£ f ! V - . t .

bos c f ? r i !l r c i ^ , l Tv a,i\s Imp r : ; > t ~f/ k t:Xu

tr 'v arch vp. 2 ih - i t '&n apparatus ' wao warded,- .-tbs f lew- Xx*om.V.O-.-a .

.w;i,,U cccili t r y •,c tiroe ily . u®; ttia/feacl #"';... - I t is afcetm in -

■ilia;- id s ijD t i t t ar. c i ilv.zi r£ id© t; po ^

can ; be mcl© ,to approxi??*i<» w ry c Xosely indeed tea--s.- S3 ire i , %% ■ -

XI m fo r & given raepp o f m ud H % s u ita b ly " .the

v&lues o f ;p# .-q and r *■ fO a '-f irs t' term m n tx* supplied Ij$. &m '

o r i f ic e , or i t s © b iv a le n t# ' d lso t^rg lng under tlse •ear# bead

ai* fch© w eir and the mast too tmmm. m n t»^provided % a ••'

s u i ta b ly afaoaeis w e ir # " - :: ; :

fm thesis £lx®m*itm& tbs - &» serai- EBthod' o f c n-H ctln g

tm ®%%®rlmnb® and the sy®eiul |a * u |« '• taseclV t?o' detaraio©

the f i la e s o f q a 13d r in the ■l^eio ''or- n ] , -q

wfere a ** the flow in eusees • and I! *» the' 3^*0 I n ’i W t j -

eSperihBiits were imde various^ M rs "of §>p the urf-te o f ■•'

s Io -g o f each weir, wide .to .the v e r t ic a l# - -f! iw w 3xaj o f r can'

le 1 mm& M.& simple fu nction of $ -but :q'wss found to to

a -plied care complicated fun--tl©n ^nc! 1b lo s t road o f f from a

graph* Tlo foriaila© are .oXfcl&ad le f:; lw Its secure ia w ith * •

In &t Irpafc 2% over aest o f tbs' rsn©i o f loads# . _

&»98rg # Dour ley and Criisp c&nduotod w ith -

tra |,©aoid.al weir a but with only p o s itive ' P l m s t f fc' {X#e# "’

■when the aide a alopo outwards)* .f my © w ived t .-'ferEisla .-■ '

t *n (where b » ttm w id th o f ■

thn$ " s i l l ) h» j tab les arid tvnylm are . given c o t^ r ln g tidis ■■'■

it rc a b . w ltd cd- re s u lts of. the present ro&e^rch# :.'

fBm f in a l deduction was th a t a w e ir !:^¥f,n.s bs=o*32f.-"feot

# ** « 1 S 14* «, id: 5a. w ith a e l r m la r 0r . l f 1001. or i t s @quiv~ '

a le r t ,a s x m t ^ « c « y * 1 0 3 5 3 ^ would r i w s d io e m r w ':

mfy c lo se ly d ' o ^ U o a i l to I I# tap to 0 w ir e o f H « 6 1 nclmo# i ■■■■■•.-■■• ' ■.

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¥ “\ /' r, C\ ’ '

There t n m been m n j experiments to determine .'the flo w

in s r rec tang u lar weirs and t r ia a & t l r r notches from.wMah

fo r mu la a bev® been derived which give'., wary good re s u lts $ w

th e 'p a r t ic u la r range o f each se t of experiment®# .-.:Jpata about; -

Symmetries! trspesold& l w e irs .is however very' scant w ith the

ekeeptlon of ' t foe sp ec ia l case o f the O lp p o le tti weir' and the

results- o f Hessra Gourley and €rlmp*Sftexperlmants# f b : was

w ith the Idea o f g e ttin g some, formula. In c lu d in g a fu n c tio n of.

the angle o f slope o f ttm side# t h a t . the present re soars h. was

undertaken*

The **ideal** formula fo r th e flow over a symmetrical

t ra p e a o id a l w e ir i s 4 ® c jS g K3/ 2 {.|S 4 ^ s t e n * ) where-,G

is~ the c o e ff ic ie n t o f d ischarge* 1 is the he&d o f .w ater* b

is ' the w idth o f the w eir a t i t s base and & is the in c lin a t io n

o f the aides to the v e r t ic a l* th is formula, is of. lim ite d use

o n ly* f o r the reason th a t 0 is . not found to remain' constant

when H is varied# M m n B&rr found a s im ila r discrepancy

in the ease o f the tr ia n g u la r notch and accord ing ly advocated

using a graph fo r f in d in g the value o f 0 fo r every, value ©f H

In fa c t i t is probably la rg e ly due to th is .varia tion , i s 0 l a ­

the tr ia n g u la r n o tch .th a t a s im ila r v a r ia tio n occurs 'in the

©ase o f the tra p e zo id a l w eir# ■

Messrs (Sourley and Crimp in th e ir paper* flow o f ■ '

water over Sharp Edged Ho to has and i-Hrs*1 describe experiments-

* Vb l* CO# p* 388 Minutes o f Proceedings o f Z#C«S*

w ith tr&pezoiclaX w eirs o f crest lengths 3# 8# 12#.: 18# 24 and

■BS inches and aid©- slopes o f 5 (v e rt# )# ' 3 * 'S. sn d \2 -to .1 --out*. ®:,;

'wards w ith head© ranging from 0*15 to 1*0 f t * . i t the ©am©. ..,'.

'%%m ttm f were concerned w ith the flow error■■■ tr ia n g u la r

■ fo r wliieh they reeorasnded the- fo r m ic % » E H ^*^ where-. E 1® .

a ■ constant depending cm S* and O* The advantage © la ire d t o r

'..the- index 8*47 instead, o f 8 #Scrwas th a t w ith the fo rm er a ■

m iu # cou ld b® found f o r ’ g;w h ich r c m im d ' co n s tan t wheh-H ’:'.

'■ v a r ie d * T h is ■ suggested u s in g the in d e x 1 #47 v im toad o f 1*50 ■■■.-■

f o r the re c ta n g u la r w e ir a n d 'th e ir experim e'nta e o n firs B d th is

th e o ry * I t is in te r e s t in g t o ’ m t© th a t Francis:-; I n 1851 came

to : th e co n c lu s io n th a t the- i i t « should- be- T#47;vbttb :la . ia r

re v e r te d to the' va lu e 'of: 1*50 o w in g ’W ■•'the ineroae .o 'd":-fao liity"'..

o f m lm lM t io n * T h e ir :b » s lc f o r m la th e ro fo ro ’'-'--hoi©a'iiie 4®

* » E lba1 *47 ♦ K g # *47 « t w * Kx la a eoBatant a«d :Kg is a

cob®taut fo r any ©no value o f -9 and in fa c t equals- K$ tan 9 *

"'■■They then found th a t i t was d i f f i c u l t to work th is '.fo rm u la -'

: for'-the "reason th a t in" the -esse o f a re eta na ile r.' w e ir (when

■ the; M ta r s ’ beeemes aero) $ d id not vary d ir e c t ly w ith b ■ '

when !i was leapt constant a.nd © m u tu a lly they oast.-the''‘formula

%'■■■'«#■ from fu rth e r ' exeat ha t ie s ' o f th o ir

■ re s u lts th e y - fo u n d - th a t 'a sh o u ld ha w the va lue l #nS-and so

" t h e i r ( f i n a l gm m rnt. form ula" beeane, ■ a f te r -d e te rs d n in g : the

-.values o f % .and Eg

; % » > ^*-48 tan g rli2 * ^ '

■'and they ’claimed th is to give resu lts ..aeo u r& ta ly w ith in® & 2fs*

This fo rm in 'o f course* is designed- to apply eq u a lly w e ll to v

rectan g u la r weirs# tr ia n g u la r notches and tra p e z o id a l w e irs *

(n '

I t is u s e fu l to observe* In th e above e x p e r ls n h ts * t i n t

1&»ears g e u r ls y and Crimp used re c ta n g u la r w e irs § inches to

$ 0 'inches w it® f o r d e te rm in in g the flow ® * u s in g W@mm Siawaid

and |o o g » o ll* » o b se rva tio n s a t the Boise f r o je e t o f . the- W.S*

B e e le v a tio n S o rb ic# mhmt the year l i l l * Experiiaents a t 'B o is e

si® o gave da ta abou t a- 4 t l w e ir and these agreed w ith the ■

r e s u lts o f the in v e s t ig a t io n by H tssrs G ourley and d r l» p * I t

is ' ve ry d o u b t fu l I f the f o r m la ' j -

*1 ** + 2 *48 ta n §

w i l l gin® r e s u lts a c c u ra te ly w i t M r p ^ l ^ ow ing to ..the .-fac t

th a t r e s u lts c a lc u la te d fm m I t d i f f e r from t h e i r experlissnfcaX

r e s u lts by as m $h as 4 |I* These d iffe re n ce s . .e&.nmf ,be passed '

ove r as e x p e rim e n ta l e r ro rs un less the r e s u l t s / o f each, p a r t ic u la r ■

e x p e r i» » n t a re cons idered and the ^regae11 re a d in g s m 'Jested

a f t e r In s p e c t in g a graph o r by seise o th e r means*.' It,. la a ls o

no te d t ha t e x p e r lm mt» were no t e© nduote d to te a t the f o rn u la ;

I n the ease © f w e irs w i th the s ides s lo p in g inw ards i# ® * when ]

$ & n e g a tiv e * I t was w i th the Idee o f g e t t in g a fo rm u la * i f «|

p e a s !h ie * o r f a l l i n g w h ich * a m th o d o f c a lc u la t io n * w h ich ... '.;!

would g ive r e s u l t s very c lo s e ly approaeh ing those o b ta in e d by '

exp e rlsen b and w h leh wmuM sis© a p p ly when # waa N ega tive# ' . J

fbase re s u lts were a ls o re q u ire d . in i n in v e s t ig a t io n ' to d e s ig n

an appa ra tus ih s f lo w fro m w h ich was d i r e c t ly i r o p o r t lo n a l. to'■ ■■ !

the bead# The va lue o f such an appara tus is obv ious a n d -m a n ifb Id : !

one .advantage is th a t f lo w re c o rd in g appara tus i s the .ifto re '■''j.: !

'e a s ily designed and co n s tru c te d mad a n o th e r is : th a t, a v a ry in g j!. ’ {■-

■ i '

f lo w can tm e a s i ly s p l i t up in to tw o* the two parts- a lways j

te a r in g &om d e f in i t e r a t io to each © than* I t was m t lm d tb e tt' : ?____________________________________________________ - t. _J>

a fo rm la o f the type <4 * pStV& 4- q # /^ 4 r # / ^ could* fo r

mtsy d e f in ite - rang® o f E be made to olm mXj approxim &te to a

s tra ig h t I I m « The f i r s t term com 14 fc© supplied by the flow

from 'an o r i f ic e and the- second and th ird terms to gather ecu Id

probably be supplied by a traps&eld&l w e ir* To do th is o f

course fu rth e r data about the la t t e r was necessary*

I t mm dec ided a f t e r sosoe th o u g h t to adop t

as tlas b a s ic fo rm u la * The q u e s tio n o f us ing -•Ind ices- 1*47 and

2*47 was cons ide red and re je c te d * i t be ing hoped th a t seme

f t i r l y oonciae fo rm u la 's lig h t be o b ta in e d u s in g 1*50 and 2 #$ o j

i f t h is hope d id no t m a te ria l i s a then I t would p robab ly be le s s

cumbersome to read o f f the va lue * o f % and r from graphs r a th e r .

than have to work out f ig u re s ra ised to th e powers 1*47 and'2 *47*

fiim- n#jct q u e s tio n mm the method to be used fo r d e te rm in in g

the f lo w o f water and i t was considered best -and also moat

.eoavenient to use a s p e c ia l ly sharpened 90 #¥ n o tc h . The- f lo w

was computed u s in g l r * James B a rr*» graph f o r the. value o f 0

in the fo rm u la % ** 01®/^*

Thu appara tus co n s is te d o f two tanks one a bo to- the o th e r

as shown d ia g ra m s t l© a l ly i n d raw ing Ho* 1* W ater was

'd e liv e re d by a c e n t r i fu g a l pump from a Xargt re s e rv o ir i n the

f lo o r to the to p ta n k w h ich con ta ined tbs- V- notch*, the f lo w

b e in g re g u la td d by a s to p v a lv e . The w a te r flo w e d over the 7

no tch In to th e . low e r ta n k and the n over the tr& p e s e ld a l w e ir

back in to the r e s e rv o ir * Each ta n k had two b a f f le p la te s

and ths> f lo w o ve r the n o tch and w e ir was found to be p r a c t ic a l ly

f re e from surges# The e x p e rim e n ta l w e irs were c u t o u t o f a '

» ^ ^ i ^ ^ ^ i i 1ftffWihhiffiii'rrtMWWWiiMr»>iinin " ~ . . . . . . .r : . . . .......... ’■"* j

{ $ ) ■ . . ' ;

a *1)30 p la te * - th e in s Id© edgo* Im ping b e’en c a re fu l ly . sharpened* '-

th e f i r s t experim en t was w ith 0 a t i t s g re a te s t nega tive value

a f t e r w h ich i t was found p o s s ib le to c u t p ieces o u t o f each

■aide i n rea d ine ss f o r the nex t- 'e xpe rim en t* th e base o f the '

w e ir b was a lw ays- w r y - n e a r ly 4 inches a n d 'tb s values' o f f used

m re '-~ 1 5 **6 *» «7 *« 4*» , O ** +©**80* and « 3 0 % 0 * 'W a te v t

values be in g ea le u la ted f r o i t l in e a r m a s u re m h ts i n each case , |

fbe,;,r«Bge o f head ove r the w e irs was a p p re x l la te ly from 1 /5 W

t o '3 ^ * - Am the w e ir opened o u t i t was n a tu r a l ly more d i f f i c u l t

:;to - 'g e t ;fche h ig h e r heads ow ing to th e 'f lo w te ud i rg ' t o ' : be eem |

tu rb u le n t and th e l l is t t e d 'd e l iv e r y o f the pamp. * I t sh o u ld !

be- m n tio n e d th a t the pump* w as 'd rlvO n by a» e le c t r i c ®iotor Isif i t t e d w i th a - v o l tm ta r and an aiameter w h ich 'gave an im m ediate- j

■ ■ ■ : .'■ 1in d ic a t io n o f any v a r ia t io n in ' the H * f* ' o u tp u t« I n the \

l i b r a r y experim ents each ta n k was f i t t e d w i th an o rd in a ry

Mock gauge w ith w r s ie r re a d in g to 0 *0 1 ** ■ j|!

■ . - lie s u its - were taben w ith the f i r s t shape o f w e ir and ow ing

to a doubt as- to w hether the a# rea d ing s would be the, ease on i

a n o th e r o cca s io n they wore taken a g a in * ' O n 'p lo t t in g ’s graph

f o r 'esoh s o t o f r e s u l t s they wore found- n o t to agree*" The

- -sasthod-of re a d in g - th e beads was ■ iu ^ ied la te ly ''''su spe c te d and i n

f a s t nom d o u b t h a d 'b e e n 'fe lt beforehand i n t h is res-poet*

The f i r s t tro u b le was th a t i t was e xce e d in g ly -hard to ge t the '

aero re a d in g * the m l i* reason be ing ; ttse ' d i f f i c u l t y i n d e c id in g ’

when the w a te r was J u s t '5 b v e l w ith - th ® bottom ,o f t t n w e ir o r 1

n o tch ow ing to the fa e b ■ th a t 's u r fa c e te n s io n caused the w a te r

to curve up o r down*- as the'.-.case' may 'be*, to the s i l l o f the w d ip *

The.-eee©nd tro u b le * a lth o u g h m% m a r ly so serious- was ■ the "

d i f f i c u l t y i n defcersdaitig w i th r e a l accu ra cy w han 'the ' gauge

p o in t was ju s t i n th e -s u r fa c e o f th e w a te r and any s l i g h t

r ip p le wads.: t h is a lanes t im p o ss ib le # . ”

. Accordingly a- mw method o f measurement 'ted' to -he;;' found

and. fo r t h is purpose a: special-.gauge was ■ designed vM eh . i s '

shewn .in Drawing No* 2 * The method o f use was "a s 'fo llo w s ,

{1 ) «orew clown the threaded bush A a llo w in g - fcte rod point

. -to iBswerse in tbs l iq u id #

(2 ) .■ l e t the eye in to such a p o s it io n th a t the r o d 'p o in t '

i s seen from he low and through the w ater*. I f the

.hush Ik la now a lo w ly - tu rn e d *e th a t the. .-rod i s ra is e d * '

a p o s it io n w i l l he -found when th e rod p o in t breaks c le a r

o f .th e -w a te r# f M l p o s it io n is q u ite c r i t i c a l as ow ing

- to s u rfa c e te n s io n the ro d takes up a - p y ra « d d ''o r w a te r ■

■whloh suddenly -breaks away* The re a d in g on-'the' s ca le

and v e rn ie r i s then ta ke n i n the o rd in a ry way* S e ve ra l

te s ts wore mads w ith t h is in s tru m e n t w i th a d e f in i t e

-.-:., .he ight o f w a te r I n a ta n k* The le v e l'w a s .'re a d a number

■■■of-times and in e ve ry case th e re a d in g was the same *

This, m e a n t-th a t le v e ls -could be read a c c u ra te ly to w i th in

.0 *01 in s * - A no the r advantage was th a t ow ing to the-.

- o o m p s ra tlve ly s m a ll p ipe co n n e c tin g the in® t r u a n t w i th '

the ta n k * . s l ig h t and tempe-rary ' v a r ia t io n s ■• o f ' le v e ls were

n o t eo-sjfflunicated to the gauge a n d -th e 'im p o rta n c e ”, o f . t h is ' '

can .hardly- be exaggerated#-- A d ju s t in g - th e gauge was fou nd

to be g re a t ly f a c i l i t a t e d by hav ing a- w h ite r e f le c t o r /

vn

board S Im d to the ta n k by s u i ta b ly f i x in g the

: p o s it io n of. an e l e c t r i c l&Kip#

fh# --quo a t i e ft o f f in d in g when the water; in ta n k w&t le v e l

w i th the bottom o f the wain an no t eh was ne x t ta c k le d &n4 hero

a g a in s. s p e c ia l pi#no o f appara tus was d#sign©4 s M i i shewn.

In D raw ing lo # 5# Bo fo ra t h is in s tru m e n t cou ld bo used the

p o in t o f the brass ro d k had to he a& Jus ted m th a t i f . la y i n

the plan© re p re se n te d fey BCMn the aid® e le v a tio n # •. T M s . plaxse

eurf&ee mm $M m d cm m s te e l t& to l* w h ich was known to be. -

p e r fe c t l y f l a t * so th a t ' t h e p o in t 4 p ro te s te d o ve r-th e .e d g e #

4 b lo c k o f s te a l s&ehlned end f in ie h e d fey g r in d in g | rt square

I n eroae s e c t io n and l | | . lo ng was p laced on "the ta b le beside

the in s tru m e n t end ~mr®& so th a t i t s unde rs ide ' eaiso tap a g a in s t/■

o r over-,the p o in t A# The " lo c k m l ,X> was s lackened t r i the

h e ig h t o f A a d ju s te d fey moans o f . th e m il le d screw E u n t i l the

b lo c k ' Jus t s l i d - ove r the ■ p o in t A-* ■ B w as. t ig h ts m d a n d : the

a 4 ju a t m mb e be e k® d * To a d ju s t the leve ls- o f w a te r, to- th a t o f

th e feotfcon o f the no tch o r w e ir the fo l lo w in g o p e ra tio n s were

c a r r ie d ou t**-

• ., p iece the In s tru & s n t so th a t e i t h e r (a ) tb& .90°V prism

■ • f i t t e d in to the f no tch o r.( fe ) the . f l a t s u r fa c e ■& re s te d

on t t e fease.of. the trspe-so idsl..no.teh.# A 's e n s it iv e .

s p i r i t le v e l was p laced on -the to p face J and, the screw

-■ H sd Jus te d u n til-J r.. was dead le v e l# :. Water mm then-added

o r w ithd raw n u n t i l - t h e p o in t A ■ was ■ i n the surfsee.i o f the

l iq u id * , s SBm ll g lass beaker feelng used f o r the f i n a l

■ ' ad jus tm en t# The aero re a d in g was then take n on the

CS)

c o rre a la n d in g gauge th e s id e the- t a r t * ' 'fhe -

■ instrttHienfc was -eery easy to o p e ra te 'In t im m m o f the

f m tn h h©cause the s id e screws E to u c h in g the-.-ins ide

o f the n o tc h p la t# -s tead ied the im tru m o n t s t e i r a b l f * ■

"■■■.'■■ I is the m m o f the ' tra p s js e id a l m lP ho we w .a p o s it io n

■ o f ba lance-had to ho ffemod sp th a t the -larfem iaejst d id

: . ■ m t ' s l i p oh th e .w e ir s i l l * A f te r a l i t t l e -.p ra c t ic e t h is

' ^ d i f f i c u l t y was §0013 ® w re o i» » An. ur$^®enfc o f* -In c o n s is te n c y

■■ ■"might tm ra is e d t i l t e r e je c t io n o f the hook gauge f o r

'head r e a d in g a r t i t s reappearance in the '-Sero re a d in g •

apparatus h a t ob e xa m in a tio n th is , f a l l s to -’ground f o r the

reason th a t s t i l l c o n d it io n s o b ta in i n the :fcero re a d in g

s e t t in g a r t th e re i s o n ly one such re a d in g f o r e&eh

oxperimenfc-*

: fb§ g e ne ra l nrethoid o f co n d u c tin g an e xp e rim en t was as

fo llo w s * ' The aero re a d in g was f i r s t o b ta in e d on b o th the

gauges u s in g the s p e c ia l in s tru m e n t d e sc rib e d be fo re * Headings.

were take n a t in c re a ses o f head o f ap p ro x issa ie ly o *30f# and

about th re e s d m te s were a llo w e d a t a w r y in c re a se o f f lo w

so i t s l a toady c o n d it io n s m ight be rega ined# O bserva tions

w o rt then made-on the-gauges u n t i l two eo-nseeutite re a d in g s

on each gauge were the ■ m m *

■ The re s u lts were - tabu lated In the usual way using l r *

Janies Barr*a graph fo r determ ining the flow ocer .& f o #f netc&#

A . graph o f f lo w a g a in s t head-wag then c o n s tru c te d so th a t

any Vogue*1 p o in ts .might be re je c te d in the subsequent in -*

c a s t ig a t io n # For each experim en t i t was re q u ire d to f in d . th e

nhm%n our to o f the -typo * qJfV& ♦ r s V & m p p ro a s ii^ tiAg­

io the r e s u lts .o f the' ex;perliaent # • I t t» . obv ious th a t* in .

genera l# a curve o f the-above typ o can bo made to go th ro *hecessafvj

on ly , two e x p e rim e n ta l p o in t# and i t ' i s t * e re fo r e AtO 'f in d Q,

and.'-W to th a t the e u rw w i l l go as near to a l l the p o in ts 0.0

p o s s ib le * ftie-. bea t curve w i l l bo. th a t i n w h ich thsbsuis o f

the /squarea o f ' the re s id u a ls i s a'B&nimuau For e a c h 're a d in g

the va lu e * o f # / ^ and ore Known and-a .aeriea :'o f

equa tions w i l l thus be o b ta in e d v l& «*

Q i a q d l 3/ 2 ) ♦ r { H 1^ i # . . . , M . , . , . . . , . ! I }

Gtg' » q(Efe3/® ) p ( %®/ 2 ) I D ■

•< f ts * «CSs3/ 0 ) + r ( B 3 6/ 2 ) , , ............ „ ( m )

'•:By 'the method o f 5auss* fo r determ ining Ife ' va lues

o f q and r #" I f 'e q u a t io n X is m u l t ip l ie d -fey e q u a tio n

IX fey e q u a tio n I I I fey e tc *# e tc * * a n d 'th e

r e s u l t in g equa tions added-' to g e th e r* then 'one ■ o f the-' norm al

e q u a t io n s 'i» ob ta in ed # ' Ifh ls i s sym bolised -belour and-. A i s the

nor » ! '■ equa tion#

Q i(H x3/ 2 ) ' * # rH ^4 '

♦ rife4

; * t % 3 rf% 4 -

S im ila r ly i f e q u a tio n X is m u lt ip l ie d fey *

e q u a tio n XX by equation XXX fey ( % &/^ ) e tc * * e tc##

the o th e r norm al e q u a tio n B Is o b ta in e d * f id s I s sym bo lised

as .follows s 1'

( 1 0 )

* » %Ux + arBj.5

% » (% S /S ) - « 3 4 * P % 5

» <ma* * jfH.®

S tuB 5? ” » (q I 4 S' B

By s o lv in g equa tions A ana B tbs v a te e o f q. a M r -are

o fe ta imd B-ml the 11bast** curve de te rrdned*. I t i §■ o M 'e n s

th a t tha above method fee corns f ^ r y te d io u s I f a great'., hamber

o f re a d ing s are used and i n th e p resen t in v e s t ! j j^ t io n ,s ix

so lee tad readings were used in eaefe sxperlm nt.*. A t f i r s t i t

wan a ttem p ted to use p o in ts fM e h were, e ve n ly spread ove r th e

le n g th o f t te graph h u t th is .had to .be. abandoned In f a w a r ■

o f u s in g s ix p o in ts near the top# because the' v&lues o f

and. H® when I! was sm all# were n e g l ig ib le compared to t l »

co rre spo nd ing values when H was la rg e * &Xso ths, .re s u lts had

to fee reduced a c c u ra te ly * u s in g lo gar I t hsas# as t lB m u t e o f

s ig n i f i c a n t f ig u re s a f t e r s o lv in g e q u a tio n s A and Bwas le as

and the accuracy o f ths values f o r q and r consequently la s s *

I n t h is manner a .forasala was d e r iv e d f o r oaeh o f tbs ' f iv e

e x p e r im e n ts * . ■

ffee flo w s o b ta in e d from the fo rm a lae were now compared

w i th those take n I n the experim en ts ( a t co rre spond in g heads}

and ths d if fe re n c e s were in a l l cssses found ..to f esvs r y s s s l l

and n e a r ly always under*-I?£* The fortaa l&e were a lso spo t

chocked s p in e t the re m in d e r o f t i» e x p e r im e n ta l're a d in g s

(re a d in g s o th e r than tho-'S s ix s e le c te d i n each ©see) and

n a tu r a l ly tbs e r ro rs were o c c a s io n a lly somewhat g re a te r here#

e s p e c ia lly a t the lowest heads* fh# m xiim m ® r rm was about

m >

th re e per c e r t * T h is was m b cons idered tandsily laege

c o n s id e r in g tbs u s u a l u n c e r t& in ty o f f low® i i l t i heads*

4s soon a i the bead reached ll* * 1© I f 1* the aeouraey in c re a se d

to '.a b o u t the l f »

" . The isext s te p was .to ' t r y t© f i x th® r e la t io n s h ip between

r .a u d q end 0 # it graph shewing r a g a in s t # l a In d ia n s was

d'j os t ru s te d (g ra p h tfe# #} end a f t e r exa**d m t lo n I t was ©on*

s ld e re d reasonab le to w ork out the bea t s t r a ig h t Hu® th ro u g h

t te f iv e p o in t© * T h is 'sm a n t son© o f th e va lues o f r would be

a l te re d a e©*jalderabl© arsonist h u t ©wing to tbs magnitude o f

the : sV ® ta rn compared w ith the ta rn i t was. seen' p o s s ib le

th a t a a l ig h t c o r re c t io n i n q would n u l l i f y the much la rg e r

a l t e r a t io n in r • 411 the 'seme* r eon Id not tie a lte re d a w r y

la rg e amount o th e rw ise the *co rre e i© d *fe rm u la would no t h o ld

ove r th - rang© o f If* T h is point i s b rough t o u t mu eh more

c le a r ly la te r In connection w ith the 4 t h ex p e r i .meat*' A cco rd*

Ih g ly the beat s tra ig h t l in e was worked o u t* using a' s im i la r

method to th a t adopted in w orM ng out the values o f. i a id r

in ouch in d iv id u a l e x p e r iw r t * The l i n t waa found to to

*■** S *$e*o*04 and is shewn a ls o on graph m * 6 *

fh© c o r re c t io n 5% to the va lu e © f .q# on ■account © f ' r b e in g

made- to l i e on the s t r a ig h t l in o r « 8>8e~0*$>4* was ne x t

found l a each e xp e rim e n t* An a l t e r a t io n o f^ r to r m um ® an

a lte ra t io n .* , to the f lo w * © f<JrHs/ 8 and an a l te r a t i .s u o f f to t

causes an a l te r a t io n 'b o S te f S q l# /^ * I t fo llo w s tb ^ e fo r e

tb & t^ * H # r arid consequen tly i t i s Im po ss ib le 'to ha la nee an

a lt@ ro .tio n i n . J r by an a l te r a t io n i n # q p * 'if H v a r ie s * Th©

e r r o r I n so d o in g w i l l m% to g ro a t however I f $? i® no t

u n d u ly - la rg o

An in s p e c t io n o f the ta b le s a t the ©nd w i l l shew tow

th is c o r re c t io n has been determ ined and a new for-saila f o r the

f lo w 'o b ta in e d * T to pore© n to go e r r o r f a Baking th is ad ju s tm e n t

is .g iv e n In each ease* Experim ent 'id * 4 g ives, the. g re a te s t

e r r o r because <|r is g re a te s t the re j. the m#.%tmm d i f fe r© ro e '

b e in g 9 *5$ I n a l l the- o t t e r expertise at® however th e 'e r r o r f®

lo s s th a n 1 $ and g e n e ra lly co n s id e ra b ly lo s s * - U n fo r tu n a te ly

i n t h is experim en t and c o n s id e r in g rea d ing s o u ts id e t-to s ix

chosen-ones* the e r ro r is much la rg e r a t the low est, head

I I * # * 0*0835*) and & fo u n ts to 9*8$ b u t I n a l l the o th e r © x p t r i*

meats I t is ve ry much M m t. i n f a c t under &$*

Owing to the f a c t th a t the ^ id e a l* fo rm ula g ive * the va lue

o f v p r o p o r t io n 1 to ta n # # a fo rm u la was worked o u t i n th is

fo r a and found to . to r » 9*35 ta n 9~0*05* . Tha 'va lue o f q was

a d ju s te d I n each experim en t as be-fore and the c o r re c t io n to %

was found to t o somewhat lo ss in a l l m s ® ® m m p t the re c ta n g *

u k f w e ir * The e r ro rs 'in tro d u c e d t b i t t in # m m th e re fo re le ts

tha n to fo r© * ® oaxim m , o f 2 * 2 8 $ -over the- s ix ,* * le e te d re a d in g s

i n the 4 th Ex p e r i went and the lo w e s t head o f 0«0£2S*#

Oraph He, 7 stows the H r# r *» 8*35 i * n 9 » 0 *05* a ls o the

o r ig in a l p o in ts *

. The va lue € r to s now been t ie d down i n terms o f 0 ami

ta n 0 and i t i s re q u ire d to t r y and f i x q i n tow s- i f # a ls o *

The - le n g th of; the to ss o f w e ir was no t q u it# con s tan t th ro u g h *

o u t the f iv e i experim ent®* i t v a ry in g from . 0*3833♦ to 0*387*#

I t was th e re fo r© IsapostlfeM'' to cons i& e r the m t values o f %

w ith re sp e c t to S o f fcaa 0 a m a c c o rd in g ly tha va lues o f <j/b

> t m m woFkod o u t f o r e m r j © a*** l a d o in g , t h is th® aaawtiip-

t to n was made th a t q * Kb and w h ile I t i s m b . known th a t ib i s .

i@ s t r i c t l y t r u e , the e r r o r in tro d u c e d d u r in g th® rsag©

fe « 0*3333* to" 0*30’?* m a t o b v io u s ly tm q u it# n e g l ig ib le *

These m imes © f ' & Im w been p lo t te d on graph Ho* 8 t© the two

h o ri& o 'n t& l sca les o f # i n ra d ia n a a m ta n a tte m p t mm

made to f in d th»' e q u a tio n o f a curve to ip tb ro ug h es.eh s e t

o f f iv e p o in ts * Owing to the aeeur&oy to # iIc h JC smash be fo u n d ,

i t was soon re a lis e d th a t the r e s u l t would fee ©usdrorsor * pro**

feabiy ■ in v o lv in g f iv e te rm s* The q u ie te s t way o f t im in g % i s

to rea d o f f the ew ves in 'g ra p h 's © * i * I t i s ■ reeosw nded

th e re fo re th a t the f lo w shou ld bo ©aleuXahed fro ® the e q u a tio n

q '■*» KfeH3/® ♦ r I s l§ : 1» found from gpaph tfo* T (o r from

r * 8*35 ta n 0 -0 *0 5 ) and K i s to 10 read © f f from graph Ho* $

u s in g the con tinuous l in e curve * K© s u i ts a re s l i g h t l y isor©

accu ra te than I n u s in g graph Ho* 6 and tbs d o tte d H m in

graph Ho* 8 * f is t rang© o f the ’p re se n t re seareh m is t be

eow plied w ith and is d loussed be low *

■The a u th o rs re s u lts were then to a te d a g a in s t t in f ©net la

evo lved fey Messrs dour le y and d rlm p* A ’ ©ompera h i we tab le -

(Tab le id * 33) is- g iven a t the o w l and graphs- Ho&« §-15

{ In c lu s iv e ) shew, a t a g lance# the d if fe re n c e s i M e l i n mo s i

eases a re under 3$« I t i t in te r e s t in g to net# t h a t tbs

5© urley and <3rinp for©** la to M i $>&& w e l l when #

Is n e g a tive a lth o u g h i t was never designed, to && so * ■

■ fh a range o f the p resen t must too co n s id e re d *

H '■'varied from {on an a w ra g e ) 0 *€#3I* to 0 *3 3 # and the e n ra g e

value o f to was o #320* • f a t ra t i© -5 g iw s & ise&eure- o f . t inb

^sbap#1* ©f the m&r and varies from 0-*09§ to .1 * 0 * . ' I t i»

f a i r l y sa fe to say th e re fo re th a t p ro v id e d K/ t r H.«* ' between

0*096 and 1*0 then the rests I t 3 o f the present work emy bo

used w ith confidence. 0 w r the rang© o f boad© © * H r ; to 0#331

the-., accuracy o f th® re s u lt® ar® much p e a te r y . t i » t la if^ /to

i # ;between 0 *395 am! 1*0 the re s u lts w i l l tot- accu ra te ' t o ju s t

o tf^ r and g enera lly very tauch c lo a e r than th is * fo r va lu e *

o f ^ /b between 0 *095 and 0 *595 the accuracy w i l l be less*,

the d iffe re n c e being as stteh a s -ff l a t the lowest heads* the.

d o u r le y and Crimp forma 3a g iv ing a eorreapond ing d iffe re n c e

o f I t is c la im ed th a t a® Inng the ra t i© I/to is

r e s t r ic t e d as a bo w th a t the p re se n t re se a rch w i l l g im r e s u lts

e q ua l to the G jourley and Crimp fo rm u la and in mmnf oases b e t te r

tout I t i s re a lis e d th a t in d ie # a i l #4? and 2*4? would ■ p roba b ly

have given our wee user© c lo se ly re se m b lin g the e x p e rim e n ta l

r e s u lts a t the low er heads # These odd wain®a fo r . th e - In d ic e s

e n t a i l an amount o f la b o r io u s c a lc u la t io n to. f in d '- th e . f lo w

and th e re Is no dounb th a t tbs r e s u lts @f the p re sen t re s e a rc h

ensure quisle r e s u l t s * to o b ta in g re a te r accuracy a t the low e r

heads i t would have boon m ceaaary to wary I w i th S ju s t as i n

M r*.-Barr*a r e s u lts f o r the $0#? notch# T h is :w ou ld . h a w 0'

co m p lica te d -mattera a 'good d e a l becaue® i t would p ro bab ly

have been d i f f i c u l t to determ ine the . v a r ia t io n i n £ when 9

v a r ie d *

( I B )

: . As gfesap* 6qw?1®j a M O r iimp eosypared-fchsir r e $ $ i t * w ith

those o f C ip p w ls tt i- fo r ttoa w # ir # ■» ta n {#44*. ap3^ws^*

iK)ateX3r) and fenpd agreaiaenfc# i t fo l lo w s tfcat''thar;-enmpsrison';:

between ib a A n ttoo r1® re a n lta and tfaoaa o f Is saris Q &nriay and

Orlmp; anffflcaa.#

m )

s m i a t f i r r flow*

subject is a subsid iary om to tra p © so Id a ! weirs

H i was ®m o f the reasons f o r u n d e rta k in g tbs rese&r&h in to

the la t te r # A t tb s b e g in n in g o f the paper i t was m sntioned

th a t a fo rm u la &f tlm typo h ** ptjl/S 4. q||o/S + y i^ /S could be

m da to very close ly ) approximate / to a a tr& lg h t l in o f o r any

given range o f heads .* T m f i r s t term was to ', fee supplied

by * n o r if ic e d is c h a rg in g under tbs- ease lie ad as the w e ir and

i t seems c e rta in th a t th is o r i f ic e would have to fee designed

very c a re fu lly so th a t, the' loss ©f head due, to f r i c t i o n - I n tbs

p ips e t c * /s h o u ld bo nmde as low m possib le*

from, i s inspection, o f the above fo r ’mu la i t is .evident

th a t the r a t io p s ftr determines the shape o f the ’curve,

re s u lt in g and i t is necessary to f in d f i r s t ’the r a t io , o f Q.:r

such th a t the-’ re s u lt in g curve s h a ll approximate to a s tra ig h t

11 ne #. #Consider the equation

. Q * pH1/ 2 + q a ® /2 + rK 5/ 2 C)

"■'■’■ i t ' i a desired to nsko th is equation* as nearly as possible*

coincident w ith Q, m sS {where s is a constant) over a range

of. hs&d 0 to -h| ■

i . e . p B ^ 2 + «H3^ 2 + rH 5//2 s te u ld equa l *3 o r

tH 1/ 2 + UBS/ 2 + TH5/ 2 chon34 ©qua 1 $ ♦ ♦ * * * . . , *****{13} -

■-.By .tb© method'of d'auas* as-used be fore *. i t would be

possible to do terrain© the va lu es -fo r t , u and v fey s e le c tin g ..

a number o f values o f 1 w ith in the range 0 to b* Obviously'

the best values fo r t# u and v would be obtained by considering

( I f )

m i n f i n i t e m & fc e r o f o f 1 { w i t b i n tb© ra n g ® 0 t o h )

a nd t h i s m n 13® as f o l lo w s 1

t ( b ta il ♦ « r H% a * » f * A n « (h » , . . { ! }* ■ . ■' ■ V© ■ % *0 %

" t ( h b% s * t t ( h # d i i + * ( h :A a «*(b ss/ % 8 , . . . . . . * .» (p )'# m m '0

: t ( h # 4 8 ♦ a t** A h ♦ * ( & # 4 8 . . . . . . 4 0 )Jo Jo h fe

Seducing e q u a tio n *' { B } * ( f ) t M { § ) we gets

t # * a t# * vh4 , 8 |»B/2‘T * T " 5 . . . , . , . . . . . . , , , . , , . ( H )m

tfe? , «h£ , wh** $ b?/^.n.nnwuMi •jf .Mimwiwfc «lp —«www»- Urn -mm3 - 4 6 7

th fe * u h ^ 4 v # . m 8 fc?/*54 $ ' 6 ' f » l i i , M i M . | « * I . I M ! f l

S o lv in g e q u a t io n s f l ! } * 1.1} a nd ( $ } wo ip fei 9. ■m

$1 » #

a n ti t * eH§

* * MStiO O f |j* *® J*. d lf*V O

I f £1 * 0 * 6 tb& rm nip o f t ip ex n ta w i l l Imm boon

eaoooded « l ig h t l y ' b a t i t imsfc bo t lrn t the heads

■were u p I s a b ou t S1* when # woe ■•16® and a lo e a v t r j good line

« tra .ig fe tAw i l l i n s u l t oven i f the range is extended to CHS1# •#

• X V Is no* ' m m B m v j to f in d fro ® the © xperi p o r ta l .

r e s u lts when £ « |** th e r a t io £ fu** e & e h e xp e rim u fc i»

shewn in ta b le Imq * 54 and i n g raph -fte * • M * \ f h v : va lue / o f &

ims -^been takon m 0 *32p t m th a t tb s -ranges-O f .the- aefcual

experim en ts are- adhered to# &Xs© the r a g a in s t' t a n # re s u lts

have--been used* 1 f M r a t io £ «■ ~ o *6667 i» - s l i g h t l y w ith o u t

the range o f the experim en ts b u t ' oactr&poXatiug 0 l i g h t l y .from.

g;-« »?®*43* and «*1@®*0* " i t i t found th a t th e requ ired r a t io

I s whan ta n O' * ***0.#t?E2 o r 0 « ~15CV14* * ftm e q u a tio n o f

f lo w becomes: •

■ Q ■ 0.10-35 H1/ 2 * 1 .035 H3/ 2 — 0.6897 l / 7^ ................ (K )

■ f be d ie * o f o r i f ic e * assum ing no lo ss o f h-ead is 1 *538 In s *

th e re s u lt , o f . th is s u b s id ia ry in v e s tig a tio n is th e re fo re t l s t

a tra p e a o ld a l w e ir w i th a base 0- *529* and % » ~XS?h*14*»

wording l a conjunction w ith an © rifle ® o f d ta * 1*558 in s *

should g iw a ve ry elose a p p ro x im a tio n to a s tra ig h t 11ns

f lo w * ■ th e s t r a ig h t 11m. would b@ Q » 0*0405 H* (L ) . t& b lO 5§

g ives a com parison ho twee a e q u a tio n s {& ) and f t ) * the d i f *

f erehee when H ** 0*0 5 9 1® d*7# h u t whoa S is a hove- 0*10* the.

d if fe re n c e is always u n d e r - Graph io * 17 shews th e .p & in ts

in fab le 55*

f-he -apparatus designed above- has no t been t r ie d o u t by

experiment but there is m reason why i t should m l fu nc tio n

i m

as swpeotod I t m m to avoid losses isa M M

and" o r i f i c e * -

: ■.' " J t i t u s e fu l to «9t« th o t the angle ft is not e r l t l e a l *

X f say tfee upper l i m i t t o r h m s suds 0 *6* * Ine te& d © f 0 *B# *' . -0-555

tbs ra t i© £ « *•» ft would to IS^JSO-i-4-(appro*#).#% 3*0 *ftA

Tha.,f,i8e ©f o r i f i c e would o f ©ours© fe w to,.-M. a lte re d ., t u t

th s 'A te e t11 equation o f ,t.fc© typo (C) ©to? a *•«»$&■ & ** © t© 0*6

would s t i l l to i w p y good app roas liia tion over tta© rang©

h * ft to 0#S a n d - th is f a s t g ives a e e r ta iu a s ^u n i o f la t i t u d e

w-iaou d e s ig n in g &s apparatus fo r a p a r t ic u la r purpose*'

■>** *•>**©-O ft

%n the fo l lo w in g r e s u lts i

f w,bs&d i n inches f notch#C ;«* H r# M m ® B a r r * ® %0 .n s fc tn |^ f © r f i n d i n g t h e f i e #

'■; ever i i o 9 V n o t c h e u « f t * p®r *atn«)1 <*. head i n ' f e e t e ve r the e x p e rim e n ts ! w e ir#

• f t » f l e w o f w a te r I n m s e e s «

f l lB ta X

T ru e 'v * C

I p © f t e a le u lA t e df r o m d e d a e e f i

f o r s a l s

0 . 9 S 0 ,2 0 5 0 g% #^©$10 0 .0 0 4 3 2 31 .5 0 0 . 8GSS 0 .0 5 8 0 0 *0 1 4 0 31 .6 4 0 .3 0 5 0 e .o c o o 0 ,0 1 7 5 0I .S O 0 .3 0 6 0 . . 0 ,0 7 8 8 0 ,-0 2 2 1 ?1 , 9 ? 0 .s o c o 0 ,0 9 0 0 0 . 0 2 7 7 ?2 .3 3 0 ,5 0 5 6 0 ,1 1 2 5 0 . 0 3 7 ®S . 54 0 #3043© ■0 *1 4 3 3 0 ,0 5 2 2 5

* 3 ,7 3 ’ 0 * 3 0 4 ? 0 * 1 6 5 5 0 .0 6 8 5 5 O .0 0 1 0 5S3 .9 3 ,. 0 * 3 0 4 8 0 * 1 3 7 3 0 , 0 7 4 5 0 .

* 3 .1 3 V« 4 -iw# CU2 1 B5 0 ,0 9 1 2 0 ■ 0 , 091.5 ■S3 .4 3 0 #30 33 0 #8550 0 ,1 1 2 7 0 ,1 1 2 4o 3 .0 1 0 #3033 0 *8 0 3 3 0 ,1 2 5 1* 3 .9 4 . ■ 0 # 3031 0 *5 3 0 0 0 ,1 5 5 0 0 . 1 r 5O*4 .1 1 0 *3 0 3 0 .. 0 * 5 5 3 5 0 ,1 7 2 9 0 ,1 7 2 5* 4 . 8 1 0 ,5 0 2 3 ft 0 #8 lJ§0 0 .8 1 7 4

The s i# re s u lt# m arfed # were used f o r deduc ing the ^b e s t*

f o r m la o f fetea type Q » %S^/^ 4 rH&/&#

f lo w i n cuseoe m fm m w h ich the va lues Q, i n the

s tove ' ta b le ..ere ob ta ined# .

From sn in s p e c t io n o f the m # t two'pages t l ’O

o b ta in in g the two b&sle e ^ u s t le m # w ith o u t an u Juo smounb;.

o f srithEEsetic# can h# seen# 'C , *'V

The point mrlm& 0 i n the ta b le has been s # tided i n deducing the ^best*1 fo rm la f o r tl^- reason t i n t on i r e a c t in g t*# cjuph I t d id not appear to conform to the general 11 n r o f * t o i ie r p o in ts »

(»>

' 1s t m zm m 'T W { m m * }

f m ing «xsd as doa»nsferat©d .lu tfea' basis aquation (using tbs ■■ m tbo4 o f ■ G$xm&) was

' f a r i n g tlrds in ir&nd t tm fo llo w in g tablaa w i l l -btrebvlcmft* ■ ■•-■". J •

t& fg H » tog B3/ 2•J£

tog # ■tog IS4 tog Q

1,2X50. 1.3391 ' 1,4065 1,5185 . 1*5543'" 1.6427

,1.8195 ' 1 ,0086 1.1097 1,2777 : 1,3314 1.4640

.,1,6390 1,0175 1,2195 1 ,5555 1 ,6629 5,9281 '

1 ,8520 1.5564 1.6260 1,0740 1 .2172 1*5708

1,7062 1,9603- 1,0819 1*1680

■ 1 ,2378 1,3585

tog H3 tog Hi - i^ s ' t f /g jq ■

H3 ■ ||4 Q ,X I0 % ~

1*79431*8195

& #0300 1,8620 ■3*81571,96031.0086

0,004 ,355 0.600,7X1*2 0,004*123

1,0173 f,3SS4

1,1097

0*010 *400 0,002*272*0 0.009*509

1,2188 1,6260 1,1616*« *»

3L 2®0,015*580 0 ,0 0 4 ,2 2 6 ,0 0 ,014 ,510

IT 1*07401.27771.46971.2378

■1.3314

0.035*920 0 . O i l , 850*0 0.029*490

^ ,6620 1,2172 ■P SOP’ 1jg»1 ,3385

0.046 ,010 0,016*480 ,0 0.037*090

1 ,0281 1 ,5708 ”1,8025" 0.084*720 0 .0 3 7 ,8 10 ,0 0.063 ,460Tota ls 0 ,197 ,983 0 ,072 ,749*2 0 ,157 ,987

#t . 1s t b a s is a q u a tio n 1ft

0 #l9S0q 0-#0*7 7051* ** 0 *X&$|0 # * • • « # » ♦ * * * * t * |(4 )

( 3 )

1s t e x p . r i v e w (cn fc& .S

'F3P01&' %fa& tex t;;vtta9:::-2jid'.|3a»le &$u&tlo& was£0 gS/S a ^£j|4 4 r & f i

< !# tm& alre&dy'-tseen fountl'$n t fee pr# irisus 'paga#

t o g a L o g H ^ /S L o g I # l& g t

1 . 2 1 5 0 - 2 .0 3 2 5WPM* ^

-1 ,7 9 6 21 , 3 3 9 1 . 2 ,3 4 7 7 1 *6 9 5 5 .8 * 9 6 0 51 . 4 0 6 5 . 2 .5 1 6 2 *$ *sOS^S 1 ,0 6 1 9

1 ,5 1 8 5 ' tyr»/•**■><S» « ? *» KjZ* a *5 9 0 0 1 .1 9 8 0

; 1 ,5 5 4 3 ; - 0 .8 8 5 7 a . m s . 2 ,2 3 7 8

1 ,6 4 7 2 , 1 *1 0 6 7 8 * 8 1 3 5 . 1 ,3 3 9 5

L o g a 4 L o g I l 3 L o g .a4 ■ - # S ixgS /S

1 .7 9 6 3

? « 0 6 8 0 4 ,8 2 8 7 0 .0 0 0 , 11S , 1 0 , 0 0 0 , 6 7 4 ,1<4 5 ,9 6 0 3 <ao 5 , 5 4 7 7 . £T

o•H-PCij

4 ,6 9 5 5 3 ,3 0 8 0•H . -Po5 0 , 0 0 0 * 4 9 6 ,0 0 . 0 0 2 , 0 3 2 ,0

Sa1(D

‘ Ph o<H©1—1 ,£2

1 ,0 3 2 5

1 ,0 5 1 95 5 5 1 6 23 ,6 6 3 1

2CT©

o 0 , 0 0 1 , 0 7 7 * 0 0 ,0 6 3 ,6 9 9 ,0I , 192eT5 ,7 9 6 2

m© i—i

ctS-PC

3 ,8 9 2 5 3 .8 8 8 3•yjgiMMoww. TWij'Hiuujwaoft1 ,2 3 7 8

oj-pfl•H

0 . 0 0 3 , 9 1 2 ,0 0 ,0 0 9 * 7 3 1 ,0

CO<

5 ,8 3 5 7 MI . * m s 2 ,1 2 3 5 <! 0 *0 0 8 , 9 0 7 , 0 ' 0 , 0 1 3 * 2 9 0 ,0

1 ,3 3 8 51 ,1 0 6 7

2 *2 1 3 5 8 * 4 4 8 3 0 .0 1 6 , 3 5 0 ,0 0 .0 2 7 , 8 7 0 *0t o t a l s 0 . 0 7 2 , 7 4 9 ,8 0 .0 2 7 , 8 5 3 , 1, 0 ,0 5 7 , 2 9 6 ,1

’ *

, . 2 nd b a s ic e q u a t io n I s

0 . 0 7 2 , 7 5 q, ♦ 0 . 0 8 7 , 8 6 * ' ** 0 . 0 6 7 , 3 0 B )

1 s t re *? {c b M .J

S tlld is g ©$*ia$l©»». |4 ) a is l f i )

m i # t p ** ^ c t f ( y ^

s i i t > i« o 4 & l

* # -fIs# nlmntm e u w fc&r#* ih© ci:t points I t

. % *■ 1*0421 H3/ 8 « . .0*6646 H5/®

fid® Itoraalft wt« eeed to e& le«a*ia .th a f l# » t fo r feh»

taiaa &im hm4M m» mr& mmd in it» &«&

t t m m mim® mm f t mn in ifet l&afe, ^© te ia ©f tsts© f i r s t

tab l#« 4 l i l t a grajph Im ^ # b t i d i n g t in

utotirn ttm m tita i s r e la t io n to a l l

r e & u l t r * ’

Tm®0

Wsa»a* £|

C a lc u la te d from deduced

fo rc u lA

0*8940 ' 0 .0250 0*0940881*39 ■: O,5040 0 ,0492 0.01184x * e r 9,5060 0.06 50 0.01730X*8S. 0 ,5001 0,0053 0.02473p p*?'<SS #4* f 0.3056 0,1153 0,03954

«e»5®- 0 ,30 SO 0,1423 0,05323 0 *v SjTQ2 .7 ? 0,5040 0.1C42 0,004032,0*? 0 ,5041 o , i r s*r ■ 5.07708

*« * !© ' 0 ,3033 0,2073 6.03313 0 ,0 113M .4 S 0.2035 0 .£425 0.1113 0,111?J63.C5 0,5052 0 ,£6C7 0,1209 0.15c©*S ,t’3 0,5031 0,2002 0,146? 0 * !& t44.C7 0 ,3C f>0 0 ,32,5.5 0,1633

» i ,3a 0,3030 0 .53S2 0,1004 0 ,1703

f 'tm » ix r ta n ifc s m wmm nuM- im da&ueisg t i n *$!&8fcv

fo ra a te * o f ito r %jpm C|- m % # /^ * r s V S *

f&s fw M ts g f o r IM s , la ' m t wiwmm b u t ttm m ttm d

■'Is a i s l l a r to th a t riood In %lm X»t mvzt*

Wtm , boax© w®m

o * xx& w ♦' o i05So4r * 0 * m mand G»O$0CHU| * O*0O f i t l r » O *$204-8 *

ffo k 'w fe lo h t ■** l * 00iX 01*1',.** » **$#2808 *

Tiha "b a a t* earvo ite ra * %fc# « l l p o in ts i s tfco ra fo ro

*4 m X #906X11^/** «** 0 «2802sffi^B

from w hloh tfeo f i |p l* # s Is . th$ 3&&t e o ta ® ®T tfm t&'tew

t& b lo eaXoui& toa*

TABLS 3

3 rd EXPEE1ME MT *

9 « 0% B « 0*52®*

Truevn G

TrueH*

FlowQ

Q c a lc u la te d fro m deduced

-fo rm u la1.21 0.3015 0*0383 0.0080931*80 0*3059 0,0808 0.01650-1 *84 0 *3061 0,0792 0.02342

£2,25 0 * 3 0 57 0.1100 0.03869 0.03767s&2 *82 0 *5049 0.1442 0.05645 0,05854£2*94. 0 *3042 0*1750 0.07511 0,07558£3 *27 0.3038 0*2075 0.09783 0.09761£3,54 0 *3034 0*2375 0 ,1 1 9 2 -- 0 41195*5 *88 0.3031 0.2758 0,1497 ' 0*1496

The s ix r e s u lts im rked * were used fo r deducing the !lb©stff

fo rm u la o f the type Q ***' qH3/ ^ + r l ^ / ^ ,

The w o rk in g f o r th is experim ent is no t shewn hu t the method

is s im i la r to th a t used i n the 1s t expe rim en t* >

The b a s ic equa tions are

0*0'530Qq + 0 *0 l2 3 4 r » 0,05473 and 0*018344 * 0,Q02979r * 0,01274

from w h ich 4 «■ 1*032 and r « o

The "best® curve th ro * the s ix p o in ts is th e re fo re

q * 1.0S2H3/ 2

from w h ich the f ig u re s in the la s t column o f the above

ta b le were c a lc u la te d * '

« thwsRSBSsate '

E 4 »;,« 49°#»S9*, b » 0*529 t

TrueVs C

'True• H* ■ , 'i

Q, c a lc u la te d from deduced

fo ra tu la

0 *92 0*2230 0,022$ 0.0030651*38 0'i3031 0 a0469 0 *0 l o l l1*65 0 *3060 0 ,0617 0.017831 *94 0 *3060 0 *0017 0.02673

*2 *81 0*3057 0 .1025 ' 0,05699 . 0 ,03608i£2 *48 0*3052 0*1842 0,04927 .0 .04902^3*80 0 #5044 0*1542 0 *06658 0.06801‘ 6*12 0*3039 0.1853 0,08710•3*30 ■ 0,0055 0,2192 0.1159 0.1160*3 #90 0 #3031 0 .2817 0,1517 0 .1318«4 *19 0*3030 0 *2933 0,1314 0.1808

fh e .s ix r e s u lts ■ marked * were used f o r deducing the- n:best®

, fo rm u la o f the type h .» %H$/S * rB V & *

ffae w o rk in g f o r t h i a e xp e rt ms nfc is no t a hewn t o t the

method i s 's im i la r t o ’ th a t used I n the 1s t exp e rim e n t*

fh e b a s ic eq ua tion s are

0*06053% ♦ 0*0X631r * 0 #06841and 0•01631% *-O*0Q4050r « 0*01738

fro m w & ich t ** 1*107 end r ** 0*1064#

flie •b e e t* .warm t f e r e * . tbs s tx r p o in ts la th e re fo re

i» «* l.XOVgS/ 2 +

from w h ich the f ig u re s in th e la s t column o f th e abo^e

fca.hi© be we bee n ' ea le u la te d *

f r e e ■ v» 0 ■ M t .. **T

P lo wH

Q, c a l c u la t e df r o m d e d u c e d

fo rm a la-

■ 1 *8 0 ■ 0 * 8 0 1 3 0 . 0 4 1 ? 0 *0 0 7 0 2 11 *4 S 0 * 3 0 4 4 o .o s o a 0 *0 l 2'10i #04 0 * 3 0 6 1 .- 0 .C7 5 3 0 * 6 2 3 4 23 *310 ■ 0 # 5 0 5 9 € . ( n 17 : 6 * 0 8 2 3 3

■ 2 iSsm ** ***«!» 0**5054 ■ 0 .1 1 2 5 0 * 0 4 4 4 3m3 * /S 0 *& > 4 7 e . i a r a 6 * 0 0 1 0 7 .. 0 4 0 6 2 8 5 ..«§*© # 0 *w0 4 1 0 . 1CC0 0 * 0 8 0 0 7 ' 6 * 0 8 0 8 1 :.H3 #4S ' 0 * 3 0 3 5 0 ,1 0 1 7 0 * 1 0 0 5 © * ie ^ 07115*7 © 0 * 303® o „ 2 s s a © * 1 5 0 0 - : - o * t e ? i -* 4 * 1 1 0 .3 0 3 0 ■ 0 . 3 5 1 ? 0 * 1 7 2 9 . 0 * 1 7 4 5 ---H4 *4 0 0 *5 0 8 0 • 0 ,3 8 3 3 O *2 1 5 5 0 *2 1 5 2

f t# r n m im ■* tm m uaad fo r dsdtaeiiig tha- ^bcat®

t&wmiM o f the - t u # % ** f l # /^ 4* rE ^ /2 * ..ft# wort&isg'for

thi® experiment 1» s&t shown t o t the nmtfacd la e ii it la r - to

th a t used in the l i t experim ent*

f lu basic eQuatlom are

0 *005,081 * o * o i6 f i 8r * o .o s o ,!®' 0*016*156 * 0,0O3t 750r * 0 *080*80

.from w h ich % * 1 *02? and r » 1*41

fb a hoot eorr® th ro * th e «1* po in ts . io tho ro fo ro ...

■ Q. » 1*0278$/^ * .1 *4 1 b V &

from w h ich -th e f ig u re s i n t te lo o t column o f the ateve

ta b le woro c a lc u la te d *

( 9 ) -

A bstract o f re s u lts fro® the flw -e x p e rim e n ts *

fABXB 6 *

S degrees & radians fan ft b ( f t ) <1 S *k p

—X5°—6 t -0 .2 635 -0 .2698 0,333 1.0421 3*126 *■0 *6645- 7 V 4 3 * -0 .1347 -@*1355 0.328 1.0061 9.067 **0 *3802

0 0 0 0 .329 ' 1,052 9.197 m m©^-SS* +0 .1743 ■to. 1760 0,329 ' 1.107 3*364 0 *1064

so°-o* +0,5236 40 .5774 0 .327 1.027 3 .1 41 1*41

from th is tab le ■ the ' ' fo l lo w in g graphs' have been p re pa red **

"'. : ' r A g a in s t 0 graph ffe* I • r a g a in s t ta n 0 «** graph Ho* 7

or ra th e r the points. have beer p lo t te d ..w ithout h a v in g

been Joined up*

I t . was do e lded to work on the -t 'a g a in s t 0

(flo* 6) f i r s t and . to f in d the 11 b e s t* s t ra ig h t" l in e thro*'

the f t re p o in ts as e xp la in e d in tb® te x t * TO..-do th is

tbs m- thod o f Cause was used a pa in aw l' the oq.ua t l on o f the

lin e worked o u t to bt r « 2*58 *^0.04 and th is has been

p lo tte d a lso ©a graph lie* ©*■

Having 4# e lded to mlm r conform to the s tra ig h t

lin e r « 2*5 0 * 0*04 i t was m m n m rf to ad ju s t s l i g h t I f

the .value o f t so th a t the accuracy o f -..the. f i n a l re s u lts

would no t be im paired* .T h is Ims boon done in tables lies 7

to 11 ( in c lu s iv e ) be low * I t w i l l be seen th a t I f t iw value

o f r M s been a lte re d fey an asaount then a c o r re c t io n

to the value o f f mast fee ma&# sueb f o r

®$rjt# I t fo llow s th a t w i l l w r y w ith H &nd an s w a g ®

m lm » s t be t&lsan i f f i s to be. a l id a d # y-1:

fim error in f i l i n g ^ fo r any 0 m m ^m of $ w i l l m% '

he i f is not large#-' In the 4th Bxperimjat

{# ** ;40^»S0^|Jr is Jmrifsstp the $ e rro r a t tfaa l a r i a t

mitts, ©f H &'m\%nt® to t j j f * fh ie la 3&r$sr. ttmii .had been

hap&d.tait in the four the errors are

eooeiderebly s e l l e r * in feet- Its# then IfC*

l e t Experissent*- l?e« r « «*0#ePS0* o ld r « -0 » i6 i$ * i & f f * i n

II ( f t ) - WrfV'B (3 Vcy^ ' e rro r

J{ e rro r

fk ■*&***« e ,06600 0.00660 0 *00448)0 *06600 *0 .000805

0 *40

0.3183 0 * 1080 6.00760 0 .ooscow) .lose m .ocoi’cs

0 .29

0 *25fs0 0*1207 O.OO0T2 0.00130X0*1237*0 .000175

0 .1 6

0 #^300 0*1938 0.01130 0.00182*0*1835*0 ,00023

■' 0 .1 5

1% trns 0.814S ' 0*01830 0.00283X0,2145.*0*000478

0 *2T

0.4303 0 .8011 © .eisos 0 .0G407 XS ,2© 11 *0 *60145

0*60

i f f t 1*0421 * 0 *02^1 * 1*0822fr iw w iir^u ifljjw itpMOij iS jW ip .

2nd &xpertia»»t# 9*87611 c&a:i*« » 0 #8898 * D i f f * i n r « 9*0078

X*t# / 2 #s ^ a d d it io n a l '. ' a w n #

fC m m r

0 * 1483 0.U6S7® 0*0123 0 ,CC08O ® * t r0 ,2073 0.004 31 0 *0 181 0 *00035 :0,3423 O * X i0 4 0 *0210' O*C0CC7 ■ §*O i0,2667 0*2377 ■ ,:w t #00022 Cl *170 .2003 - o * iBm O »02S 1- : 0 *O0Ofi 0 #480.3393 0*197 § 0*0200 0*00174 ■ 0 #OT

o »q£13

. B f 4 * I S M I .4 0*0218 «r 1*6878

ta r r r■irfrwtw^rinw iii'im airiiipm xwr.

M Eaparliaanfe# SW »«M>*©4# a id n « a e ro * B i f f * i n r « ®*®4

if f ft* } - lx ||3 /8 , ^ * 0 a d d i t io n a lt r r a r

. Jf e m r

0*1390 ■ ' 0 #O4ts40 O*00440 0*00012 0 #S:20 * 1442 0*05478 ■ ©*C0S?7 0*00011 #% Oft #«*%#0*1730- 0*0731® 0 *0070® ■■ O #00008 0.0?0.?O7£ ' 0*09454 0,00030 -..-0*00006 o ,ee0*247 i 0*1137 0 *00® 00 0 *.®00§1 0 ,13■0*2708 O«M 4§ ■ 0 *0 HO 3 0*aoo4B o . s i

. i f ! * X*®H0 + 0*0077 » 1*040 •

TAT'A* 3© •4 ih ISw r« 0 #$©$$*& M r » 0 * l0 8 4 * 2 i f f * i n r*0*28O 4

l « j 8 /2# > y '.a d d it io n a l

e w e r .£ e r r o r

0.1085 ©,05291 O ,6235 6 .06006 •2,30.1842 0,04376 0,0353 0,00006 1,70,1642 0,06084 0 ,0445 0 .00067 0 ,0 90*2398 0 .102 6 0,0634 0.0000 . © ,690 *2f l l? 0,1339 C.C7S3 0 .0027 1 .8©,S§33 . 0 ,1503 ■ 0,0045. ©.6046 2 ,5

1 * v'i.

®i£i5552.0 .0 856

%iyzi <-l *» 1 « 107 •«■ G *0 550 ra 1 «0 1

( » ■ >

m a tg i i «

5 th E xp a ri n e a t. flaw r® l«SgS5t o M r « l» 4 1 . B i f f , l a r*©«14

g r y a d d it io n a l. et-r-oj?

Jj 0PTOT

e » ia ® ' 0 . 0 S 1 4 4 0 #0104 0 ,000495 0 . 7 9

0 . 1 6 0 0 0*06416 0 , 0 1 . 2 5 0 . 0 0 0 4 8 0 .5 2O .r '1 7 0 * 0 0 5 C 2 o .cseo ' 0 . 0 0 0 I / S 0 ,17o z - ir? 0 *10^6 0 ,0805 O.0CO152 0 .1 1

.e ,s s i7 0*1S€6 0.0C53 0,0008 jfs ,i*£ .■$+v0,288$ ' 0*1509 t ,C855 0,0018 f t r*r,

w t » «/0i % #k |%} < if * * 51 »

C'.U’t'O4MW»»fWnK-.iyn'

4- o *c ji§ ** i#oS6

have' new a mw ea t-o f- give a i « fa b le . I f he low t

v e to ** i m % and r and th e * * a re

0 d#gr*e® # rad ian * new r ' new §JOB* q, m j.

*1 5 **6 • * 0 »mz& *u *0f 09 1*^522 8.5333 3 .1 §7*7 <*46 $ •0*1347 ■ •C# *4/””€!3 1*0279 0 ,3 28 3,133

■. Cl •0 *04 1 .*040 0 .329 3.101§"•59* 40#1743 ^0 *S0b3 1*051 0,329 .-3.383

5 0 ^ 0 0 * 4-o*seai *1*ST&5 1*050 0 .327 3.219

’ The va lu e * o f K g ive n above have been p lo t te d a g a in s t 0

in . graph $e# 8-and a l in e p a t th ro * the p o in t® * fb o

new va lu e * o f * 31# on the ‘ U na r * 2*56*0 *04 (g ra p h Ho* 6)

a# a lre a d y aba ted*

- I t ® ia te d :t » the t e x t ' t h e w lu e » " o f x* were a ls o m&e to

31a on a lin e o f .th e type r*®a ta n 0 *n mud the ^b s a t11 m in e s f o r

m a n i a woro da tw a& ned s o . in the p re v io u s m m * " tfm a q u a tio n

vra*' found to b * > « 8*55' t * n © * * 0 .O i and t t o l i ' ha* been p lo t te d

oh grfcph He * ■ 7 * ISeist -’the va .iu ^w .^ f q-were c o rre c te d i n e x a c t ly

the m m way a * 'be fore and the ( lio a * 15*17) in w h le h

I M i baa been aom are 0 .ven below* I t w i l l be n o tic e d th a t the

value® o f a re gensTO'ily law* tha n w hen 'us ing r«@#S8*0#04#

* » )

I n th» tfce 0ag® e rro r tfm M rg e a t

natal of I is mw S*S8 wlicfe is eotOTfet 'less tfc&n te fo r e .

there is & ©ooai&erfcbXe isayprorssent iu tiis a ttm r ©xp&ristrata

te e * &a an ..tm jp e e iio n © f fcfc© tp fc le * id X I shew*

I I S I

1st Eatparlneist* lee r*» 0 *6842# old ;?«*0*5645» B i f f * ' in r«0 *019*7

K (ft« ) ' - IX # /2 1? 5^ a d d it io n s !e rro r

J& rre r

©*1633 0,08600 0 .C03S 0 *&0026>C #06000 • •« *CCC17X

0,80

0 *2183 ' 0 *10^0 0 #0043 0*0015*0 *1020 ■*0*000X53 •

0.1?

0*2550 ' o*i2SP7 0 *m m 0 #C00.8»sQ .1887 * 0*000105

O *09

Q.3300 0*1895 0 *0058, 0*0007MO*1^C30 *000 X*/*i*

o*o8 '

0*3583 . O *2X4$ 0 •007 X 0«C013mo»8145 « 0*00028

. 0*15

0 *4308 ■ ©*89U 0 ♦eeSfy 0 -*0020X0 *20 XX + 0*00.034$

. 0*39

>)'.*■ *>4BQ.oc r-6

litsW q m 1 .0481 + 0*0088 » 1 .Q4VQ

fABIK 14 ,

Snd Bscparlwsnfc. lew r=-O .SS34* o lfl r=«O ,8808, D i f f . In r«O,0792

1{ f t * } i*s # /2 a d £ l t lo t * ls n o r

jS e r ro r

' 0*1425 0*0557© 0.0113 0 .00045 0 .870 *0075 0 .00454 0.0104 0 ,00o31 O'.38

■ -0 #249S 0.1181 0*0183 0.C 6C06 0 .0 50*0007 0,1577 0 .6 - U 0 *00' > 19 0 *150 #209«3 0,163? 0.6236 G.CO0C4 0 ,430*3802 o ,ie ? s 0 .0868 0,0014 0.7S

10 *1184 0 * 0 107

<j » 1*0061 + 0 *0 IS? «* X.0SB8

Srel fcsperlm snt flew r«~0 ,0 5 . o ld r » jsero, D l f f . I n f * © *06jL----- --^ is /qI kH / (Ml&ltlQml

ewerO .ll.b l ,03040 < M m 6 *000 IS 0 *4410.1143 o . ’. &4; o 0 #vy72 0*00013 0 *®1 .ITiXJ v ,(i"31S C* *\ y ) i C **U.069 Li *00u. U ,cX4 t *0. 0075 V #000 , '^ 7 & 0 a i m 5 *0 XX t *W wSS 0 *8 X0 ,27(53 (j * 144 0 y 30 3 0*00061 0 *40

6 )£; ,v V,,.€?>* f Q

IfeW Cb m 1 #0SB * 0*0090 «* 1*0416f »i»iqt«!lHww^ M w woet»gr

io *wnycj!; < figt.yWftnjiMiDH wrwvryw

4fcb E x s w la fts it S#w r .z *3o36 . 0 Id f * j «lOCi* . 1)I f f # i n r *0

E f f t .> 1*03/8w r o r

fi e r r o r

0 #10250.134® O *Xr-4® G*2X0J ■ L *20170 *8,, %W

0.032310 *04376 u *06054 0 »X0E0

■ 0*1330 0*1000

0 *02640 *0S®0 0*0597 Cl *01:04 0 *00730 *0700

6 # tv 076 0*600769i *000594 0 *00071o.ouaasC? *0:. 4X3

2 #07 X *88 0*87 0*61 X*8X 2*28

6)0 #2973 0 .0495

|i®«? q » X.X0? *** 0 *,0005 «* 1*0578

';>M K X?.r»fcH K x s ^ r i i is f i t tsw r*»X #>$07 it o Xd s*«l#4.1# £ H ff* i n ***0 *103

, . ( « * ) l x # / a g r < v a d d it io n a l6FFW

$ e r r o r

0 *1303 ;Q # 1*300 0*10X7 0 *2X0® 0 *2517 0*1833

0.08144 0.06446 0.C03920.1026 0 ,1263 0.1509

0 *§ M 8 0*0165 t #t3C7 c *> 3 O *O«s50 0.0292

0*6003650*0003096*0001340#0001240 *00058 0 *70X2

O' *59 0*38 0 .12 6 *09 0*33 0*56

•WiWiwiini»irfi»',!, ii<<«f.tiw t.m

fi®w % » X #087 # 0 ** 83u> ** X S3

We fonre mm a mw m t o f va lues f o r % and r and .these mm•given i n fABIB IS t e l tm*

\ is *

# dogrot® m s 0 mw r • mw »t V ;t ,:f t * new IS,*. «r4/C.o

^10*3*6 * ~7iS**41*

,9w-£®*S0a**<fC>*

•0 *^ 0 8H *14£S

0 ‘ 0*Wi© 0*8774

'**0 *GVI5 *. *5034 <*0 *05

*v, *s* *<* **£» * *HbA,*A>'I.SC?

1.0479 1*&25Q 1.C416 1,0575 1,0483

r

o *r/*r3C *520 0 *5551 0*55?

3*145 3,127 3.XC5 3 *215

r ’t f l * * *~ V O

• *rtn mw value® o f r II© on the l l tm r t*3 S te n #**0 *O§

and are s tew s i n g ra p li So* ? us a lre a & f’' s ta te d # The mw m in e s

K p lo t te d on ip*®i>h $b« i and are ' jo im d up i>f* the f u l l l in e

I t 1® s tagna ted th a t p*aph So# 7 mm %tm f u l l l in e i n

pmptj fie* S be adopted fo r f in d in g the equation o f flow a t any ■

m lu e o f # * S l ig h t ly m re aeeur&te r e s u lts w i l l be o b ta in e d

w i th th is m tb o d o ve r u s in g grmph lo * i and tb s d o tte d -11 m I n

grapti 10* 8#

J*s a tte m p t to ess he 1 a fw e t le n o f # was. a te rate ry *& $ I t

be in g re a lis e d th & t . th s fu n c t io n would be i^ B p lie s te d and

te d io u s I s uses i t i s j&xeh **» icto :r to read o f f th e value o f E

from graph lie* 8«

I t i s mm u s e fu l to te s t these re s u lts ®imim% V.mmm

Ceurley and Crimp1® formula 'm a o I f .

* ** S .lS tJ1*08!!1 *47 * 2 .4 8 fc»r# H8 *4 7 . . ............

The ran ip o f head In the present experiment® has teen

from say a #031* to 0'*S3f and-the te«e w ld th .e s an i w r t p 0*529

The r a t io o f heed- o w i’ base ( t#e« | | wrdefc is a imofmr# o f the

9shape® o f the w e i r ) 'has varied from say 0 *0 i5 to 1*0« te r

purpose® o f comparison i t was eomfei&ettt to ta te a tea# » o#329

1*®$* the Goofier & Crimps Slid W0g4f tW&M % f©s*l i> t 0*OS

't* , ? o f 0 *5 0 * * 4a »t&t*<l In it® fceaefc tlB Q &bav& mg

/v fivd fro»* «.***♦.» r i* k'tp'XM u l t t i b *» 5** is vO’* &n& Si ** 0 *1$* to

l*d f £ fcr# v*$t l © «J than k i, ^a:n 0 »0S ant 4*0 wniets r^sip I©b

ttofrt ooobtM bf iba p*8®©nfc « p D r i^ n t s * I t was

■’te s ^ fo r^ 0ob#1ik!#iS th a t © f a i r emijmrlsdii w§bM Ib x*&&® ©n tfe©

M s s lt i' § i f9 i j abow #

«tr@ eottj&wed fo r s@^n vsateta o f 0 ¥is# *15%

•?5% 0%. *7-5% *X$% 422|d! .aisl *50%. In. ea<sh eat# tha <rslu©a

# f !!• "mmn w@r@ d *0 5 t 0 *1% C ufs* 6 *1 % 0*28*, . fcn&'0#30'# For a l l

thsfc© c a l^ n la | i0 f i i l l ** 0 *$2§ i*Bd » 0*3$ id *

1% $ #i ^ lS #*Ci0 * v.

:i{tt) ts f s- .to * I> ‘W to:;, sic*'i? 3 .3Sbl*CV«« •-, L0tr.A!£S**i7

<*V 30 »ISa * is*» *#<1 V #«%##%

0 **S0

S.CfC’QI.CWQ1 ,1 7 6 1% *$ jf-iJL1,397©1,4771

r . ( *»&¥ ,5 3 0 0

s ,70-:sB.S72S1 , 1.149

1 ,2 3 1 8

4 .'? 365¥*C3 CO*•»«a if*ij* "V * JV -V*w*»* ‘j rfrr:*« *&* t2 «sisa2 ,7084

0 , t l 2J)O.CJS 5

© .06183 o ,o © se a ■

6 ,1 2 9 0fk 4 i&?M3»V * *6 '%# #S>

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0 *0 1 X79 w *U <3 3l5«j»

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0*08116

t) * io t^

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F or a l l i t® f© lo w in g tab l® 4 4 ||^ ,v ,fu s^ tlo n 8 o f 1 Jm$% efcowno

W i l l b® OK&etly tbo »as® o s ' i n ta b la 10 s ©Imams 1 and 5 o f

IM u to b io a ro r e j * * t o d l a ©&cb eat# f o r r # f # r « e t arcl bow

a* * t^ r as eolu&ifao- I and i *

SO* 0 at «»7o«50.t

a i n , } 5 ^ 1 , 6 % ! .47 2*48 ta r0K *% c*

©«e§ 0,01200 **© xc-oirc? 0.01260ft , 10 0 tCwtJlTO «C *tc 1306 0 ,032600 ,1 5 0,06135 *i ^£j 22 o ,653346 4-'0 C.o: 3C3 ™0 ,0c 6X80 O.037C00.2S 0 ,1£&G ,€-1004 0.11SS

.. 0,50 O .KC 0 «0 .61069 (,: , 1532

r * ^ r 21 & tt* 0 ®

■ "*'*<1..... .....st f t . ) S.lOl)1*08!!1 *-47 2,48 tan.ft i r * 4*'' h4

0*05 U *30£.15-

#*<■ V, .230,30 ■

0 .01-20%i %f r 4cuosrsd* # &;■?%* *«£

.1 ~v*r nf t AArf „ r vJ

WMPftm»#Cl

C .olSOD 0 ,t CVS 6 .Of* 135... . f%> #> k, y lv6 ft X^69t Itft? • *» *»

a a s iJ 1*^8 !!1 *4^ 2*4-8 %EU * l g#4T

0*0.5 0 ,0 1203 •H) «CC03$£7 0 *0X2400 «1.0 0 ,03380 *O#CKj1X00 OCMOX0 *1*5 0,00 135 40 #0050X2 ?, # j*A *%f*%» ft0*80 0 .09363 40#000150 U■0 #25'. ' 0 « X8£9 40#o 2jCC4 e . i i o s0 #50 0 .10SS 40 *o ie cs C.1006

V ’. ’/TK BS 0 9 +15*«&0*

l i f t * } 8*4S tax* 5

0*00 . 0*01280 40# O04C-6S 0.012610 *10 0*05500 40 #f 02858 0 .C3C050 .15 ' 0*03155 ■ '40*CCC152 0 .067430 *80 0 #00£/0%3 +0*0 3847 0.10610 #25 0*1290 40 *^8X65 v ,16'160*30 0*1609 40 #05vt O' 0.2039

24 $ » 4*82 H,

^ tl *) 3 #K,b l,0 S Hl,4 7 2 .4 8 ta n » # » 4? 4*

0 ,0 5 0.01280 . +0,06662.34 0*01203o , ia 6,03330 ■Hi .003431 0 .0372a0 .1-5 0.06133 *o .000477 0*0^0030 ,80 0 .G93C3 40 #0 X920 V ft ■)*» w0 ,8 5 0,1209 +0*03546 0 ,163-10 ,30 0.1CSX) 40*00249 0 #8*^84

. <#«*!

. # m *30 3 *

$*(?&*) 5 ' 2 .4 8 t i n * t ; * ' ?' * *4

§ &0 #xo0*15 fc *§§ ,c . s s ' ‘ ■ "

c *n§

tuOX^'-y ■ ' o *03320■ 0 *c$ ls&

/ . 0 t, V V ‘1 • f , *» yf5k W $ ■uj.-ja.'*O .’ iC 1

*s-0 • 0 C o / c- *Kj f04C53

7 ■ 40.fr13*1 '■ 40yw5687

/ ( +Q{oid63-tO'.67316 > -

OfOir.V'*c«*.£ru>0*5 /458 § * 1^0 5 § * ^ € 8 0**3431

l i i tab les ttm m rm M ^ rM .n g /m lm m fo r % are

from fch© eoncliasior^ o f fctss jprosonfc r©o®$reh*

T 'n , t i % « * l5 '*« < o t, l ** 3 #144* r * *o*67§a^WSjSBWWiiri'TOfn ^C^HftWPWliWWWitmjiW^WWil ^WWMUu lWii WWWCTfftBWaiTUWffmiBBBiwaWLiH

l i f t * ) C» # 144 ' ■ -0 »67SQHS/ a 0,

0*03 C *w ll5V -O.CCOS’JOl 0.01116CI*XCi 0 #03271 . *6 . ( C2150 o .ea So0*13 0 *CC0C$ •6 .0 CSC-24 0.054170 *2© ■ 0 »Q00§X -0.C131S ■ o .c ro s s0 *2t§ , c» i£03 -0.C2124 o . ic -n i© *3© 0 #1700 -0.O3S52 C.1SG0

v . t ", £7 fc * « .7 "*3 0 '. K « 3 .1 2 8 . r * *& .S f3P4' ^ n iinfri#;rLr#ri; n in iiMnrtHi i-VrT;7hi<>i.iiVft-.iViinrjn»)|MW

'a m * ) 3*18815 lfV ,g - 0 ,3694a8/ 2 ;

w #t s O .O llC l **0 .000 IStlo 0.01135C- *10 0 .03805 *6 .1 '1137 0 1410 ,1 5 0 .0 X-78 *0 .v v8 X*l7' 0.05605C-.2& - C *vO*»C4 -0 *000423 0.C30G1r *> tt >4 #*•>*? V # J*!*#’i l j t V * *0.01123 6.11746*50 0.1091 •0 .01773 0,1514 ■

TA5IK 28 - K • $*10S* r ** •0*05

SC f t . ) $ ,xsst> l # / a *0 .0 5 I # / 2 q /

0*05 0.01104 >O,UCC27§0 0 #§11610.3S 0 .03294 *0*0001531 O *05278C .15 0.06049 ' -0 #0004307 0*060050 aSO ' 0,09315 **0 *0008043 0 #C §2240 .6 8 0 giX'SC*'#? ~0 /X 1 0 6 3 0 »12§00 .30 0 #17 H : #*0 #002405 0 *XG0G

"" .r i/e 89 fc » 47e.«36», % » 3 .2 1 2 , r « 6 .8594

m t t . ) 3-fiLSb # / g o ,ess4 ss/ g q

0*0:0 0.01131 © .000,1451 0*011930*10 0 .03348 0.600,0804 0 .03424a .13 0.03130 0.002 ,360 0 ,063650*28 i; .C04S3 o,oo4,eso o ,eesM0 *2S 0 .1 321 0 .102,1C 6 0 ,14020*30 G . l 'W 0 .0 1 2 ,7 3 0.1365

f a s a 36 » « »16,,«QO«, K a 3*213 . r ■ O.S708

3,213 b B&/2 ■ 0 ,6793 -S8/ 8 %

e*es O .O llO ii 0 .000 ,3242 C .010X4e *18 0 .033*13 0 .001,053 0.065200*18 . ' 0.06141 0 .005 ,053 ■0.0 €0400 ,20 0.09454 . 0 ,010 ,57 0*1 (4010*28 6,1581 0 .010,11 © *15020 ,30 0,1737 O.C-23,50 0 ,8023

TAMf. 31 ■ • 0 «• +02°»BO*. E - 3*210* r • 0,9234

B U t . )*!* Jf.ffy

0.0234 H5/ 3 d ■O.S 5 c . o i n i 0.000,5183 0 #012*33O » 3© i A 3539 e .c-cfi ,s®o -0*05631©as o .o e iu S 0 .(0 0 ,0 4 0 0 *009409 ,20 0 .09445 6 .a IS ,51 O #1.3,0110e ,28 ( ' , 1520 Q »£}20 0 *1009S.5S . e .1736 6#94$9$3 0 #2 29 3L

» g ♦30l>*00« , If » 3 ,8 0 S . r - 1 .3

I f f t * ) ■" 3.806b # / g 1.S07 B5' 3 4

0*03 0.01120 0.000 ,7367 0*01263C* C. 03335 O' ,0 64 ,132 0 *037480 *13 0 .u€127 0.01159 0*0726® ■0 ^ 0 &*\A* +\t © ,02537 0 *11760

0.1313 G ,04.0 ns 0 #17260 *30 0 *1733 0 .t6 4 4 2 0 #2577

f b * fo re g o in g rm m ltB Imm im-mt pl&ead In to »

ta fc la (T ab lo f§o* 53) fe i* #

■ H H fM graph® f graphs fioa* ®«*X5 ia o lu s iv a ) hovo ha®a

p lo t tad# o m fo i* aaoh va lua o f 9; g iw n ahoos* &sd , ,

fchoa®. a te f t l a g lam ® tfe* .d if fa re n o a 1 fcotroaa tho -two

,, ra s a It® * .

■ft® author*** f m m m k g iw & <ra o u lts luwer than

th® Ctotfrlo? and € r iiif® ; tala ( l a a l l oaaoo osoapt

§ m m%30} hn% tbs d iffo rano a is m vy tn n H o s p ae ia lly

wish # I# nog&fci*©* ’ ffeta go#a to tfeiw th a t although

th o -fo sw iia m s m w w icton&ad to ba um & mmn 0 was

s^lira i t mvsrtholoda- <looa hold good# a t a 137 r& ta ■

o w f- the 2*a sgo © * » 0 t o * 1 8 a#-

*»

m0-

O

HSO'

H

.0 fie*m

m *rt

fiTRAIOT* X&ffl Flow*

fABIM 34

0 {d e g re e s ) fa n & £» K b(b*0*329) r r o r —

Kb q-1 5 ° -6 * —0 *2698. -0 *6842 3 .1 4 5 1*035 -0 ,6 6 1 3—7 **-45 * —0 *1355' \ —0 *3684 3 .127 1*029 -0 *3580

0 ° 0 —0. *0 5 3 .1 6 5 1*041 -0 ,0 4 8 0 19 °-59 * 0 *1760 40*3636 3 .2 1 5 1*058 40*543830 ° -0 0 * 0*5774 *1*307 3 *206 1*054 +1,239

fh© r a t i o re q u ire d f o r -0 *6667 and t h is va lu e i s

s l i g h t l y w ith o u t th e range o f the e xp e rim e n ts * I t i s

p e rm is s ib le however to e x t ra p o la te fro m 0 =» *>7^43* and *

When ta n 0 « -0 *1 3 5 5 ,

* » 11 * -0 J

A d i f f * i n ta n 0 o f -0 •

| « -0 *3580

r at —0 *6613 •q

* *t* it

n n

n «

it « t?

g ive s a d i f f * i n £ o f -0 *' q

-0 *1 5 43 « w it « it » _«|T ™

g ive s a d i f f *■; i n - fro mq

—0 *1343x *'~ ~ w

-0 *6667t© — 0 *6615 * 0 *002392

■ *

■4 * E s q u ire d v a lu e o f ta n .0 » -0 *2 6 9 8 -0 *0024 a -0 .2 7 2 2and 0 a -1 5 ° -1 4 * .

& was fo u n d to 0 *15 and when 0 «■ -1 5 ° -1 4 * r * 2 ,3 5 X -0 *2 7 2 2 -0 .0 5 a -0 ,6 8 9 7

* ■

• * p • -H3.6897 x 0 .1 8 * + 0 .10348 ,

The e q u a tio n becomes;

0, » o .1C35H4/ 2 + 1.035H3/ 2 — 0 .6897H5/ 2 . . . . . . . (K )

f o r th e o r i f i c e o f a rea A d is c h a rg in g w ith o u t lo s s o f

& (5 g a 0 *1035 1 and A. « *01289 s q . f t * * 1*857 s q f in s ,

(23)

I f the o r i f ic e is c irc u la r the diam eter would lb® 1 #558 ins *

The above e^uatlen \%) fo r the flow is designed to approximate,

to the s tra ig h t lin e Q 53 sH and i t is now necessary to f in d s *

From equations (0 ) and (D) In the te x t

" ' 1 88 8 A = H 2 2 j^££5 = 0 .6 4 0 3 .s 8x(0 .5 )4 ;

. * S tra ig h t 11 re approxim ation is Q « 0 .6 4 0 5 H . ................* •{ L)

Table Ho * .5§/below 'gives a comparison between equations ( K) and

( l ) , :■■; v.:; . v

TABIE 35

H (f t »} Q=0, 1035H1/^ + l .035K3/ 2— 0 .6897H5/ 2 Q=Q .6403H $51ffe re n e e

0 .05 0,03432 • 0 .03201. . . .....-

0 .1 0 0 *06328 , 0 ,06402 1 .2 $0 .1 5 0 ,09 4 21 0.09603 1,9 $0 .2 0 0 .12 6 5 0 .1 2 SO 1 .2 $0 ,2 5 0 ,15 95 , 0 ,1600 0 .3 $0 ,50 0 ,1927 0 ,1 9 2 1 0 .3 $0 .3 5 ,0.2255 0 .2241 0 .6$0 ,40 0 ,2 5 7 5 0 ,25 6 1 0 .5 $

. 0 ,45 0 .2 8 8 1 0 .28 8 1 zero0 .50 0 .3 1 7 1 0 .3 2 0 1 0 ,9 0 $

f r o m th e above ' ta b le t- , g ra p h H o * 1? has been p lo tte d * '. ;" J '’v'

I t a p p ea rs t h a t th e g r e a te s t d i f f e r e n c e be tw een e ^ n a t io n e ..

( & ) and ( L ) o c c u rs w ben H has asm 11 v a lu e s , th e d i f f e re nee

.b e in g .6**?>%. when H =* 0 *0 5 f t * E lse w h e re - th e , 'd i f fe r e n c e s a re

much le s s and g e n e r a l ly u n d e r 2 $

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