Karl Kammermeyer N CONNECTION with the development of a design method for thickening tanks, the problem of tanks overflowing a t the perimeter wa8 encountered. The overflow processshould follow the lawsofweirflow. Lawrence and Braunworth ( 2 ) developed an equation of the Francis weir-formula type:
1 I
v
-
2.0
(La)'.*
(1)
It is hmited to weir heads of less than 0.03 of the tank diameter. The experimental work which formed the ? p i s of this equation was carried out on pipes up to a diameter of 12.6 inches; but as thickening tanks have much larger dinmetem, the extension of this equation to large tanks is questionable. The comprehensive correlations of weir data developed by Schoder and Turner (2) indicate that, if weir flow dab oan be applied to thickening tanks, m a t of theae tanks rue ovedowing at quite low heads. Ab, -ental data obtained on a 35inoh-diameter tank confirmed that the heads encountered at flows correeponding to thickening practice are rather low, mostly leas than 0.02 faot.
PUBLICKFR COMMERCIAL ALCOHOL COMPANY. PHILADELPHIA. PA.
An an8lysts of wailable data on weln flowing ateatnmily low head. permlts the .ot8bllshment of a simple .prutIen nlatlng the flow per unit length of weir with the hmd.of llquld wertk.weirbya.tnlght-line nlation. .Thlraquation Is rwommendd for mlr haads uptoO.03foot. From 0.03 to about I foot of ho8d a curve u n be ntted -,the 8vali8bledLt.. whloh a n s l m i l a i to the Fnnds wrir formula. Experimental data on 8 35-inch-diameter tank 8t very low heads fall In line with the Iitaratun data. A8 mostthickeningtankraraoperrtinginthislow h a a d r a w , it is bliwod that t h e n l r t l o n eatabilshed from the low head data oan be applied t o such tanks owmowlng at th. per1m.t.r. The dat8 presented am for the flow. of w8tm but should sewe as 8 0 1 0 ~ )approximation for many ofthe in. themioal plant pnotioea. dilute. cdutlons enwuntered .
The ph-nph wlmlo. N. Y..
AVAILABLE DATA
he Schcder end Turner macer includes mny contributions of other inveatigatora and conk& a great -o&t of eXperimental data on weka flowing at large an well ra very mall heads. It is believed that the data for the lower range of head8 oan be applied to the ovedow of tanks. Although the flow at the head8 which are d v encountered in weir installationsis such that considersble &&tion of the w e t Btreem takes p h (high velocity of approach with latersl wntraction), thie distortion beoomes 1 and diasppears almost entirely as the rate of flow beconbes all. In suppraseed mira there. ia no end contrsction. It is . felt that data on low heads mn he applied to t h e w - .
-
. . . ,
,
shorn v m w Durudinp
,
01c
.
t h l e k m I rMn In tk
m t n n n )plant i o w w r . Th. DWP Comp.w)
of water o m the rim of b k s . As the .weir diecharge is' influend by a great 'many factors, aucb =.Bharpness of weir, width of arest piece, velocity of approach, velocity distribution, eta, the um of s gDmeral equation, such 88 the Francin weir formula or a rncdi6cation of 'it, cannot be expected to give . great . RCCurSCy.
8Choder and Turner take up this point in coneiderable detsil and show t b t extremely large deviations will occur at low h 9 . Ab, they point out that many prewrutiona have be o h 4 e d in wnstrudjon and maintenance of the weir and auxiliary equip *&attain an accuracy of 2% in the measurementg,provided ..
March, 194.4
IN "D -U S T R I A L A N D E N G I N
RING CHEMISTRY ~.
a 'good 6dhration is avaibble.
.
A a m y of the data m t e d in thek paw revesk that the we of the h a i s 6 I m d a may rasult in deviations from about 20% at 0.08 foot of head to -W% and more at 0.012 foot. A t them very low heads the Fnrncis weir formula or zany other of ita type fails completely, as it predicts a 0ow helow heads of 0.01 foot w h , 88 a matter of fact, Bow over a weir dons not occur unless the head of water ia llpar or slightly m Rxe€aof thin d u e . F i m 1shown a plot of weir head H sgsinat Y/L, the volume rate of 0ow per unit of weir length The valuen used to estsblish the curves were taken from Bcboder and Turner's paper, and a nunmary of the low head data up to about 0.04 foot of head is given in Tabb I. The part of the curve above 0.04 foot of head 'RIYI drawn as a compoSite curve given by &boder and Tumer for sharputstedweila. , Theplot shown that, in the low head range, two t y p of 0ow occur with a reswMhly well defined change a t about 0.03 foot of head and a V/Lratio of 0.02. Thin change in flow a m wall with Lindquist's work (91, which showed that the sheet of liquid clings to the face of the weir until a head of 0.029 foot is resohed and may become free at a head of about 0.036 foot. The portion of the curve below 0.03 foot of head is plotted on a larger scab in Elgum 2, together with the Francis weir-formula curve. Tbe loweat value of Schoder and Tumer's data is a t a head of 0.0133 foot, and it was felt that points a t lower heads should be determined. E%PERIYLNTAL DATA
Head measurements were carried out on a tank 35 inch- in diameter sud 12 inchea deep. Resdings were taken a t qix looations ofthe periphery. The tank was provided with an overfbw mllecting trough, and the o d o w i n g water was measured by weighing. The uest mnaiated of a strip of tinned sheet iron about '/a inch thick Sasrpened to give the conditions of a ahupcreated reir. The feed inlet (*/,-inch pipe) was lmted a t the center of the tank about 4 inches from the bottom and & k e d upward. In -e C I L B ~a~ g i b stilling well was used, especially in h i g h head runs. The feed wm obtained from a c o h b h e a d tank to eliminate line &ctuations. Observations of the fluid heads were made with a cathetometer which permitted resdings accurate to 0.06 mm. The head wm observed by focusing the cathetamater on a strip of metal held agaiast the c m t inside of the tank. R e p t e d trials in thin manner enable the operator to observe the head without the strip at the proper locatiobthat is, at a point just back of the weir edge-and permitted c l k agreement in repeated readings. &a0 MEASUBEYENT~. LindquiSt (8), in a discussion appended to &hoder and Tumer's papor, states that flow over a weir w i l l not occur with water at 11" C. at B head less than 2.8 mm. A number of head measuremate were carried out to observe when flow over the edge of the tank would occur by suwesively adding ~ m a Uamounta of water to the tank. It was found that flow did not begin until a head of 3.60 * 0.05 mm. ( 0 . m foot) of water was obtained. The temperature of the water in theee tests wm 60' F. (15.58' C.),and as the extent of this static head is lrrgals determined by Burface tension, the agreement with Lindquint's value is reaeonably good. It should be recogniaed, however, that whether or not a Buid will 0ow over the weir a t very low heads will also depend on the interfsoiel tansion bc tween the we& edge and fluid. Low HEADMEAS~EMENT~. Ten rum were made cnverhg the range 0.0107 to 0.0146 foot of head. Table I1 nwunmum . theexpenmental mults, and Figure 3 shown a large scale plot of the points together with the curve for low brarl v r l m a from t h m Arts. nf
TABLE I. LOw-€hm WEIR DATAWY
n. Ft.
cu.
TURNER@)
V/L
Ft./E/ec. Ft.
~ O D E R AND
'
&marks of Ex rimenten (8b.r. crwt UnieM f&d OtharniaO) Part or old orat. sohodor(L ~ o r n ~ . aariac B0Ikd-b- &te, amsf& d t r i n e d Bchcdar & Tumor. wia D
0.08~
o.oaoi
0.0281 0.0818
0.0176 0.0216 0.0246
8ahoder & Turner,aeriw E
0.0878
0.0181 0.0247 0.0275 0.0178 o.oaa9 0.0012 0 . m
Sohcder & Turner. .uiw G
0.0113 0.0267 0.0119 0.0168 0.0861
8ehcder & Tumer.seri- H
0.oOW
&hcdar & Tumer.setieaJ
0.Oasr
0.0.0898 0.0288 0.0342
O.oZo7
0 . m 0 . m 0.9119 0.m 0.0810 0 . m 0.0210 0.0840
o.oaa6 0.-
0.088a 0.0170
0 . m 0.08E4
0.0235
o.oa84
0.0252
0.0110 0.mbo
0.0148
0.0567
Bahcdsr k Turner. acriaa I
&had- & ~ ~ s r . . e r i a i
0.0136 0.0108
O.MQ
&boder & Turner..eria K
0.0870 0.0188 0.0276
0.00.36
( l o b i & & Turnor.seri-
0.0282
0 . m
0.0087 0.0173 0.Onl 0.0117 0.0561
I
0.0210
Bahcdsr & Turner.. . r i a M 0.0198 0.0244 0.0013 Bchcdar (L Turner.=rim N 0.01~ 0.0180 0.0236 0.Mewr and 8ss. set 1. seriea F O.Mw7 Joone..MeaA o.Mo88 O.Oo9901 Jonaa.&ricaB O.Olon6 O.onO6 O.OOi3108 Crest rounded 0 . a in.. Jona. a s r i r C o.om362 0.01W Crest rounded 0.0120in.. Jones. eriu E 0.01029 0 . w 0.01035 Crat rounded 0.0165 in.. Jonw, asriw F
0.0201
0.01116
0.0175
0.007447 Mhvp orat, Jona. n a i e a H
0.0146 0.om 0.0347 0.0123
o.om
0.0894 0.0842 0.08W
0.OaOa 0.0808
0.0301
o.om1
0.0891 0.0185 0.0804
0.0.02Ss 0.0363 0.0234
0.0810
0.0045
0.01960
0.02a70
eat rounded O.Ml5-i~.Sonam. e a r i s G
o.oas0
o.oim
0.0212 0.0316
0.01067' &ugh b d o r erwt, Weber. .arise I1 0.011)88 0.01243 h u h below orwt. Webe.. ncriea 111 0.01869
0.08808
0.0249
0.0800 0.0891 0.0186 0.0277 0.0895 0,0172 o.oa94 0.0872
0,02636
0.02664
0.008769 Rough below m-t, Weber. Series IV 0.01776
0.Oma
0.00767 0.01888 0.02649
Rough below orest. Weber. mriw V
-
PLOT OF H V S V/L
H*FT.
V=CUFWSEC.
LIFT.
about 15%. EVALUATION OF AVAILIBLE ?AT*.
The curves which fit the availsble
HEAD FLOW
"
,,
.
n be expressed em-
pirically by the following equations: CASEI. For flow at heads up to 0
V f L= H
- 0.0105
(2)
This equation represents the solid curve below H p 0.03 in Figure 1and the solid curvea in Figures 2and 8. The e x e e n tal points reported in Table I1 and plotted in thasa frgurea 88 triangles all lie a b v c the empirical mWe. It must be membered,however, that this curve weedetermined by appmimately thirty& points reported in'Table I at heads of less than 0.03 foot. CASE11. For tlow above a head of 0.03 foot of water (this ease holds to about 1.0 foot of head, and above this value the Fmn& weir formuls should be sUitsble): V/L 3.2 H'."' (3)
-
This epustian represents the solid curve above H = 0.03 in Figure 1; the dashed line m e in this 6gwe is a plot of the Francis weir formula for snppregsed weirs.
.
.
,
,
..
ConaiQeriqg the many factors which enter into w w flaw, .it$ believed that the corralntiow presaoted can aatidbe W$ in enghwing calculatjoas~. ; All of the data presenWand oited am for h , & w Qf w s k , but Bhould 5 3 ~ e0a a d o s e - a p p ~ tion for many of the dilute solutions encounsred h che&d plant p ~ c t i ~ e s . ... , , AqKNQWLEDGMENT
'The Bxperimental work ws'a carried out by R. Bowditch, Q. F. K e y , R. P. Sphtig, and E.W:Vesey, and the E h W & data were largely correlated.by R. T. in partid 'f& fillmppt..of the repuirements of a'senior a~urseinchemidsleasineering at Drexel Imtitwta of Te~hnology.
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NOMMCUTURL
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