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40
[DISCHARGE or LIQUIDS
HYDRAULICS


not done; and such a bell mouth may also have the form of the con- ' C oejicients of Discharge from Circular Orij'ice r tracted jet. Fig. 19 shows the proportions of such a bell mouth or bell mouthed orifice, which approximates to the form of the contracted jet sufficiently for any practical purpose. the coefficients with different heads.

Temperature 5 1° to 55 °.

iHead in

Diameters of Qrifices in Inches (rl).

h 1 I§ II§ 1I§ i2'2§ |2;|2§ | '§

Head0ver0rifice, inft.=h 1 -66 I-64 11-48 55-77 337-93 Coefficientof velocity=c, , . -959 -967 -975 -994 ~994 ICoefticient0resistance=c, . -087 -069 -052 -012 -012 As there is no contraction after the jet issues from the orifice, c¢= I, c=c, ,; and therefore

Q =ciw/ (21:11) =w~/ {2gh/(1 +c, >}§

20. Coejicients for Sharp-edged or virtually Sharp-edged Orifices.-There are a very large number of measurements of discharge from sharp-edged oritices under different conditions of head. An account of these and a very careful tabulation of the average values of the coefficients will be found in the Hydraulics of the late Hamilton Smith (Wiley & Sons, New York, 1886). The following short table abstracted from a larger one will give a fair notion of how the coefficient varies according to the most trustworthy of the experiments. For such an orifice L. [ lVeisbach found the following values of feet I l

Coefficients (C)

1-0 -613-612 612 611 '6I2 611

-604

-608 -609

-605 -605 -606

-603 -607 -605

-604 -607 -605

-604 I -604 -60

1-50 -610 -612 -6II -606 -610 -607

1-75 -612 -611 -611 -605 -611 -605

-75 -616 -614 -616 '6IO -616 -612 -607'-607 609 2-00 -609 -613 -609 -606 -609 -606 5

I-25 -613 -614 -610 -608'-612 -608

The following table, compiled by ]. T. 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 Coejicient of Discharge for Vertical Circular Orijices, Sharp-edged, with free Discharge into the Air. Q =ca»~/ (zgh). discrepancies.

Coejcients of Discharge for Rectangular Orijices, Sharp-edged, in Vertical Plane Surfaces.

Head Diamefefs of Orifice' éiead tof Ratio of Height to Width. 1

m€:2;L;'; 0o;0 '02 | -04 | -10 I '20 ' -40 1 -60 I I-o 4 2 If 1 % é i A 1 Orifice' Values of C. A A A -5

213 " .657 23; '° ~~ ~~ ~~ reef. 25 5? .5 as -5 55 if “~;£§ 0-6 -655 -630 613 601 -596 588 . “lf 'Sf "li 'Qi 31 of si 0-8 -648 -626 -610 -601 -597 -594 -583 '—I-0 -644 -623 698 699 593 595 '591 0-2 — ~ - ~ - ~ - ~ ~ ~ ~ ~ ~6333 2'0 '632 '614 004 599 599 597 '595 '3 - ~ - - - ~ 6293 '6334 4-0 '623 -699 602 599 593 597 -596 '4 ~ ~ ~ ~ '6140 6306 -6334 8-0 '6I4 605 600 598 597 596 -596 -5 . . . 6050 -6150 6313 -6333 20-0 '60I -599 596 596 596 596 -594 -6 . . -5984 6063 -6156 6317 -6332 -7 . . -5994 6074 -6162. 6319 -6328

At the same time it must be observed that differences of sharpness '8 » '6130 -6999 6032 '6165 6322 '6326 in the edge of the orifice and some other circumstances affect the '9 - - '6134 '6006 6086 '6168 6323 '6324 results, so that the values found by different careful experimenters, 1'0 - - '6135 -6919 '6090 '6172 6320 '6320 are not a little discrepant. When exact measurement of flow has I 1'25 °6188 '6140 -6018 -6095 '6173 6317 '6312 to be made by a sharp-edged orifice it is desirable that the coefficient 1 '50 °6137 '6144 '6026 6100 '6172 6313 '6303 for the particular orifice should be directly determined. 1'75 - '6136 '6145 '6033 6103 '6163 6307 '6296 The following results were obtained by Dr H. T. Bovey in the 2 ~- '6183 '6144 '6036 '6104 '6166 6302 '6291 laboratory of McGill University. Q50

2

Coejicierzt of Discharge for Sharp-edged Orifices. 2-75 -6280 -6173 -6136 -6046 6101 -6155 6274 -6273 3 -6273 -6170 -6132 -6048 6100 -6153 6267 -6267

  • F0¥m 0f 0"f1C@- 3-5 -6250 -6160 '6123 -6050 -6094 -6146 -6254 -6254

S Rectangular Ratio Rectangular Ratioi 4 6245 '6150 '61 10 '6047 6085 '6136 '6236 '6236 quafe- of Sides 4:1. of Sides 161. 4-5 -6226 -6138 -6100 -6044 -6074 -6125 -6222 -6222. He? "1 Ci | ' Long Tm 5 '6208 °6124 -6088 -6038 6063 -61 14 6202 '6202 cular. Sides DIG- 1-0112 Lfmg Long Sides angular. 6 '0158 '6094 '6063 '6020 '6044 '6087 '6154 '0154 C, ,, C, ,| gonal Sides ig? Siqes hor# 7 -6124 -6064 -6038 -601 1 -6032 -6058 -61 IO -61 I4 "°f“fa1- Vefflcal- zO, ml "e"'fa'- zoutal 8 -6090 -6036 -6022 ~6010 -6022 -6033 -6073 -6087 3 » 9 -6060 -6020 '6OI4 -6010 6015 -6020 6045 -6070 1 -6 -6 -6 -6 6 -6 6 -6 6

1 I 62° '627 '628 '642 °643 663 '664 '636 1; -6323 -egig -ei-ii; -egii) cgi; -cgi? 633; -6262 Z 20 -6045 '6024 '6012 -6012 '6014 -6018 6036 -6074 -5 8 -6 8 -6 -6 -6 6 -6 6 -6 8

6 1 607 '614 '616 '626 '627 637 '637 62° -62114 -6234 ~6iii; -cgi; siiis -633; eiiiiii -629; 8 '000 '0I3 '614 '023 '025 034 '035 '019 .35 -6060 -6039 '602I -6014 -6022 -6032 -6049 '6IO3 10 '005 '0I2 '013 '022 '024 032 '033 '0I0 40 -6066 -6045 -6025 -6015 6026 -6037 ~6055 -6114 ii 45 -6054 -6052 -6029 -6016 6030 -6043 -6062 -6125 I6 603 mo 6 62O 622 630 63O 6 7 5o -6086 -6063 -6034 -6018 6035 -6050 -6070 '6140 18 -603 -610 -611 '62O -621 -630 -629 -616

20 -603 -609 »61 1 -620 '62I -629 -628 -616 § 21. Orifices with Edges of Sensible Thickness.-When the edges of The orifice was 0-196 sq. in. area and the reductions were made with g=32-176 the value for Montreal. The value of the coefficient appears to increase as (perimeter) / (area) increases. It decreases as the head increases. It decreases a little as the size of the orifice is greater.

Very careful experiments by I. G. Mair (Proc. Inst. Civ. Eng. lxxxiv.) on the discharge from circular orifices gave the results shown on top of next column.

The edges of the orifices were got up with scrapers to a sharp square edge. The coefficients generally fall as the head increases and as the diameter increases. Professor W. C. Unwin found that the results agree with the formula

c =0-6075+0-0098/4 h-o-0037d,

where h is in feet and d in inches.

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. 20). The plan of all the orifices is shown at S. The planks. forming the orifice and sluice were each 2 in. thick, and the orifices were all 24 in. wide. The heads were measured immediately over the orifice. In this case, Q=cb(H-h)~[{2g(H-{-h)/2}.

§ 22. Partially Suppressed Contract-ion.-Since the contraction of the jet is due to the convergence towards the orifice of the issuing streams, it will be diminished if for any portion of the edge of the orifice the convergence is prevented. Thus, if an internal rim or border is applied to part of the edge of the orifice (fig. 21), the convergence f0r so much of the edge is suppressed. For such cases

G. Bidone found the following empirical formulae applicable:-