# Page:EB1911 - Volume 14.djvu/62

50
[DISCHIARGE FROM ORIFICES
HYDRAULICS

Bazin arrives at the following values of ma-

Coejicients of Discharge of Standard Weir. Head h metres. Head h feet. m 1 0-05 -164 0-4485 o-10 -328 0-4336 § 0-15 '492 0-4284 Q 0-20 -656 0-4262 1 0-25 '820 0-4259 § 0-30 -984 0-4266 0-35 1-148 0-4275, 0-40 1-312 0-4286 0'45 1-476 0'4299 . 0-50 1-640 0-4313 0'55 V304 0'4327 0-60 1-968 0-4341 I Bazin compares his results with those of Ftele and Stearns in 18 Y 77 and 1879, correcting for a different velocity of approach, and finds a close agreement. I nfluence of Velocity of A pproach.-To take account of the velocity of approach it it is usual to replace h in the formula by h-I-au*/2g where a is a coefficient not very well ascertained. Then Q =#l(h+<»1¢'/2g)~/ l2g(h+au”/2g)} =#lh' (2§ h)(1 +fw2/2gh)3~ (2) The original simple equation can be used if m =;i(1 -l-au”/2gh)% or very approximately, since 142/2gh is small, m =/-(I +%-w”/2gh)- (3) Now if p is the height of the weir crest above the bottom of' the canal (fig. 52), u=Q/l(p-l-h). ""~ ~—. ' Replacing Q by its value L i in (1) rf—'-=Q2¢zrz-;t.~;@>”* H

m

"¢i"" P x“.: so that (3) may be written 4

'ge, ia s m=~u+/-th/<z>+h>s21. <0

```'~ ..c
```

}— - . Drowned Weirs.~Let h WW//#yy/M///5 (fig. 54) be the height of FIG head water and hi t at of ' 54 tail water above the weir crest. Then Bazin obtains as the approximate formula for the coefficient of discharge fl = I '05m1lI +%h1/1>li/ lfh '° hx)/hi, where as before ml is the coefficient lor a sharp-edged weir in similar conditions, that is, when the sheet is free and the weir of the same height. § 48. Separating Weirs. - Many towns derive their

"';"': {e-t-:¢;-*é f § // ' =u[I +0°55lh/(l>+h)l”l-Values of p- Head h metres. Head h feet. p 0-05 -164 o-4481 0-10 -328 0'4322 0-20 -656 Q°4215 0'30 '984 0'4174 0-40 1-312 0-4144 0-50 I'640 0-4118 0-60 1-968 0:4092 V An approximate formula for it is: /l=O'405~i-0-003/h (h in metres) / fu . f Z %1 § ' § /, s s water supply from < < - < . : "' “ streams in high moorland districts, in which the flow is extremely variable. The water is collected in large storage reservoirs, from which an uniform supply can be sent to the town. In ff? si e '§ “§ s § FIG. 55. Plan, of Ccwt Iron Key /4=o-405-{-0-01/h (h in feet). I nelined Weirs.eExperiments were made in which the plank weir was inclined up or down stream, the crest being sharp and the end contraction suppressed. The following are coefficients by which the discharge of a vertical weir should be multiplied to obtain the discharge of the inclined weir. Coefficient. Inclinauon up stream . 1 to 1 0-93 n sy 3 to 2 3 to 1 0-96 Vertical weir .... . . 1-00 Inclination down stream . 3 to 1 1-04 3 to 2 1-07 1 to 1 1~10 1 to 2 1-12 I to 4 1-09 The coefficient varies appreciably, if h/p approaches unity, which case should be avoided. In all the preceding cases the sheet passing over the weir is detached completely from the weir and its under-surface is subject to atmospheric pressure. These conditions permit the most exact determination of the coefficient of discharge. If the sides of the canal below the weir are not so arranged as to permit the access of air under the sheet, the phenomena are more complicated. So long as the head does not exceed a certain limit the sheet is detached 5%//¢'r;' //¢/;;<e/f;/tgegg.;

9"=' 5 =;5'f-3'f¢'i'~§ 3?<f'~'3»3Z1»~3“ '¢ f ¢=zs3e.==r<ss~.-¢¢?2t€'¢>;ias-fi-ef'/% sggfgr.-if g;~'1.°f.;9r~1;»a=.-feafw V. /7/ 4 as:—Arsf if.-x-f.="»§ t>= .9 ff W/ /A why .R-1-"H-: '< ” "@§ < 1' 1 f f"" war LKQQ, 7 ¢.'.. Edgy /V Li .1 wi-44, L- ~ - '1. ”;, .=;— f /', N//7 ~//" “' - %"f@'?r,

150/////;, ,, , 57' fx '/ '/ /4, .Z A, T/Q" 1-7 f// W/A %% ///” %//5 / /» - ~ / /4./3/.mn / M * i:»'°;'L.§ N 'F *csv* V f 1. ...s-..<=.;; -=~ . ///f/, .>. azrfw 11,1-y.q°, ;':£-T.; V Tr; ix* - ':ie"G£; 7 . - ”, /4.=':»;;{;;, g “ »» 'J 'r. Vi.. ~ 1 J <:MU 'r -8 C., ».. 'Y Q: =& Q-, sgfysg-Q2-:ig ~, > .- = ..<- s.e.° § ", -UH -

W Z/ 2 ~, ,, -, '° fr; 'nh XY /tl 9 / / / / '°., e§ ¢.' 5//f @/”/// > ', 1. 1” / 1/ // / / f/ / /., / ge, ” . — /5°-°, , / /i / /

H ¢-vii; 5/ / ////Q/ § / 'Q /':bf-H" sr/// /9 /'/'/

```/ °.-sw / / / 5 5
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§ "° ' //A 2 3.

```U, ” 'l W /7 /, »°:", § f,
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W c/ / .es

• , '§ 1'////Q /.fe es

pw »¢=¢-, ,~/ / //, as ° //{, -»s'..s¢, Q /s, ,{) > - .- L . /, f, - e, //. ., -. me-“;- “=“..?, ,.' .f..;'§ >;/ //~ / -///., /I 1 f/ /, y, -;f-¢“£'e, .i-0. m~'— .M wg-.r =...'-»1a, / ////-' /, , f .~».», :, »;, - .e-;°qsif

• »'“%s.f. 2? !fl '-, // /6 /Qi//, j~*>»-»;-5 vi(

/ of .~ = ff' A / fs* Wi" / / '§ \$~"' ' SEM/ //'”/f/ //4 V A "'; [;LQ*@i;.: 142.-'J 5.6/Ze, / /°» Q-.', :1";.~s . Ts.;..="¥»l'lWg/I § “, ~Ig2-i5 .f:i'¢-1-1-". .';.—f:="*3:=?' .gin-* ~ *J-'“¢.>l 'i'€S ww .ws ":~1~*'.'f'=¥rt~1?° ~'-2'<€°"'>¥ he -e=7-*"-'silos, —fr, -r-°\$*r:~, .t2 “Ff

• .s—J~'°=;-:-+1 {»*f;~'§ .=Sf-:~;:¢f~° r”.¢~s~ ~;~. a;'~>'3ie—www 1 'l“"l~1

-cs -i1§ >'r<»e'°-.J .t ~,1¢~=»=.~, \$v ~:':, 'a;'.-' -'.=fg.». »- -fi . ~ ~ - . —: 'J-f- wni-s 'I°-2..—.¢r—f'“~"—f=-=§ ?~.- f'-fm 5-“;%;i-; |, ,,5¥-b Rr mtg;-515-5-, fi-F:ss-}%1::C "'~':'Fft'§ :, ;§ L'53<§ 2: Agrffa m¥, mfh5' 3, ;, 'a;&g, emo s metre e, L.r...;, , w¢, ,~ 13, ., . .g FIG. 56. such cases it is desirable to separate the coloured water which comes down the streams 1n high Hoods from the purer water of ordinary

flow. The latter is sent into the reservoirs; the former is allowed