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Hydraulic model of Alberni harbour Nuttall, John Blakely 1951

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HYDRAULIC MODEL OP ALBERNI HARBOUR by JOHN BLAKLEY NUTTALL  ; . «_ . J oU  &U,fct,U^  A THESIS SUBMITTED I N PARTIAL FULLFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF A P P L I E D SCIENCE i n the Department of MECHANICAL  ENGINEERING  We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e s t a n d a r d r e q u i r e d from c a n d i d a t e s f o r t h e d e g r e e o f MASTER OF A P P L I E D S C I E N C E .  Members o f t h e D e p a r t m e n t o f MECHANICAL ENGINEERING  THE UNIVERSITY OF B R I T I S H COLUMBIA V a n c o u v e r Canada October,  i  1951  ABSTRACT  A hydraulic  m o d e l o f A l b e r n i H a r b o u r was b u i l t  to s t u d y t h e m i x i n g o f f r e s h and s a l t w a t e r , t h e d i s p o s a l of i n d u s t r i a l changes  sewage, a n d t h e r e s u l t o f p r o p o s e d  i n the Harbour.  The m o d e l was b u i l t  to a  o f 1/1000 h o r i z o n t a l l y , a n d l / 8 4 v e r t i c a l l y . form of L o r d K e l v i n ' s  physical scale  A modified  t i d e p r e d i c t i n g machine i s u s e d t o  compute t h e t i d e s a n d t h u s c o n t r o l a p a i r o f v a l v e s a d d s a l t w a t e r a n d remove m i x e d w a t e r . manually adjusted. the  River discharge i s  A method o f r e m o v i n g w a t e r s a m p l e s  from  o p e r a t i n g m o d e l f o r c h e m i c a l a n a l y s i s was d e v e l o p e d  as a means o f o b s e r v i n g s a l i n i t y d i s t r i b u t i o n . the  which  model i s r e a d y f o r v e r i f i c a t i o n  At present  and experiment.  TABLE OF  CONTENTS Page  I. II. III.  IV.  INTRODUCTION .  1  MODEL LAWS'  3  CONSTRUCTION  10  1. M o d e l B e d  10  2. T i d e C o m p u t e r  11  3. C o n t r o l V a l v e s  15  4. C o n t r o l F l o a t a n d S e r v o - m e c h a n i s m . .  16  5. T i d e R e c o r d e r  17  6. R i v e r Headwords  17  INSTRUMENTATION 1. Methods  of Observation  2. V e r i f i c a t i o n V. VI.  18  . . .  18 19  DISCUSSION  20  L I S T OF WORKS CONSULTED  27  L I S T OP  ILLUSTRATIONS  Figure  A f t e r Page -  F r o n t e s p i e c e : L o c a t i o n Map  of A l b e r n i I n l e t  1.  A l b e r n i Harbour  2.  V a r i a t i o n of Resistance C o e f f i c i e n t  I iv  w i t h , t h e R e y n o l d s Number f o r P i p e s  5  3.  C o n s t r u c t i o n of the Model B a s i n  10  4.  Harmonic Constants f o r P o r t A l b e r n i  12  5.  M e t h o d o f Summing T i d a l Components  13  6.  Tide  14  7.  C o n t r o l Valve  Computer design  15  8. ' C h a r a c t e r i s t i c s o f C o n t r o l V a l v e s  15  9.  16  C o n t r o l Valve  Linkage  10.  Servo-Motor C o n t r o l C i r c u i t  11.  Height  12.  Water Sampler  of Tide Vs. Model Surface  13 17 P h o t o g r a p h s of the Model Incl.  16 Area  16 18 26  ALBERNI HARBOUR Sooo  16,000  Figure 1  1  HYDRAULIC MODEL OP A L B E R N I HARBOUR BY JOHN B. NUTTALL  INTRODUCTION This thesis describes the construction hydraulic  model o f A l b e r n i Harbour.  of a  The m o d e l was b u i l t  to s t u d y t h e m i x i n g o f f r e s h and s a l t water, d i s p o s a l o f p u l p m i l l sewage, a n d t h e e f f e c t s o f p r o p o s e d changes i n t h e h a r b o u r . many B r i t i s h C o l u m b i a are  As A l b e r n i  physical  Inlet i s t y p i c a l of  f i o r d s , the results of this research  e x p e c t e d t o be w i d e l y a p p l i c a b l e . The  oceanographic aspects of A l b e r n i  Inlet are  d e s c r i b e d b y T u l l y ( 7 ) , who u s e d a s m a l l m o d e l o f t h e harbour i n which the scales horizontal vertical A simple harmonic  were, . . . .  1/4308 l/288.  t i d e was r e p r o d u c e d a n d w i n d  effects  2  were s i m u l a t e d . its  A l t h o u g h i t gave much v a l u a b l e i n f o r m a t i o n ,  s m a l l s c a l e d i d not a l l o w the p r e c i s i o n o r d e t a i l ex-  pected w i t h the present model. The s c a l e s u s e d f o r t h e m o d e l d e s c r i b e d i n t h i s paper a r e , horizontal  . . . .  vertical  l/lOOO l/84.  The a c t u a l s i z e o f t h e m o d e l i s t h e r e f o r e 23 f e e t l o n g b y 7i  f e e t wide,  and covers  model bed i s b u i l t  t h e a r e a shown i n F i g u r e 1.  of concrete  S i n c e no l i t e r a t u r e  The  s e t i n a wooden f r a m e w o r k . on t h e c o n t r o l mechanism  of  d e n s i t y s t r a t i f i e d models of t h e s i z e  of the p r e s e n t model i s  a v a i l a b l e , a n e s s e n t i a l l y new  problem  was p r e s e n t e d .  c o n t r o l r e q u i r e s an a u t o m a t i c  mechanism  and a p p l y i t t o t h e model.  Tidal  t o compute t h e t i d e  A m o d i f i e d form  of L o r d K e l v i n ' s  t i d e p r e d i c t i n g m a c h i n e i s u s e d as t h e c o m p u t e r ; i t s o u t p u t i s f e d t o two v a l v e s , one a d m i t s mixed water.  A f l o a t mechanism  w i t h the model t i d e and o p e r a t e s  s a l t water,  a n d one  compares t h e c o m p u t e d  p r o t o t y p e date  tide  a servo-mechanism which  makes m i n o r c o r r e c t i o n s i n t h e v a l v e s e t t i n g s . t i d e and p r o t o t y p e time  removes  The  computed  a r e r e c o r d e d on a m o v i n g t a p e ;  i s r e c o r d e d by a m e c h a n i c a l  d i s c h a r g e i s c o n t r o l l e d by a manually  counter.  the  River  a d j u s t e d vee n o t c h w e i r .  3  C u r r e n t d a t a i s t o be o b t a i n e d  by observing the  movement o f i n j e c t e d dyes a n d n e u t r a l l y b u o y a n t d r o p l e t s o f carbon t e t r a c h l o r i d e and p e t r o l e u m e t h e r . was  d e v e l o p e d i n o r d e r t o remove s m a l l  model f o r s a l i n i t y be  analysis.  used simultaneously  Several  A water  sampler  samples from t h e o f t h e s e s a m p l e r s may  t o produce a s y n o p t i c  survey of the  model, MODEL LAWS It characterize  i s accepted that the flow  y i  the f o l l o w i n g  o f a homogeneous  quantities  fluid:  l i n e a r dimensions V  velocity  Ap  pressure  ^  difference  . density  |£  a c c e l e r a t i o n due t o gravity  /JL  dynamic c o e f f i c i e n t of v i s c o s i t y  By  rr*  surface  tension  €  elastic  modulus  B u c k i n g h a m ' s if  T h e o r e m (3), i t may be shown t h a t a  f u n c t i o n describing the f l u i d motion i s :  4  I n o r d e r t o have complete  s i m i l a r i t y between model and  p r o t o t y p e t h e s e v e n t e r m s i n t h e a b o v e f u n c t i o n must  be  s i m i l a r f o r both. The Gauchy number, V ^ j £  may be n e g l e c t e d i n  f  water-ways models s i n c e minute.  the e f f e c t  of c o m p r e s s i b i l i t y i s  S i m i l a r i l y t h e Weber number,  tVcr"  p r o v i d e d s u r f a c e t e n s i o n has a n e g l i g i b l e p r o t o t y p e and model.  may  be o m i t t e d  e f f e c t i n both  S i n c e v e l o c i t y i n t h e model i s f i x e d  by the c h o i c e of d i s t a n c e and time s c a l e s , t h e Reynolds number, ^^f/ju.  c a n n o t , i n g e n e r a l , be made s i m i l a r f o r  model and p r o t o t y p e .  T h i s i s because  v i s c o s i t y c a n n o t be a r b i t r a r i l y t h e v a l u e o f ^Vf/yu.  fluid  chosen.  d e n s i t y and  I n waterways models  i s less than the prototype.  The  effect  o f t h e d e c r e a s e d R e y n o l d s number i s t o d e c r e a s e t h e s c a l e of t u r b u l e n c e i n the model.  Where t h e R e y n o l d s number i n  the model i s l e s s t h a n t h e l o w e r l i m i t f o r t u r b u l e n t  flow,  t h e m o d e l c a n be e x p e c t e d t o b e a r no r e l a t i o n t o t h e p r o t o type, i . adse's  e. n e a r t h e b o u n d a r i e s .  By a n a l o g y w i t h  diagram of f r i c t i o n f a c t o r  v s "E.Vjo / /  At  Nickurf o r pipes,  F i g u r e 2, i t a p p e a r s t h a t d e c r e a s e d R e y n o l d ' s number i n t h e model w i l l have r e l a t i v e l y s m a l l e f f e c t i f the f l o w i s t u r b u l e n t , p r o v i d e d the model roughness enough. difficult  I t has b e e n shown by A l l e n  c a n be made l a r g e  ( l ) t h a t i t i s sometimes  t o make t h e b o u n d a r i e s o f a d i s t o r t e d s c a l e  sufficiently  rough.  model  5  In the f o l l o w i n g d i s c u s s i o n as h o r i z o n t a l d i m e n s i o n s , and The s u b s c r i p t s /*»v a n d &  T£  and  y  as a v e r t i c a l  v- t o t h e r a t i o  q u a n t i t y i n the model t o t h a t i n t h e p r o t o t y p e . represents  a time  the  c a n be s a t i s f i e d  are chosen.  letter  I n order  provided  that  Now  therefore  U n l e s s the v e r t i c a l are  of a  equality  must be s a t i s f i e d .  and  The  proto-  interval.  The F r o u d e number V s u i t a b l e model s c a l e s  dimension.  r e f e r t o t h e model and the  type r e s p e c t i v e l y , and t h e s u b s c r i p t  ~t  are taken  equal,  t h e E u l e r number,  and h o r i z o n t a l s c a l e r a t i o s ^ ^/A  f>  , a characteristic  of the f l o w  p a t t e r n , c a n n o t be made e q u a l i n m o d e l a n d  prototype.  The change i n t h e E u l e r number i s s m a l l  By w r i t i n g t h e B e r n o u l l i e q u a t i o n  f o r turbulent  flow  however. (4)  O.IO0.08 0.06 Resistance Coefficient f  . 0  \  \  !  r/k = 15  \I  0.03 0.02 •  •^r/k = 30, ,6 ^  r/k»6o  \  1  r/k=I26 r7k=252  ^—r/kT  v  507  1  0.01  2000 1000, 10,000  100,000  1,000,000  • R e y n o l d s Number VARIATION OF RESISTANCE COEFFICIENT WITH REYNOLDS NUMBER FOR r = Pipe radius k = Height o f a r t i f i c i a l F i g u r e 2.  PIPES  roughening  particles  where  ^u.' ,  /v'  , a n d >«r' r e p r e s e n t i n s t a n t a n e o u s  u r e s f r o m t h e mean v e l o c i t i e s i n t h e X directions  respectively.  the v e l o c i t y  V  .  From t h e above  & p i n  between model and p r o t o t y p e  becomes  since  -  .  y  f  a n c  :  The mean f l o w i s t a k e n t o h a v e  t h i s value of  Substituting  f  depart-  equation  ^Vy^j,  ^ the r a t i o  By t h e Froude r e l a t i o n s h i p ,  s o t h e m u l t i p l i e r o f A % . 2g i n t h e a b o v e e q u a t i o n becomes unity.  The m u l t i p l i e r o f t h e £«*ryL  t e r m s does n o t s i n c e  7  This  means t h a t k i n e m a t i c  s i m i l a r i t y c a n n o t he o b t a i n e d i n  a d i s t o r t e d s c a l e model and t h e r e f o r e similarity  mechanical  i s precluded. The  only  complete  requirements of  -*/y  i f t h e model i s g e o m e t r i c a l l y  a n d ^/k a r e s a t i s f i e d s i m i l a r t o the prototype.  A r a t i o n a l b a s i s f o r the r e l a t i o n s h i p between vertical (1) w h i c h  and h o r i z o n t a l scales  i s a v a i l a b l e i n Lacy's  rule  states •z.  The  basis of this  r u l e i s t h e Regime T h e o r y o f a l l u v i a l  c h a n n e l s , o f w h i c h L a c y was a n e a r l y c o n t r i b u t o r .  Blench  (2) h a s d e v e l o p e d t h e Regime T h e o r y t o i t s p r e s e n t  state  in  which  where  V  i s t h e mean v e l o c i t y o f f l o w  i s t h e mean d e p t h , a n d ^  O  i n the channel,  i s a constant  depending upon t h e  m a t e r i a l f o r m i n g t h e c h a n n e l bed and upon t h e s u p p l y o f bed  m a t e r i a l from sources other  called the bed f a c t o r " . M  w  than the bed i t s e l f .  The s i d e f a c t o r  *  W  is  i s d e f i n e d as  8  where W  i s the c h a n n e l w i d t h and  m a t e r i a l forming the cohesive channel  S  slope  s»  depends u p o n t h e  s i d e s of the channel.  The  i s r e l a t e d t o the o t h e r v a r i a b l e by the  relation  _v2 where  C  ,  •  fvw)4  c  i s a non-dimensional  constant and  ^  i s the  k i n e m a t i c v i s c o s i t y of the f l u i d - s e d i m e n t complex. The s l o p e may be e x p r e s s e d  as  Q where  Q  %  i s the r a t e of flow i n the channel, i .  e . Q ^ V W D  I f t h e same m a t e r i a l f o r m s t h e c h a n n e r b e d and s i d e s i n b o t h the model and p r o t o t y p e , t h e s l o p e  equation  may be w r i t t e n  f o r the model, u s i n g the Froude s c a l e s t o r e l a t e ;  and  -  *bor t h e p r o t o t y p e .  > L ? .  5"  _  _^L>  Taking the r a t i o of  2u*to  and  9  but  and  therefore  The f o r c e , can  e f f e c t of the E a r t h ' s  o n l y be  simulated  on a r o t a t i n g b a s e . step are  The  t h o u g h t t o be  by m o u n t i n g t h e  e r r o r s due  of the  experimental  the  e f f e c t of C o r i o l l i s ^ w i l l not The  errors i n this  x. - ' / i o o r  l a b o r a t o r y s p a c e and 1  /8>4-  0  * s e l e c t e d on  water supply,  , selected with regard t e n s i o n over the  the  follows: the  basis  vertical  the of  scale  i n t e r - t i d a l area of  the  H a v i n g f i x e d t h e h o r i z o n t a l and  law.  Therefore  the  model.  from the Proude  as  t o L a c y ' s r u l e and  of s u r f a c e  becomes  this  simulated.  effects  time s c a l e  o m i s s i o n of  p a r t i c u l a r model. be  1  e n t i r e model  of magnitude  m o d e l s c a l e s w e r e c h o s e n as  horizontal scale  "£.v*  to the  same o r d e r  the  -forces  rotation, Coriollis  vertical  scales,  the  CONSTRUCTION The  l a b o r a t o r y i n w h i c h t h i s m o d e l was  constructed i s a  t e m p o r a r y f r a m e b u i l d i n g 20 by 40 f e e t , a n o f f i c e and room o c c u p y a s p a c e o f 8 b y 20 1.  MODEL  m o d e l i s s e t on e i g h t c o n c r e t e  laboratory floor. support  base.  The  feet.  BED: The  and  wash-  two  Ten  i n c h s q u a r e beams r e s t on t h e p i e r s  by e i g h t i n c h l o n g e r o n s  s u p p o r t i n g f r a m e w o r k was  a maximum o f 0.2$  of the  the model i s f u l l  of water.  p l a n k i n g was  w h i c h form the  designed  span between the  b u i l t upon the  the;..model b e d .  p i e r s i n the  A wooden box  to  deflect  c r o s s beams when made o f two  s u p p o r t i n g framework to  Female plywood t e m p l a t e s  model  inch  contain  cut one-half  inch  b e l o w t h e r e q u i r e d m o d e l b o u n d a r y were s e t i n t h e b o x . l a y e r o f g r a v e l was first  p l a c e d on t h e f l o o r o f t h e b o x  l a y e r of concrete  i n c h below the  top of the  d r i v e n i n t o the ed boundaries  poured.  This  templates.  and  the  l a y e r extends to  one  S m a l l n a i l s were  then  p l y w o o d , t h e h e a d s b e i n g p l a c e d on t h e r e q u l :  of the model.  A final  l a y e r of concrete  then t r o w e l l e d to the s u r f a c e d e f i n e d by the n a i l The  method of m o l d i n g the model bed A co-ordinate  s y s t e m was  T h i s c o n s i s t e d of machined r a i l s t h e m o d e l box  A  and a c r o s s r a i l  was  heads.  i s shown i n F i g u r e used to place the  fixed  to e i t h e r side  complete w i t h  vertical  3.  nails. of  Nails Pinal  Used t o P o s i t i o n Layer of Concrete  Datum R a i l  First Layer of Concrete  Gravel Plvwood Templates  CONSTRUCTION OF MODEL BASIN  Figure 3  11  measuring  rod.  The a s s e m b l y  that  h o r i z o n t a l measurements  inch  on t h e model,  measurements or  three  accuracy  or five  c a n be made  inches  Figure  of  tide seven  flats  order  flat  i n the prototype;  charts  fathoms  were  These  vertical  on the model  are equal  of the area  to the  and are  i n operation  later A  built  spray  will  tests  are begun.  this  r e g i o n was  up w i t h  left was  sharp  a r e shown  f o r the t e s t i n g  This  supply  area  at a scaled The  and water  made  depth tide  t o f i t male  of control  and adjustment  studies i n  poured.  sand  o f p o r t l a n d cement  be r e m o v e d  Water  b e d movement  when t h e c o n c r e t e  " f i x " the area  was  gear.  before  i s shown i n F i g u r e  used The  the  F r e s h water S a l t water  14.  0.03 0.11  Supply  Maximum  c. f . s. c. f . s.  43 31  Hydrographic  predicting Office  uses  the tides 61 t e r m s  at Port  Alberni the  of the series  (6)  Head  feet feet  COMPUTER. In  final  t o t h e l a b o r a t o r y i s as f o l l o w s : Maximum  TIDE  l/32 inch  o f the model  t o accomodate  area,  crust  2.  to within l / l 6  13.  templates. to  and s e t so  adequate.  In the  feet  i n the prototype.  Photographs in  c a n be made  to within  of the available  considered  i s a c c u r a t e l y made  12  where  \r\ i s p r e d i c t e d t i d e a t a n y t i m e cl  , i s the a n g u l a r speed of t h e c o n s t i t u e n t which is  c o n s t a n t f o r a n y one component  a n d depends on  astronomical data only, , f a c t o r f o r r e d u c i n g mean a m p l i t u d e  to year of  p r e d i c t i o n a n d depends o n a s t r o n o m i c a l d a t a o n l y , , mean a m p l i t u d e  of c o n s t i t u e n t determined  analysis of t i d a l <*.  records,  , phase a n g l e o f c o n s t i t u e n t d e t e r m i n e d tidal  by  from  r e c o r d s a n d may be a d j u s t e d t o b e g i n t h e  s e r i e s a t any time. The  t i d a l h e i g h t may be p r e d i c t e d w i t h good  a c c u r a c y b y u s i n g o n l y f o u r o f t h e components F i g u r e 4 and t a k i n g t h e v a l u e o f components a r e and  K,  and  $  ^ A x . due t o t h e moon,  listed i n  equal t o u n i t y .  These  due t o t h e s u n ,  ^» due t o t h e moon's d e c l i n a t i o n .  The s e r i e s  t h e n becomes M  =  +- M - t cos  C  I f a l l t h e r e m a i n i n g t e r m s o f t h e s e r i e s were i n p h a s e a t  0\ «\ oo ^  o v£>  U  o o g o o o o  0  o  0  ^>^>  HI. V  V»  ->0  M  0 0  5  0 0  «  N o  00  <D  eg  0 •o-o Q  0  .vfl  0  0Y  to  l/i  eb CO  0 >o «6 •— j$ > . N.  (Si  N  o o  Q  8  ^ £ ^^  5  *0 W-  »0  o  Oo > V>  o  K > *S ft ^ >. tt ig ^  ^  to .6  fv\  ^- ^  to  «d ^1 M  oo v> K ^ ^ - 0 > •o r\ o P -O 0* 9 N  0  0  N  0s  W  \o w» > 0»  00 ^ N  0  0 0  O >  o  ^  «v  K  •to  0  0 <i  o  CO  ^  0  -  to  s&  0 o  0»  to \p  ^  0? 0  N  00 ^  M ^ >0  k  0\  v> S> ^ /V)  o  Q  5  3  £  0 5 Q fl  O  9  ^1  0  i  N  13  some t i m e ,  the  14$  maximum r a n g e .  of the  general,  be  error w i l l  out be  of  than  results  in opposition  result. of  the  The two  repeat the  these  When the  M  t  and  variation  (differences  w a t e r f r o m the  tide components  (minimum r a n g e ) i n the  height  the  two  i s a maximum when t h e i r e f f e c t i s shown t h a t  the  c a s e b e i n g the  tidal  cycle  will  however, o c c u r s  never  frequently,  monthly r e p i t i t i o n  of  the  tides.  rate  a p p r o x i m a t i o n of  of  the  model.  change valve  of  the  opening  tidal  dl-t  height  required  Thus i f  c o s C ^"t -*- ° 0  but  shown g r a p h -  sequence f o r a s p r i n g  "Near r e p i t i t i o n "  neap  The  be  in  resultant  t i d e computer are  t o e a c h o t h e r , neap t i d e s  I t can  be  components w i l l ,  s u c c e e d i n g h i g h w a t e r s ) i s c a u s e d by  itself.  and  the  shown.  diurnal  most o b v i o u s  spring  model t i d e w o u l d  14$.  of  d e c l i n a t i o n terms and additive.  i n the  Since  5 where t h e  i n Figure  (maximum r a n g e ) a r e are  error  phase w i t h e a c h o t h e r , t h e  less  The ically  resultant  is a  t o add  or  first remove  A  where  i s surface  area  Q ~ A, a ^ Therefore  the valves  o f the model,  CXJS  Qoih -v- oc  c a n be c o n t r o l l e d  so that  x^ by a series  similar  S o rv\tv\cx"\ «0%-i  to  that  used  components  f o rthe t i d a l  must  components A  ative, the  system,  and cable these  of the height  series  Figures  6 a n d 15, i s  and the r e s u l t i n the case  summation.  i s  fed  of the deriv-  and the t i d e  recorder, i n  Power f o r t h e t i d e  i s supplied by a one-quarter  induction  o f the height  pully  and t o the c o n t r o l f l o a t  case  horsepower  electric  motor.  By  using  further  maximum  sidered  negligible.  angular  Owing  i n advance  proportional to  to the c o n t r o l valves  computer  the  radians  and of a l e n g t h  used, t o i n t e g r a t e directly  ~$jz  be  c smut a t t e s t e x c e p t t h e  height  cables  the t i d a l  e r r o r 0.6$ i s i n t r o d u c e d , Spur  velocity  maximum  gears  ratio  t o t h e expense  velocities,  t o sum  which  a r e employed  between  of precisely allowable  components, i s con-  t o produce  t h e component reproducing  error  a  cranks.  angular  o f 0 . 0 0 3 3 $ was  selected  v arbitrarily The  long  manually  and the gearing  period  tidal  designed  components  within  this  limit.  c a n be s e t o n t h e c o m p u t e r  a n d w i l l r e d u c e t h e e r r o r s i n t i d a l h e i g h t somewhat T h e t i d e c o m p u t e r may b e s e t u p a s f o l l o w s : the  T I D E COMPUTER  To C o n t r o l F l o a t and Tide Recorder  Height Integrating . Cable  ± \ • Manual Adjustment  Derivative I n t e g r a t i n g Cable  . 5?  teeth  59 M,  87 88  115.  K.  Figure 6  118 119  123  o.  15  angular  position  o f t h e components  prototype  time  component  i s locked  cranks  adjusted  driving  3.  a t which  gears  CONTROL  the experiment  to their  proper  locked  the motion  available  was  nearly  linear  characteristic  sleeve  valves  with  The  the  the  5  T  remaining  positions,  and the  shafts.  VALVES.  valves  7)  relative  to their  f o r the  i s t o begin,  i n a known p o s i t i o n ,  a r e then  Since  (Figure  i s calculated  t o operate  proportional t o the discharge,  because  equation  were  no s u i t a b l e  of discharge  valves  required.  rectangular ports type  were  the c o n t r o l  Two  having  a  brass  specially  i s available  made  commercially.  f o r the valves i s  where  port the  area discharge  coefficient  f a c t o r p r o p o r t i o n a l t o the head l o s s e s i n the approach piping.  £ solving  Thus  i f  nearly  Q  f o r  X,  maximum a v a i l a b l e h e a d o f water. and expanding  i s small,  linear.  by the binomial  the r e l a t i o n  The observed  between  characteristic  Q  theorem,  and  curves  /S i s taken  Retainer Nut  , Packing Washer  Cap  Sleeve  CONTROL VALVE DESIGN  Figure 7  0  10  20  Valve  Opening,  CHARACTERISTICS  OP  Figure 8  '30 Degrees  CONTROL  VALVES  l|.0  16  "in  situ",  together  The  method  of  ative  cable  Figure  4.  the  drawings,  connecting  the  control valves  and  servo  motor  CONTROL F L O A T AND  stilling  Figure pared the  basin  16.  The  with  tide  the  The  probe  is free  of  the  i s hunting  When t h e  and  will  move  Figure  the  8.  derivin  11,  i n the and  to  arm  cup  centre  above of  on to  probe such  the  is  the  comto  forming  the  control  give  stepped  as  shown  or  in  model,  connected  that  the  the  in  either  voltage  that  the  floats  of  wires  surface  surface,  end  end model  platinum  mercury  discharge  fulcrum,  model  probe  is in error  the  which  the  lower applied  a p p l i e d when  centre  probe  and  the a  results.  further oscillation  variation  the  increased  river  the  a  i n the  i s arranged  the  about  correction  tide  mercury  mercury  is  box  downstream  by  the  tide  i s touching  servo-motor  rapid  motor  to  i n Figure  schematically  metal  Three  about  When t h e  probe  surface  the  tide  into  control  upper  the  the  servo-mechanism  proportional 10.  of  output.  dip  is a  into  height  computer  float.  Figure  built  computed  element  more  shown  shown  SERVOMECHANISM.  control float  probing  to  is  are  9.  The a  with  Figure  about surface  normal  this area  hunting.  is 9,  varied, to  a  the  new  mean p o s i t i o n  p o s i t i o n i s due with  tidal  servo-  to  height,  S a l t Water Inlet Valve  Prom T i d e Computer  Servo-motor  Fulcrum  j  Mixed Water utlet Valve  Schematic  Diagram of  CONTROL V A L V E  Figure  LINKAGE  9  I H.F. M o t o r D.P.'O.T.  Upper L i m i t \ Switch  \  Lowei* L i m i t Switch  Probes MercuryCup N.C.- N o r m a l l y C l o s e d C o n t a c t ) R e f e r e d t o P r o b e N.O.- N o r m a l l y Open C o n t a c t ) P o s i t i o n Showen D.P.D.T.- D o u b l e P o l e D o u b l e Throw R e l a y D.P.S.T.- D o u b l e P o l e S i n g l e Throw R e l a y  SERVO-MOTOR CONTROL CIRCUIT Figure  10  Figure  11  17  The shunt to  give  This a  wound an  motor. output  hub  Limit  switches  limit  to  This speed  i s connected  threaded  5.  servo-motor  by  a  which are  prototype  the  computer.  tide  accuracy  RIVER  and  a  of  Stamp  able  from  indicate in  the  and  a  chain  screw  to  the  records  the  a  of  strip a  i n speed  to  a  attached  fulcrum  to  reducer  minute. sprocket  to  the  give  the  of  adding  experiments  actual tide  the  computed  tide,  with  fulcrum.  a  maximum  machine  actual tape.  selsyn motor-generator  During  control  i n Figure  flow  the  being  mechanism  tide, The  system  computed  recorded  from  tide  when a  is required.  check A  17.  i s manually  d e g r e e Vee  overflowing  and  built  HEADWORKS.  30  Records  a  r e v o l u t i o n s per  sprocket  by  i s shown  River using  on  operated  i s recorded,  photograph  6.  nine  attached  time  is  the  of  has  o n e - f i f t e e n t h horse  RECORDER.  recorder  on  motor  engages  This- d e v i c e  only  is a  i t s movement.  TIDE  and  used  into  daily  notch the  the that  Water  Somass  is  join  at  River the form  and  channel, discharge the  of  except  ijt  model, a  basin  Figure  14.  of  Sproat  Somass,  Drainage  intervals  sufficient,  i n the  discharging into  of to  Resources  adjustment  prototype)  weir  observations  Rivers, which  controlled  Board, hours  i n times  the are  avail-  and (weekly of f r e s h e t .  18  Very in  accurate  this  r e p r o d u c t i o n of  manner w i t h  river  relatively  flow  little  can  be  obtained  expense.  INSTRUMENTATION  1.  METHODS OF  OBSERVATION.  Current available  instrument,  photographing chloride good  and  dye  has  requires paths  low  its  density  or,  i n the  the  sewage.  be  case  of  water  a  to  sampler The  a  vacuum  required.  i s to  taken  sample  to  the The  rinse water  feet  to  by  position  sample  at  by  tetra-  a  12  and  of  the  The be  since  the  It Flow  a  specific  dye  with  salinity, density  c h e m i c a l l y from  of  small  during operation. i s used  i n the  i s thus  may  however.  immersing  the  give  second.  pattern.  studies,  model  i n Figure  bottle  per  introduction  determined the  or  carbon  accuracy  flow  disposal  be  of  equipment  the  i s taken  predetermined  the  and  from  shown  0.1  correspond  sewage  Meter",  i n c o n f i n e d areas  on  by  commercially  c u r r e n t meter w i l l  excellent  effect  to  droplets  above  a  Current  The  velocities  adjusted  of water  samples. tube  ether.  observed  Salinity  The  buoyant  c o n s i d e r a b l e time to  o b t a i n e d by  "Midget  gives  negligible  are  samples  be  velocities  method  very  a  the  neutrally  at  photographic with  can  petroleum  results  used  data  to  the  model,  time drawn  the  remove  the  withdrawal and  applying  sample  through  is  the  To Vacuum System  Rubber T u b i n g  W i t h d r a w ! Tube Scale: Actual  size  One u n i t o f WATER SAMPLER  Figure  12  withdrawal bottle  until  valve. close  tube  and sample  the water  The f o r c e s  certain  The r i n s e  moved f r o m  their  samplers  2.  water  bottle  on n y l o n  kept  bottle from  ball  check  cause  i tto  further  i s employed  bottle  the rinse  t o make  sample i s  are then r e water  thrown  In practice  i n banks  of taking  "bottles"  ball  rinse  the previous  and sample  a r e t o be u s e d  water  the  preventing  f o r analysis.  t o the method  several  thus  rubber stoppers,  away a n d t h e sample  correspond  The r i n s e  no r e s i d u a l  and i n t o  reaches the nylon  of the water  of water.  that  present.  where  level  the end of the copper tube  withdrawal  water  bottle,  of five  water  o r more t o  samples  are lowered  the  on a  i n nature  cable.  VERIFICATION. The  model  will  be v e r i f i e d  by comparing the  7 distribution under It bed  of s a l i n i t y  comparable  will  conditions  portion  o f the model of  The  validity  will  existing  a t some  of t i d e  and r i v e r  the roughness  i n order  to give  of the results  a  (#)  discharge. of the  fixed  realistic re-  pertaining  be c h e c k e d b y s i m u l a t i n g time  as t o r e p r o d u c e A  observed i n nature  turbulence.  movement  occur.  that  be n e c e s s a r y t o a d j u s t  production  so  with  i n the past  some  comparison  natural  of results  conditions  and o p e r a t i n g  phenomena w h i c h obtained  t o bed  has been  the  model  observed t  i n the model  with  the  natural  hed  phenomena  will  provide  an  index  of accuracy  of  movement.  DISCUSSION It ally the  to the  as a n example consequences  bed, the  and r i v e r  quired  physical  to the harbour.  the proposed  is  ready  between  salt  Keulegan's  exchange  the  coefficient  will  studies  be n o  to determine  works.  water  i n the  river that  i n relation  by  observing to the  temperature  of the currents  of the mechanics  and  investigate  corresponds  are re-  of the the  At present  system.  consequences the model  experiment.  f o r the s c a l i n g  presentation  turbulent  there  engineering  and f r e s h  for  which  i s required  criterion  investigated  oceanographic-  requires  be  f o r verification  A  This  discharge  f o r the expression  of  changes  and i t s variations  Corresponding  study  and to  structure  d i s t r i b u t i o n since  movement  the harbour  estuary,  d i s t r i b u t i o n of s a l i n i t y ,  gradients.  In  of proposed  oceanographic tide  to study  of a t i d a l  and i t s approach  density  Bed  i s proposed  may  of density  be e s t a b l i s h e d  difference as  follows:  of the Richardson-Prandtl  of density  a t t r i b u t e where  of d i f f u s i o n of s a l t ,  and  number  7^  i s  i s the co-  efficient unit  volume by s h e a r  and the is  o f eddy v i s c o s i t y ,  rate  shown t o  the r a t e  stresses  is  shown t o  d o i n g work  per  be  o f d o i n g work p e r u n i t volume a g a i n s t  gravity  be  I n o r d e r t o have the vertical  of  transfer  same r e l a t i v e  amount  of  of  salt  i n b o t h model and p r o t o t y p e ,  the  v e r t i c a l v e l o c i t y of  salt  transfer,  of  doing work against  and hence  the  g r a v i t y on a p e r u n i t v o l u m e b a s i s  t h e m o d e l , must be i n c r e a s e d i n t h e r a t i o o f t h e to the h o r i z o n t a l s c a l e s ,  4£  -  that  s i m i l a r flow  type,  that  ±jv Jit then  r  m  vertical  4*  t h e r a t i o o f t h e w o r k done  conditions  ic  in  as  d i s s i p a t e d by the v i s c o u s  same f o r so  *«-/x  Wit  t  Assuming t h a t g r a v i t y to  rate  at dX  action is  against the  i n b o t h model and p r o t o -  22  or  from  which  since  the  Written  Froudian  f o r the  taking  ratios  Nov/  "^Ai  if  is  Therefore  the  the  of  ratio  density  vs.  model  scales are  prototype,  "the  this  equation  same f o r b o t h  density difference the  depth  scale  distortion  curves  used  f o r both  model  should  i n which  »  R  becomes  and  be  i n order model  V  and  prototype,  diminished to  give  then  in  comparable  prototype.  23  The assumptions  1.  validity  which  The r a t i o  2.  by viscous  conditions  The r a t i o  result  a r e n o t "a p r i o r i "  o f t h e w o r k done  dissipated flow  o f t h e above  ^/z)  correct.  against  action  o n two  These are  gravity  i s t h e same  i n both model i s t h e same  depends  to  that  f o r similar  and prototype, and  f o r b o t h model and  proto-  type.  The er  relative  greater be  assumption  movement  proportion  converted into  further  small  1.  i s probably i n error  i s required  i n the model.  o f t h e w o r k done heat  reduction  energy.  by shear  I f such  i n the density  because  Therefore a  stresses  i s the case scale  fast-  would  a  ratio i s  required.  The by  validity  experiment.  (8),  who  with  density  The above  suggests  result  tide  1.  Requires  2.  Is d i f f i c u l t beginning  an i n i t i a l  in  angle.  Elasticity  deal  and cable  o f space  to set to a  crank  on t h e b a s i s  be  proven  w i t h von A r x  of experiments  system  to  integrate  disadvantages;  an experiment.  of  can only  models.  has the f o l l o w i n g a great  2.  i s i n agreement  result  use o f a p u l l y  the  3.  t h e same  stratified  The  of assumption  specific  cables.  instant  o f time  The o p e r a t o r c a n n o t  setting  and c l e a r a n c e s  f o r the  within  about  three  i n t h e mechanism  be  when certain  degrees  results  i n a  slightly ?v hile  the effects  r  negligible desirable tide  distorted  are expected  n o t be p r e s e n t  results,  i n future  t o have  they  arenot  designs  of  computers.  "0 r i n g " valve  control valves  seal  shaft  gland.  was  t o be u s e d  should after  have  between body  pitted  lapping valve  H  before  shaping  hydraulic  advantage  This  8,  of the valve cotton  surface  h a d t o be  could  washer  The v a l v e  sleeve  was  f o ran  turned clearance  and the valve increased  obtained.  b e made  shaft  by  The  linear  by  ports.  use of e l e c t r o n i c model  valve  b u t do l e a  however, t h e  Original  operation  Figure  the valve  a fine  fitted.  diameter  studies  had the author's  been  devices  h a s many a d v a n t a g e s  and c o u l d  have  been used  knowledge  and the funds  here t o avail-  sufficient.  A  tide  computer  b e made u s i n g  dicting  ring"  satisfactory  washer,  surfaces.  large,  inches.  characteristic,  The  could  extra  well  called  impregnated  of rough  and an 0  0.003  design  the brazing  and a graphite  t h e 5.187 i n c h  properly  able,  during  b e e n made  was a b o u t  functioned  of the packing  because  brazing,  have  The o r i g i n a l  i n place  s l e e v e ^component  in  points  on t h e e x p e r i m e n t a l  and should  the packing  had  curve.  o f t h e above  effect  The at  output  machine  adaptable  the design  as a b a s i s ,  t o any h y d r a u l i c  of Lord  but having  Kelvin's  tide  the output  model pre-  taken o f f  25  in  the  form  of  a  control  valves.  yoke  each  on  tance. and  These  compared  which  with  a  the  The  with  tidal  being  Model,  of  the  probe  wire  An  accuracy  this  of  hunts 0.003  to  replaced to  a  summed  operate  by  a  scotch  variable  by  a  the  resis-  series  circuit  be  i s the  at  A the  shows  replaced  only  material  probe  of  promise.  inches  is  this  National  continuously  with  about  probe  contact  type  Research  In  thought  in  a  is Council,  operation  the  the  surface.  to  water  be  end  obtainable  in  way.  The which the  "t  and  be  could  surface.  developed  River  be  used  height.  i n c h wire  Fraser  he  connected  could  control float  0.002  could  could  crank  resistances  model water  currently  which  cables  component  The in  voltage  compared  probe with  control valves  The advantages  of  could the  the  tide  through  method  be  a  connected computer  a  potentiometer,  output,  would  operate  servo-mechanism.  described  present  to  above  system  and  has  none  of  the  is  completely  dis-  adaptable.  ACKNOWLEDGMENT The -Pacific at the  m o d e l was  Biological  Nanaimo,  B.  Department  C.,  constructed  Station  of  and  machine  the  of M e c h a n i c a l  the  on  the  premises  F i s h e r i e s Research work  Engineering  done at  i n the the  of  the  Board, shop  of  University  26  of  British  Columbia.  The to  author  Mr. P r e n t i c e  wishes  Bloedel  to express  of Bloedel,  who  provided valuable f i e l d  and  Welch F e l l o w s h i p i n Oceanography  search  possible;  Oceanographic direction Richmond  this  and  Stewart,  Group,  Fisheries  w o r k was  carried  Stewart,  this re-  of the P a c i f i c  Board,  under  whose  o u t ; a n d t o P r o f e s s o r W.  of B r i t i s h  criticism  made  Director  Research  regarding the mechanical  f o rinvaluable  which  gratitude  and Welch, L t d . ,  and the B l o e d e l ,  t o D r . J . P. T u l l y ,  of the U n i v e r s i t y  suggestions  data  h i s sincere  Columbia, aspects  f o r t h e many  o f the model  of the manuscript.  0.  The  Model I n  Operation  T i d e r e c o r d e r i s on the l e f t , c o n t r o l v a l v e s b e h i n d t h e man. D i m e n s i o n s o f t h e model a r e  25 f e e t by 7 j f e e t T  The The the  Model  b o t t l e s i n the f o r e g r o u n d are p a r t of dye i n j e c t o r s u s e d f o r c u r r e n t o b s e r v a t i o n s  FIGURE  13  Tide  Flat  Area  T h i s a r e a i s b u i l t up i n s a n d and ' f i x e d ' w i t h a s p r a y o f cement and  River  Headworks  R i v e r f l o w i s r e g u l a t e d by the h e a d b e h i n d the weir.  FIGURE  14  varying  water  Tide  Computer  The i n d u c t i o n m o t o r i s v i s i b l e on the T h i s d r i v e s the computer by a l e a t h e r  Tide  right belt.  Computer  The c u r v e of t i d a l h e i g h t i s t a k e n f r o m t h e u p p e r c r a n k s , t h e d e r i v a t i v e f r o m t h e l o w e r . No d e r i v a t i v e c r a n k was p l a c e d o n t h e l e f t h a n d c r a n k ( o , ) b e c a u s e l e n g t h was short.  FIGURE  15  Standpipes V e r t i c a l v e l o c i t y d i s t r i b u t i o n c a n be p a r t l y c o n t r o l l e d b y t h e shape o f t h e o p e n i n g s  Control  Float  0.005 i n c h c o p p e r w i r e s c o n n e c t moving p a r t s t o remainder of e l e c t r i c a l c i r c u i t . T h e p o s i t i o n o f t h e p r o b e arm i s c o n t r o l l e d b y the T i d e Computer. FIGURE 1 6  Water  Sampler  The wooden base i s u s e d f o r s t o r a g e o n l y , When i n u s e the copper tubes a r e immersed i n t h e model t o a predetermined d e p t h . -  Tide  Recorder  T h i s i s u s e d t o r e c o r d t h e computed t i d e d u r i n g an e x p e r i m e n t . P r o t o t y p e h o u r s a r e marked: on t h e t a p e e n d a c o u n t e r r e c o r d s t h e d a t e . A c t u a l m o d e l t i d e c a n be t r a c e d on t h e u n d e r s i d e o f t h e t a p e f o r c o m p a r i s o n . The t i d e r e c o r d e r i s d r i v e n b y a S e l s y n motor-generator from the t i d e computer. FIGURE 17  27  LIST  OP WORKS C O N S U L T E D  S c a l e Models i n H y d r a u l i c E n g i n e e r i n g , Longmans, Green & Co., London, 1947.  1.  Allen,  J .  2.  Blench,  3.  Buckingham  4.  Kalinski,  A.A  R e l a t i o n of the S t a t i s t i c a l Theory of T u r b u l e n c e t o H y d r a u l i c s , T r a n s . A . S. C. E . , V o l . 1 0 5 ( 1 9 4 0 ) , p . 1 5 4 7  5.  Keuligan,  G.  M o d e l Laws f o r D e n s i t y C u r r e n t s , f r o m t h e Proceedings o f the C o l l o q u i e m on t h e Flush-of Estuaries. Woods H o l e O c e a n o g r a p h i c I n s t i t u t i o n , Woods H o l e , M a s s . U.S.A. 1 9 5 0 .  6.  Schurman,  P.  Manual o f Harmonic A n a l y s i s and Pred i c t i o n o f T i d e s , U.S. D e p a r t m e n t o f Commerce, S p e c i a l P u b . No. 9 8 . 1 9 4 0 .  7.  Tully,  8.  vonArx,  The H y d r a u l i c s o f S e d i m e n t B e a r i n g C a n a l s and R i v e r s , Evans I n d u s t r i e s L t d . , Vancouver, 1950.  T.  E . S i m i l a r Systems P h y s i c s Review, Oct., 1914.  John  and Dimensional aquations 4. S e r 2. p p 3 4 5 - 3 7 6 ,  P Oceanography and P r e d i c t i o n Pollution i n Alberni Inlet, Bd. Can., B u l l . 8 3 , 1949.  of Pulp M i l l F i s h . Res.  Synoptic Models o f the C i r c u l a t i o n of E s t u a r i e s , from the Proceedings o f the C o l l o q u i u m on t h e F l u s h i n g o f Estuaries. Woods H o l e Oceanographic I n s t i t u t i o n , Woods H o l e , M a s s . U . S . A . 1 9 5 0 ,  

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