278 275 6280 6173 6136 6046 6101 6155 6274 6273 3 6273 6170 6132 6048 6100 6153 6267 6267 3-5 6250 6160 6123 6050 6094 6146 6254 6254 4 6245 6150 6110 6047 6085 6136 6236 6236 4 5 6226 6138 6100 6044 6074 6125 6222 6222 5 6208 6124 6088 6038 6063 6114 6202 6202 6 6158 6094 6063 6020 6044 6087 6154 6154 7 6124 6064 6038 6011 6032 6058 6110 6114 8 6090 6036 6022 6010 6022 6033 6073 6087 9 6060 6020 6014 6010 6015 6020 6045 6070 10 6035 6015 6010 6010 6010 6010 6030 6060 15 6040 6018 6010 6011 6012 6013 6033 6066 20 6045 6024 6012 6012 6014 6018 6036 6074 25 6043 6028 6014 6012 6016 6022 6040 6083 30 6054 6034 6017 6013 6018 6027 6044 6092 35 6060 6039 6021 6014 6022 6032 6049 6103 40 6066 6045 6025 6015 6026 6037 6055 6114 45 6054 6052 6029 6016 6030 6043 6062 6125 50 6086 6060 6034 6018 6035 6050 6070 6140 [HYDRAULICS, Table of Coefficients of Discharge for Rectangular Vertical Orifices in Fi(j. 25. 20. Orifices with Elges of Sensible Thickness. When the edges of the orifice are not bevelled outwards, but have a sensible thickness, the coefficient of discharge is somewhat altered. The following table gives values of the coefficient of discharge for the arrangements of the orifice shown in vertical section at P, Q, R (fig. 25). The plan of all the orifices is shown at S. The planks forming the orifice and sluice were each 2 inches thick, and the orifices were all 24 inches wide. The heads were measured immediately over the orifice. The formula above becomes, in this case, Q-c6(H-/ 4 ) ^/9c / ^. Height of Orifice : !!-/<, in feet. O-S-AS 656 787 984 1-968 3-28 4-27 4-92 558 6-56 9-84 1-31 0-66 0-16 0-10 P i Q | R | P Q R r | Q R |P Q j R OT,<)8 0-644, 0-048J 6;)4 0-GOt). 0-653 0-657: 0-1140 n-r:i-> n-<:. r >ri n-f:.=,u rvrui 0-66o 0-67 2 O f;74 O-f.68 0-675 fw;77 0-G9li 0-664 0-GSy: 0-687 rvfifu n-r;nn 0-666 0-688 O-(i i-) 0-710, 0-694 0-696 0-696! 0-704 706 0-fi94. 0-70<; 0-7()f- 0-641 0-676 0-674 0-673 0-67:! 6!<-_ 21. Partially Sup- 2-essed Contraction. Since the contraction of the jet is due to the convergence towards the orifice of the is suing streams, it will _ be diminished if for rErrz^ any portion of the edge of the orifice the convergence is pre vented. Tims, if an internal rim or border is applied to part of the edge of the orifice (fig. 26), the conver gence for so much of the edge is suppressed. For such cases Bidone found the following empirical formula? ap plicable : For rectangular ori fices, ( = 0-62(l + 0-1524 and for circular c fices, c e = 0-621 1 + 0-128 where n is the length of the edge of the ori fice over which the border extends, and p is the whole length of edge or perimeter of the orifice. when the border extends over , Fi - 25- The following are the values of %, or J of the whole perimeter :- n Cc c c P Rectangular Orifices. Circular Orifices. 0-25 0-643 640 0-50 0-667 660 075 0-691 G80 For larger values of the formulas are not applicable. Bornemann P has shown, however, that these formula? for suppressed contraction are not reliable. 22. Imperfect Contraction If the sides of the vessel approach near to the edge of the orifice, they interfere with the convergence of the streams to which the contraction is due, and the contraction is then modified. It is generally stated that the influence of the sides begins to be felt if their distance from the edge of the orifice is less than 27 times the corresponding width of the orifice. The coefficients of contraction for this case are imperfectly known. 23. Orifices Furnished uifh Channels of Discharge. These external borders to an orifice also modify the contraction. The following coefficients of discharge were obtained with open ings 8 inches wide, and small in proportion to the channel of
approach (fig. 27, A, Y>, C).
