The penetration of sea water into the Dutch river mouths and estuaries

s.

II

-

C.

3

PAPER

by

Dr. ir,

J

.

VAN VEEN,

Chief EngineerA to the Rijkswaterstaat, Dr.

J

.

J

.

DRONKERS,

Mathematicianto the Rijkswaterstaat, Department of 'I'idal Rivers,

Ir. W. NOTENBOOM,

Chief Engineer to the Rijkswaterstaat, Dr. ir.

J

.

C.SCHÖNFELD, Civil Engineer to theRijkswaterstaat,

PART I

THE PENETRATION AF SEA WATER INTO DUTCH RIVER MOUTHSAN:D ESTUARIES.

(Dr J. vanVeen).

§ 1. The parties interested inefficient water control.

In consequence of the low level of part of the Netherlands, there is at many places a seepage of salt water underneath the dykes and dunes, which threatens to make the low-lyingland infertile. Owingto the dredging in some estuaries for the sake of navigation, the sea-water in these estuaries isalso pushing further inland than it used to do. Shipping locks and sluices, with the exeption of siphon-sluices, are not salt-proof either; (see part lIl). Vet another cause of the fresh water becoming brackish is found in the great increase in the salt-content of the Rhine water. All this, and also the fact that in times of drought there is not by any means enough fresh water for the requirements of agriculture, has caused the present-day fresh water economy to become one of the most important problems now being studied in the Netherlands. The purpose is to achieve more complete control of the water, both qualitively and quantitatively.

The followingare some of the interests concemed:

a. Navigation. It does not matter much to a ship whether shesailsin salt water or in fresh.Muchsalt,however,flows inland through the locks.Dredging work in the estuaries affects the salt-to-fresh proportions.

-2-b. Agriculture and horticulture. If the chlorine-content of the canals and ditches

increases to 1,200mg/litre, a decreasein milk production is already perceptible.

Agricultural vegetation shows a decrease at 1,500 mg/1. Horticulture and floriculture require water with a chlorine content lower than 300 mg/1. The salt accumulates in hot-houses unless artificial rain isapplied. The loss to agri-culture and horticulture in the Netherlands amounts to many million guilders a year. In the horticultural districts irrigation water with a chlorine-content amounting to 10,000 mg/I wasunfortunately not rare inyears ofdrought. During such dry years mortality among cattle increases. Sheep, however, can tolerate

rather muchsalt.

c. Drinking-water. Human beingsrequire drinking-water with a chlorine-content of 100to 200mg/I, but can, if need be,tolerate a higher content. The limit be-yond which it can be tasted is somewhere near 300 mg Cl/I.

d. Public health. In places where brackish water occurs regularly in the canals and ditches,the malarial mosquito appearsfrequently. In freshwater the malarial

mosquitodoesnot flourish.

e. Industry. Industry produces muchsalt that must be got rid of. On the other

hand it requires much fresh water which is so

-metimes even drawn from the soil, where its place is taken by salt water.

:/;:///~ peet

:;/'//~ snd marine deposits _deltd

Fig.!. - The small internal Rhine-Maasdelta.Between this delta andthe somewhathigher sand on theoneside and the dunes along the coast on the other side were peat marshes. whichwere forthe greater part destroyed by the sea and Man between1000B. C.- 1600A. D.

"

f. Fisheries. Many fres

h-water fish are sensitive to

sewage andsalt and to the general pollution of the water usually accompany

-ing it.

g. Recreation. Swimming, yachting, and so on are not affected by salt at all. But a high ch lorine-con-tent in the rivers and

in-land waterways is often accompanied by a high

bacteria content, asindus

-tries and population een-tres produce both.

One maynot contend a priori that all these in

-terests are so conflicting that no compromise can be found. Satisfactory so

-lutions for combating the salt difficulty are concei -vable, but they call for extensive work.

§ 2. The invasion of the sea in the Netherlands.

One of the peculiarities of Dutch morphology is that the Rhine-Maas delta is but smalI, a result of the limited soil erosion of Western Europe (fig. 1). It is situated «internally ». Between the range of dunes along the sea coast and the higher land with the internal delta, marshes or peatsoil were formed to a width of from 30to50kilometres and to a length of afewhundred kilometres, whichwere gradually destroyed by sea and by man, who used the peat as fuel. As early as pre-Roman times the sea encroached alarmingly upon the tender, not very solid land.The North Sea has a considerable tidal-run which may, withextra strong winds, beblown up another 3metres. Thus the assault of the sea has a considerably more powerful and disastrous effect in the Netherlands than for instance in the Nile estuary.

About 1570 things looked black for the Netherlands. Since approximately 500 B.C. the sea had been launching a pineer attack. In the North, the centrally situated «Flevomeer» which, so far, had had fresh water, was changed into a salt inland- sea,renamed the Zuyder Zee,in about the year 1300,because the sea broke into it from the North. In 1412 a 50.000 hectare polder was lost overnight in the South, so that the brackish water here reached as far as Dordrecht and Rotterdam. Between the claws of the «pincers» a fresh-water stretch only 60 kilometres long remained between Rotterdam and Amsterdam (fig.2). This, however, was a layer

Fig. 2. - The invasion by the sea reached lts maximum in about 1570.

Fig. 3. - In 1932 the central area containing rresh water was increased to 160 kilometres ; before 1932 the

length was only 60 kilometres. of low-lying marshland that was eventually dugout (and burnt) further than it had been before,so that large lakes came into being. The period round about 1570 is so-metimescalled « the period of trouble » in the history of the Netherlands because of political difficulties, but, as may be gathered from the above, the country had also fallen on evil days in other respects.

Round about 1600some improvement set in, especiallybecause ofthe introduc-tion of windmills. From that time onwards the wind supplied the power with which to drain scores of lakes in Holland, particularly those north of Amsterdam, and also for sawing the large quantities ofwood thought necessary to improve the sea defences. 187

-4-The situation remained more or less precarious, however, until 1932, when the Zuyder Zee wasenclosed ':>ybuilding the famous « Afsluitdijk », this inland sea thus once more becoming a fresh-water lake.The distance between the two « claws » was after 1932 about 160 kilometres (fig.3).

5ALINlTY DlFFlCULTlE5

(>00C?

)$lJ~

.

o

~p SALINITV IN NORTHHOLLAND B~FORE ENCL05UR~ OF ZUIDERZE.E 19.30 - 1934

·

·

/....·1 /

....

,

\.....,. i. " \.-. L_.-·...·-\

c:::::J

300 - 1000mgr:cVliter

P

,=

>{1JI

1000-2000 mgr:CyJiter _ more then 2000mgr:CVliter 25 i j i i ,-i i i i i ,._.- -v,-.•: ; r';' i ...\ " I ; i ...) ,.l i ,,-_' i ..., " " ;..._."

Fig. 4.- Table of the districts having salt difficulties to contend with in the lower part of the Netherlandsduring he auturnn of1947and the autumn of1949.The exact extent of thesalt problem in Zeelandis not yet known.Not every area there is saltier

than 2,000mg.CVI.

The difficultiescaused bythesalt have not by any meansbeen warded offby this. Especially in the south-west (Zeeland) there are some islands which cannot be flushed with fresh water as they are surrounded by salt water (fig. 4). The

rain-fall alone is not sufficientfor thispurpose. The map in fig. 4 is only diagrammatic. The black areain Zeeland maybe somewhat exaggerated.

§ 3. Factors affecting the position of the salt limit in estuaries.

The salt content whichrnay, if necessary,be considered acceptable as a limit, is taken asbeing300 mg chlorine/litre, aspreviouslystated.

Every day samplesare drawn at ten placesin the rivers containing brackish water at the turn of the tide, both at high tide and at lowtide. Furthermore the 300 mg limits in the river near Rotterdam are also deterrnined at each turn of the tide. Allthesamplesaretitrated, but todetermine the positionof the 300mg limits an electrical method isused. (Dionic, Philoscop,both devicesare suitable,provided they are checked with the help of titrations).

In the mouths of the Rhine and the Maas the 300 mg Cl/I limit is, under normal conditionsand at high tide,near Rotterdam (fig 5). During the exceptionally lowdischargesof the Rhine in 1947 and 1949this salt limit reached,at high tide, some 18 kilometres further inland. At that time there were 9 waterworksand 36 poldersluicesin the brackishwater area in the mouthsof the Rhine and the Maas, which consequentlycould not drawfresh water from theriversduring those periods. Fig. 5 alsoshowshowslowly a fresh water partiele in the river movestowardsthe sea during periods when the level of the water in the Rhine and the Maasislow.On the Rotterdam «Waterweg», through which about 42

%

of the Rhine water reaches the sea, the daily distance is relatively large. Even with the minimum Rhine dis-charge of 592 m3/sec (normally 2,350 m3/sec, maximum discharge 13,000 m3/sec) the seaward movement of a water partiele near Maassluisisover 7 kilometresa day.

In the southernmost mouth of the Rhine ,the «Haringvliet», which is about 3to 4 kilometres wide,through which about 48

%

of the Rhine water isestimated to flow out (10% reachesthe sea via the Afsluitdijk), the seaward movement is verysmalI.Here the daily movementof a water partiele isduring minimum discharge only about 500 metres. Moreover,with each tidal run sea-water comes from the south via the Volkerak into the Haringvliet, so that it is understandable that in times of drought the mouth of the Maas (called the Amer) becomesbrackish far inland.The highest limit of thesalt in the northern branch ismore than 40 kilometres from the sea, in thesouthern branch (Maas) this is slightly more than 60 kilometres. The pressure of the tidal run from the South is also such,that during periods oflow discharge from the Rhine(the Maas hasthen a flow ofonlyabout 35 m3/sec) both the Kil and the Spui bring some brackishwater into the Oude Maas (fig. 5). ThisOude Maas,otherwise remaining fresh, is then,as itwere, attacked from the rear. From observations it appears clearly that the river discharge greatly affects the position of the salt lirnits.Disregarding daily fluctuation there isa close relation-ship between river discharge and the position of the 300 mg limit. If the discharge of the Upper-Rhine is at its minimum,the 300 mg limit at the turn of high tide is on an average near the 990th kilometre-stone,that is 10 kilometresbeyond the bridge in Rotterdam (fig. 6) ; at the turn of low tide it isnear the 997th kilometre-stone on the surface and near the 996th kilometre-stone at the bottom. When the discharge ofthe Rhine islarge,e.g. 10,000 m3/sec., the 300 mglimitin the Watere weg at the turn of high tide is on an average near the 1024th kilometre-stone (surface) and at the 1015th kilometre-stone(bottom) , and at the turn of low tide it isoutside the piersat the Hook of Holland (the 1033rd kilometre-stone).

... >.Q o

0-1949

WESTLAND MO~TLANDWAAD OB.5ERVED LIMITOf 500mgCJtjATHWIN 1949

DURING 5TRONGW~TERN WIND

WILLEM5Ti_

i

·

fOR THE DRINKWATER COMPANIE.5 WATERINTAKE "t,. 0' POLDER5

q

5TATION5 FOR DAILYOR IRREGULAR0B5ERIlATION5

DAVI; 2 1 .

I I

b

DA.ILV OQIFT OF A WATEQPARTICLE} ATLDWE5TOI5CHARGE

OAYS2 1 OF 592mo/sec

'U ..." ft tt U

RElATION BETWEEN&X)

mg

CVI

LIMIT IN ROTT.WATERWAY ATHW AND LW AND LEVEL AT L081T

1947,'48 end '49

D!:>TANCE INkm ~34'---''---'---'---'---'---'~--.---r---.---,~~4 1030

/

NORTH5EA 1002 994

KRIMPEN 'Yo LEK 990

17.Xl

Fig. 6.- The influence of the Rhine discharge on the position of the salt limit of 300 mg. Cl/I. in the Rotterdam Waterweg.

One day differs from another. Spring-tide, neap tide, the preceding tide and also the direction and forceof the wind affect salinity in the estuaries. .

From thediagram infig.6 it followsthat as an average a quantity of fresh water of 725 m3/sec. must flow past Rotterdam to keep the water in the river by the Park-havensluice (the most important inlet for the horticultural district of the « West

-

8-land») reasonably fresh at high tide. If the depths and widths of the Waterweg and

the areas of the harbours along the Waterweg change, the 72S m"jsec figure will

have to change tOD.This figure exceeds already the minimum discharge of the entire

Rhine.

The principal cause of the salt limit laying far inland is mixing. Registering

sa-linometers (these instruments, tOD,must be checkedrepeatedly) working onthe prin

-U 200. I

150.._ ..:' __ w"W' > - .

10°0 12345678 910H 1213141516171819202122232t.t

OUDE MAASBRIDGE. AT SPUKENI55E 2..1 - 4 -1948 LEVELATLOBIT 2 DAV.5 EA~LlER 10OOcm·HJAP 2500 22 1800 1400

~woo

E

800 c 600 ". ". """.r 20°0 1 2 3 4 5 6 7 8 91011 12131415164711:',1920 2t 222324

NIEUWEMAASATVLAARDINGEN km 1012 4-5 - 1938 LEVELATLOBIT2DAY5 EA~L1E~ 936 crn»NAP

j

200~·9·"~"·~·~""~·"~·"·~rlr4-T-T~.·~".~_.~"·~""~,,...

~~_'-+-+~

.~.·,,~.~,,.~_~

...

~

.

.~

.

~

.

.

.

o

1 2 3 4 5 6 7 8 9 10 11 12 131Lj15161718t9 20 21 22 232Lj

OUDE MAAS BRID6E AT 5P!JKENI55E 27- 5- 1952

LEVELATL081T2 DAY5 EA~LJER I006Cm+ NAP

Fig.7.- Examples of registered chlorine-content.

a-c In theOudeMaas:slight mixing,see the abrupt changes from freshwater tosalt water.Brackish water periodisshort during each tide.

bInthe Waterweg: much mixing owing to underflow,open har-beurs,navigation and groynedstretches, no abrupt changes from fresh to salt. Brackishwater periods last throughout the tidal cycle.

ciple of measuring the electrical conductivity showthat in the Waterweg much more

mixing takes place than in the « Oude Maas » (fig. 7). In the Oude Maas the salt

limit suddenly passes the point at which the measurements are taken (an almost v

er-tical line) and disappears almost as suddenly when the tide has been running out

for an hour or so. In the Waterweg the increase in the salt-content occurs gradually

and the decrease is even more gradual. These are signs that there is much mixing

in the Waterweg and not muchin the Oude Maas.

Mixing is of great consequence,for if there were no mixing,the river would at

each low tide be flushed clean on the surface as far down as Hook of Holland; the

salt would,at each high tide, not come farther inland than the tide-water itself,whicb

is near Maassluis, about 15 kilometres from the sea. Owing to mixing, tbe 300 mg

limit reacbes, on an average, about 25 kilometres fartber inland wben the discharge

of the Rhine is small and about 15 kilometres farther inland when the discbarge is

normal.

The causes of mixing are the following : The depth of from 12 to 13 metres

whicb at present prevails in tbe Waterweg is great enougb to show a so-calledsalt

tongue or salt-toedge near thebottom, over whicb the fresh water flowsaway to the

sea (fig.8a). Consequently there isbere a salt under-current, wbicb moves Ior some

MOUTH SURFACE

DURIN6 H_W

Fig. 8.- a Diagrammatic iHustration of the esalt-wedge» in the Waterwegwith

mixingtaking placeatthesurfaceof the wedge.

b-c Lines of equal chlorine-contentregisteredinthe Waterweginthe landwardpart

of the «satt-wedge». .

-10

-hours per ti de in a direction contrary to that of the fresh or brackish surface-cur -rent and this causes severe mixing which brings the 300mg limit much farther i

n-TIDE-CURRENT

PETR.

HAVEN

(OIL-PORT)

HW toOi NAP EBB-CURRENT 'DURING LW FLOOD-CURRENT

_----.

IN WATERWAV --_ upper-current --_ under-current DURING HW

Fig.9. - Tidal surface and bottorn currents in the mouth of an open harbourinthe brackish water area of a tidal river (theOil Harbeur at Pernis),

land than the tide-water itself.As a resultof this extensive mixingthe isohalinesHe

far apart, seefig. 8b,c.

At high tide the salt tongue lies, ofcourse, with its tip farther inland than at

low tide. The resultant current in the salt tongue is landwardsnear the bottom and

seaward near the surface.The landward resultant current near the bottom always

contains muchsand and silt, whichenters from the sea and whose material is too

coarsetobe carriedout againviatheupper layers. Also the riversand and the

hea-vier part of the river silt doesnot pass the salt tongue. Consequentlyall brackish

water areas in the world nearly always contain an excessivequantity of silt and

sand and are,ifonlyfor that reason,oflittle use as open harbours.

In addition to this there isthe excessivemixinginsuch a brackishwater area.

As a result of the differencesin specific gravity the heaviersalt-water creepsalong

the bottom into an open harbour at the time approaching high tide and then, at

about low tide,it iscarried back to the river (fig. 9).

This peculiar filling and emptying of brackish harbour basins not only

eau-sesextra mixingin the river but also increases the silting up of the open harbours

because the floodwater,whichsometimesmovesinto the bottom, containsmuchsilt.

Consequently the construction of harbour basins in brackish water areas should

be avoided if possible. Such harbour basins should be excavated in areas in which

the water ishomogeneousand clean.

The changesince 1925 in the averageyearly chlorine-content of the Waterweg

near Maassluisis shown in the graph in fig. 10. FiK. 11showsthat a change took

5UMMARY OF AVERA6EANNUALCHLORINE CONCENTRATION

2000 '2.50 DURIN6 LW AT MAASSLUIS

r

-r-

r-....

r-

r

-r- r- r-r- I- 1-1-h ,...

Ih-f

r

1750 1500 1250 ~ 0'1000

E

C 7!:)0

._

\J 500

o

2

Ol

....

YEAR,s

Fig.10. - The increase in Cl-contentin the Rotterdam Waterweg near

Maassluis since 1925.

place in the years 1930-'34.The tidal volumes in the Waterwegbeneath the junction

with the Oude Maas have only increased by from3 to 5 per cent. So it hardly can

have been these relatively small causes which brought the salt limit to Rotterdam.

- 12

-Both the deepened Oude Maas and the new « First Oil Harbour » acted as new mixing basins however,thus moving the salt limit landwards. They were works in the brackish zone.

In fig. 12 we can see that neither the cross-section of the Waterweg nor the quantities of water flowing through it changed much round about 1930-'34;

nei-AVERAGEANNUALCHLORINECONCENTRATION ONTHE WATERWAY MAA55LUIS 4925+;",,4954 LW PERJOD o 000 000 000 ~ N ~

AVE.RA6E DI5CHARGE OF THE RHINE INmÎ'~e(

Fig.11.- Theaverage yearly Cl-content inthe Water

-weg near Maassluis at low tide forthe years 1925-1951. Mter 1935the saätsltuatlon provesto be differentfrom

that before 1930.

ther did the total area of Rotterdams's harbour basins.The mixing factors in the bra

-ckish zone, however, have changed. The shores of the brackish stretch of the es tu-ary should be smooth.Every new open harbour basin in the brackish water area re-sults in

a. much dredgingwork having to be done in the harbour basin itself, b. more dredging work having to be carried out in the harbour basins s

i-tuated farther inland,

c. a movement ofthe salt limit of 300 mg/l further landward.

Mixing is a result of the turbulence of the current, of the irregular banks, of the turbulence caused by navigation and the result of the presence of open harbour basins, but we may say à priori that we are not able to change easily any of these

causes. The best thing to do is to keep away from the heterogeneous water and give it smooth banks. Mathematiciaris of the Netherlands Public-works Department have

DI5CHARGE INm3Jsec ~ N ()I l'- (]I o 0 0 0 0 00000 00000 i880r---~r_--~--~ C.ONTENTSIN 106m3 UNDERNAP I\) ~ 0'» en 0 N

1880°r-~~°r-o.-__~o ,o~__~o

1890

o o ~

AREA IN

hd

Ftg. 12. - Changes in the volume and flow of the Waterwegsince 1885 and in the harbour areas along the Waterweg since 1920.No grea.t changesin 1930-1934appear

from these figures.

worked out formulae for the mixing resulting from the turbulence of the current at the dividing line between salt water and fresh (seêPart II).

§4. W orks and projects for combating salt.

The seaward extension of the Oude Maas, called Brielse Maas, was dammed up at both ends in 1950 (fig. 13). The reason here was mainly to check the salt on the adjacent islands. Horticulture and agriculture suffered considerable damage as a chlorine-content of 10,000 mg/l or more occurred, but now one can draw water at random from the fresh-water reservoir that has come into existencebetween the new

dams in the Brielse Maas. A diagram of the de-salting of the Brielse Maas shows

that, although the chlorine-content has greatly decreased, the 300 mg limit desired

has not yet been achieved completely. To this end further works will have to be

constructed.

At

present two ofthe four mouths ofthe Rhine have been closed,theYsselmouth

(Zuider Zee) in 1932and the mouth of the BrielseMaas in 1950.Larger projects

designed to combat salt more effectively are being studied. In doing so two gui-dingprinciplesare being followed :

-_ 14

-a. the coast line of the Netherlands must be shortened and closed as much

as possible; creeks, superfluous estuaries and river-mouths must be

dammed up. Locks in the coast line must be avoided as much as possible.

b. the water of the Rhine and the Maas, and the rain-water must be kept

pure and must be used as economically as possible for flushing and ir

-rigation purposes.

The principle mentioned under a, that of shortening the coast line, is a cent

u-ries-old one. Originally the Netherlands probably had a salt coast line of from 2,500

to 3,500 kilometres, due to the many indentations in which the ti de had a free run.

Of·_..·!::,_~......,PLLAND

- - - farmerdyke

former BnelseMddS.

now fresh water besin

VOORN!:

Fig.13. - The dammingup of theBrtelse lIlalts in1950.This created a new

fresh-water lake consequentupon the shortening of the coast (cfr.the enclosing

of the ZuyderZee).

The many place-names ending in « -dam» bear witness to an early shortening of the coast by damming up creeksandso on. In 1840 the Netherlands had to maintain a salt coast-line of 1905 kilometres. In 1930 that length was 1620 kilometres. Now it is 1261 kilometres and it might be possible finally to shorten the coast in the future to 500 kilometres.

Here are the figures for the latest shortening of the coast. The enclosing of the Zuyder Zee (1930) made the coast line 300 kilometres shorter; the damming up of the Sloe (1949) yielded 7 kilometres, damming up the Brielse Maas (1950) cut the coast line down by 30 kilometres and the enclosing of the Braakman (1952) by

210 kilometres.

In addition, the coast must be sealed against leakage. All sluices would have to be closed and any sluices other than siphon sluices should be prohibited.

As regards the principle mentioned under b - the use and keepingpure of all the available fresh water - this givesrise to great concern both as regards quantity and

quality, beeause both the Rhine and the Maas are increasingly being used to get rid of sewage, and beeause the harm to agriculture owing to drought and to the water becoming salty is very considerable. The potasslum mines in Alsace, the industries

and mines in the Ruhr district (as weU as the Liège industrial centre on the Maas) discharge so much sewage that in the

book « Der Rhein » (1951) the

Was-serstrassendirector Straat at Duisburg

calls the pollution« erschreekend »

(alarming). He pleads for better se

-wage purification and we ean fully en

-dorse this.

The contamination limit for fish

as well as for recreation is already ex

-ceeded in times of drought. Fig. 14

shows a quadrupling of the chlorine- Flg,14

content of the Rhine-water since 1895. The increase in the chlorine-content

Especially since 1945 this increase has of the Rhine water since 1935.

been apalling. The utmost permissible

limit of 300 mg Cl/litre will nowibe exceeded in times of drought. Fig. 15

shows the weekly eycle of the salt-content, demonstrating clearly that on Sundays

t

50

CHLORINE ORI61NATING fROH POl.WTION,

OI5CHAI>6EOON THE RHINEINkg/_

lrJ1/

"""

J

~.I>-_

--...t-

V

V

~ ~~~~ 50

..

0 YEMS ~ 0 a ~ ~ 0 Ii !!! ~

Cl CONCI!NTRATION IN

mq/I

ATVREESWUK(RIVER LEK)

1!47

mgCVI

~OO ~ ~ ,-

~~~~~~---r--~----~

o AUG. .5EPT. O(.T. NOV.

I I I I I I I

'

I

I I I : 7 I 7 I 7 I 7 IDAV5 100 DEc..

Fig. 15.- Owingto the decrease in the discharge of sewageonSunda.ysthe Chlorine

-content ofthe Rhinewater shows a 7-daycycle,

lesssewage is discharged on the Rhine than on week days. Cases of a ehlorine-con

-tent of 285 mgjlitre have already been registered. At such a content harm is already

done and suchwater also has but little freshening capacity.

- 1

6-As it is desirabIe to nulIify the very considerable agrarian and other harm, the

strugglecan, and is, wagedonfour fronts in order toobtain :

1. Better sewage treatment : By international agreement and also by the

efficient purification ofeach country's ownsewage it should be possible to have decently fresh, usabIe water in the rivers, lakes, canals and ditches.

2. Better sluicing, better legal means : Removing as soon and as

effici-ently as possible the salt-water that has come through the locks, pro-hibiting the digging of pits and holes in areas with salt ground water, prohibiting the construction of sluices other than those working on the siphon principle.

The shortening of the coast-line by damming up :In the tradition of the

Zuyder Zee (1932), the Brielse Maas (1950), the Brakman 1952), etc.

4. The most economical use of the available amount of fresh water :

The Rhine and Maas do not supply sufficient quantities in times of drought. Storing up freshwater in lakesand in the soil for use in times of drought both for the vegetation and flushing seemsnecessary.

PART II

THEORIES ON WmCH A METHOD OF CALCULATION FOR THE MOVEMENT OF SALT WATER AND OF FRESH WATER IN A RIVER IS BASED IN THE CASE

OF T1DAL'CURREN'l1S (Fig. 16). ('Or J. J. Dronkers ).

Drafting the methodof calculation mentioned in the-heading isnot asimple mat-ter. Even calculating the propagation ofthe tide in a river with homogenuouswater isnot elementary. Since theriver discharges fresh water and the tide brings salt-water into the mouth of the river, there are currents of salt-water and fresh in the areas of the river adjacent to the sea. Consequently the movement of the water in these areas is very complicated. Great difficulties arise when drafting a method of calculation for the tidal changes in the salt- and fresh water currents whereby we can only aim at an approximate solution. We cannot deal with the solution of this problem within the scope of this report, as it leads to th~ use of complicated formulae and takes up much space. In view of this we shall only summarize the several assumptions that need further solving.

In thecase ofhomogenuous water the velocitynear the bottom islessthan that nearer the surface, so that the vertical of velocitymaybe represented empiricallyby a parabola of a higher degree or, more theorericaIly, by a logarithmic line. These differences in velocity may increase considerably owing to the difference in salt-content, even to such an extent that the water along the bottom moves upstream, whereas that on the surface movesdownstream. This so-called «under-fIow» occurs in the mouth of the Nieuwe Waterweg for some 3 hours during the tidal period, when the tide is on the turn from low to high.

The fIuctuations in salt-content may be showncIearly in a longitudinal profile of the river and at different heights by constructing areas of equal density with the 200

aid of the data (see sketch). The positions of these dividing planes change

continu-ously within a cycle of 12hours 25 minutes, due to the tidal movement. The slope of

the planes themselves fluctuates thereby around an average value which is much

lar-ger than the slope of the water surface. The maximum of the water surface in the

Wa-terweg is about 5 cm/km,

whereas the slope of the

planes with an equal s

peci-fic gravity is approximately

100 cm/km, i.e. 20 times

larger.

The theoretical cons

i-deration of the movements

of salt water and of fresh

water is however, considera

-bly hampered by the strong

influence of mixing. For the

water particles in tidal ri-'

vers move to and fro owing

to the tidal runs, whereas

they are gradually moved'

seawards by the flow of the

upper water (see Part I by

Dr Ir

J.

van Veen).

Even-tually this fresh water pas-' ses the brackish water area

in the Waterweg and is then

SURFACE

<, <,

<,

... " sett - content

',an average oF" of 3 griL

9griL '" 6 gr \ -, \ dividing ptane \ z \-:77':ï --\ 'f'

%

grIL an average ... ... ... <, <, -, <, -, <, -, "\

"

" an average \ an average " 129'ïL \ of 9gr/L \ satt r-cont.snt, '" 2. \ \ 6gril \ \ Situat.ion 2 hours. BonOM

Fig. 16.- Mathematica! treatment of «salt-wedge».

mixed with sea-water.

As soon as the river discharge is constant and the amplitude and average height of the tidal movement may be taken not to vary, the movement of salt-water and of fresh water will alwaystake place in the same periodically recurringmanner whereby thewater layerswith an equalspecific gravity will move identically during each tide.

Mixing too, has then assumed a stationary character. In reality the tidal mo-vement and the flow of the upper water are subject to constant changes,so that com-plete equilibrium is seldom attained. Moreover, several other factors affect the mo-vement of salt-water and of fresh water in an irregular way,as has beenstated by Dr van Veen.Itis verydifficult to take these irregular influencesinto account in the cal

-culation. First of allweshall have to restriet ourselvesto the case inwhich upper water and tidal movement are stationary. The further influences might then be examined

statisticaIly. "

So let us suppose the brackish water to be in equilibrium, as weIl as the dimensionsof the river, tidal movement and flow of the upper water, so that both the density and the velocity of the water at each point are a periodical function of the time.

The aim of the theoretical examination then lies in the answers to the following questions :

1. What isthe density p as a function of the distance x along the river, the height above the bottom zand the time t ?

18

-2. What are the fluctuations in the water movement owing to the tide and the vari-able density ?

There is,ofcourse, a close relationship between the answers to these two ques -tions.

3. In whatwaydothewater movement and the density change ifthe flow of the up-per water changes ?

In the first piace the diffusion ofthe salt originating from the lower water

lay-ers with greater density must be studied. This diffusion is mainly brought about by the turbulence in consequence of the horizontal movement of the water. On the ot-her hand the turbulence is retarded by the differences in density. Conversely, the movement of the water is dependent on these differences. The vertical decrease in density is very large with regard to the decrease in the horizontal direction, so that the diffusion in a vertical direction is assumed to be

1 ap

--D

B--p

az

In this formula D, isthe diffusion coefficientwhich is,however,also dependent on the height z abovethe bottom.

For this we assume

(1) _DB

₌

_{(zo-z) Z (PZ2 +Qz + R)}

P,Q and Rare three parameters which must further be determinedwith the help ofmeasurements.

The movement of the water in the brackish area is now determined by the fol-lowing differential equations, the derivations of which are not elaborated further.

In the case of tidal movement the density p is also a function of the time. The

followingdifferential equation then holds goodfor P :

(2) _-;-tap

₊

_{u --}ap _{- --}8 _{DB --}8p ₌

°

o 8x 8z

az

In this formula t represents the time, x the distance along the river measured

from the seaward side of the mouth and z the height above the bottom. The func-tion u (x,z, t) givesthe velocityat the point x,z of thewater at the point of time t.

The followingboundary conditionshave tobe added to this :

p (x, z, t) is givenfor x

=

0, that is,at the mouth of the river. Furthermore p

=

po forx

=

b,independent ofzand t. Moreoverx

=

b hasbeen chosen in sucha way

that the river contains only fresh water in the case x

>

b. If x

<

b, we are in the brackish water area.

Asregards the current in the brackish water area weshal! assume that the ve

r-tical component of velocityis smal!with respect to the horizontal one. The turbulence

at apoint x,z at apoint of timet isthen determined bythe equation

(3) p

a

u

8t 8u

+

u 8x 8p 8-:

-

-+-

_{8x 8z}

Usual!y the term u

_ax

a

u

may be ignored, while the shearing

(4) " (x, z,t) =Di (X,Z, t) 8u (X, z, t) 8z and --8p = g - 8

JZo

pdz

=

g

[

fZ

O

-8p dz]

+

gp 8x êx Z Z 8x Zo 8zo 8x

Zoisthenthe height of thewater-surface abovethe bottom,whileDi (X,zo,t) =0

In the caseofhomogenuouswater, von Karman and others have derived a more

or less theoritical formula for Dl insuch a waythat

Di may be approximated by the formula

(zo-z)

In this formula A isa coefficient which is not further defined.

In the brackish water area a modified formula for Dl will have to be usedwhicb

contains some parameters (3, y and 8 that should be determined empirically. Analo

-gous to (1) we now assume that

(5) Di

=

(zo-z) Z({3Z2

+

yZ

+

8)

The parameters (3, y and 8, which have entirely different values from the v

a-lues P, Q and R mentioned previously, must be determined empirically in such a

way that all the data of the measurements concerning the movement ofsalt and fresh

water during a certain tide are adhered to as closely as possible. These data should

therefore be so extensive asto afford an adequate check on the accuracy af the

theo-retical formulae.

Lastly, the equation of continuity will have to be added to the equations (2)

and (3) : (6) 8s (x,t) 8x 8zo -B- -8t

in which B is the width of the river on the surface and s the total flow through

a cross-section of the river at the point x and at the point of time t.

s

=

b

foZ

o

u(x,t,z) dz

(7)

b isnow equal to the average width of the river current.

The fundamental formulae for calculating the movement of salt-water and of

fresh water have been given.

It now remains for us to determine the function u(x,z,t), p(x,z,t) and zo(x,t)

in such a manner that the above-mentioned equations (2), (3), (6) and (7) and the

boudary conditions are satisfied. This is not a simple matter. By applying some

artifices it has been proved possible to find a solution which approximately satisfies

the requirements. However,even a brief consideration of thisproblem wouldtake up

so much space that we cannot deal with it within the scope of this article. For that

reason an elementary introductory will have to suffice.

- 20 -PART III

TUE PENETRATION OF SEA WATER INTO INLAND WATER SITUATED

BEYOND SHIPPING-LOCKS.

(Ir. W. Notenboom- Dr.Ir.

J

.

C.Sehönfeld).

§1. The way inwhieh sea water enters inland waters through a shippinq-loek.

The sea-water mainly enters through the shipping-Iocks while the locking of ships is in progress. The phenomena occurring here may be pictured as follows. In fig. 17 A the outer gate of a shipping-lock is shown diagrammaticaUy. The chamber is supposed to be fuU of inland water. The water-levels hl h, of the outer water and inland water areshown in this diagram, aswell as the heighth, of the valve

-I 1--'" h

p

,

C, h, .hs ~s .... A

\:

r

2

Kz

th

'V

r,

J

t

'j

_

ih

j

v,=

_r

_t

_~

c

0 E Fig. 17.

in the gate or the culvert, the densities Pl and P2 and the chlorosities Cl and C2of theouterwater and the inland water.Since the outer water is sea-water and the inland water isrelatively fresh,C2is smallwith respect to Cl.The middle of the valve meets with a pressure of Plg(hl -h,') on the seaward side and P2 g(h2-h,) on the side of the chamber. After opening the valve a quantity of water will flow out of the cham-ber until both pressure are equal, sayat the level h, in the chamber. ThusPlg(hl - h,

Pl- P2 •

=

P2g (h,- hs·).Henceh,

=

hl

+

(h.- h.). When h,

=

hl (orInotherwords,

P2

when the valve isat the height ofthe outer water-level), h, =hl, but in practice the valve is always belowthe outer water-level so that hs<hl' and hence hv>hl' Co n-sequently thewater in the chamber ishigher than that in the outer harbour. If in this

case the pressure near the bottom of the loek is determined, one will find on the outside PI

=

plghl and on the inside

P2

=

P2ghv

=

p2g(hv- hs)

+

p2gh.

=

plg(hl - h,)

+

P2ghs,

that is P2=PI- (p'- p2)ghs

So the pressure on the inside is lower than that on the outside. The vertical dis tri-butions of the pressure inside and outside are as represented in fig. 17B.

So we see that along the bottom the outer water (salt-water) has pressure with respect to the water in the chamber, whereas the water-level in the chamber is higher. The result of this will be that after opening the gate a quantity of fresh

water will flow out of the chamber on the surface while a salt bottom-current will

enter the lock-chamber.

As the forces causing this exchange persist as long as the density of the water in the chamber is less than that of the water outside, the exchange is not stopping"

until a final stage is reached at which the water in the cbamber and that outside

will be of equal density.

The volume of the chamber is small with respect to the quantity of water out -side as a rule and so the result will be that after some time the density of the water in the chamber will be equal to p'.

Hence, through the seaward entrance first, af ter opening the valve in the gate,

a volume of fresh water B (h, - hv) flows out of the chamber seawards, and then, af ter opening the outer gate, a volume of fresh water Bh, flows out of the chamber sawards and a volume of salt water Bh, from the sea flows into the chamber. Here B denotes the surface area of the chamber. Hence a total volurne of fresh water

B (h, - hv)

+

Bh,

=

Bh2flowing out of the chamber seawards is exchanged with

a quantity of salt-water Bh, flowing from the sea into the chamber. When after

this exchange the outer gate is closed, the loek-ehamber will have been filled

with sea-water. When hereafter the water in the chamber is brought to the same

level as that in the canal, and the inner gate is then opened, an exchange of salt

water and fresh water will take place in a similar way as through the seaward

entrance. In table Abelow, the exchanges through tbe seaward entrance and the

landward entrance during one locking-cycle are given for the case h2>h, and in

table B if h2<h,. In both cases it is assumed that the loek-ehamber was originally

filled with canal water.

A

The movement of salt water and of fresh water in a shipping-lock

through the seaward entrance through the landward entrance

oB~

...

...

...

...

...

eo 0 Cl) eo ... _eo oB t>ll'" o Cl) t>ll

...

~ '" Ul Ul .... ~ Cl)

...

~ '" ~ Cl) ~~ ...

Cl)

'a

Cl)i::: "1:l Cl) ~.~ ..0. Cl)

.

~

Cl) i:::.~ ..0. _{Cl) i::: .~ '"}

... El eo ... El [l El ... El [l El El ... ~

...

Cl) ;:3..!:l.E ~ _{;:3 ... d '"}

...

Cl) ;:3 ..!:l ... '" ;:3 B '"

'"

0.

'"

0. ... ril r:: ..!:l ..- ~ s:::= u 0 '0 ~ :> 'O<;jCl)..!:l 0

_{~ ..Ë}

_{Cl) u} o <;j Cl) :>

.!::].

:> ril u _:> ril

the valve B(h2.-hv) the valve

!

Bh, Bh2 Bh, the gate Bhv the gate " -total Bh2 Bh, total Bh2 Bhl 205

- 22

B

The movement ofsalt water and of fresh water in a shipping-lock

through the seaward entrance through the landward entrance

...

....

_...

_.... .... _{... ....}

bIJ 0 .2:l bIJ (/) OQ)bIJ .... bIJ

o

.2:l bIJ .... o Cl.) bIJ

.... I=i '" I=i "C .... I=i Cl.) .... I=i cd I=i Cl.)

cu ~

.

s ca

8

:::.- ~

Q) ~ ._ ..c

8 ~

·

5

-s

Q)

_·S

8

t

8 Cl.)

·

S

8 :::....I=i

....

....

...

Q) _{;::l..c:1 ij :::} ;::l ....

a '"

...

Q) ;::l ..c:1 .... '" ;::l Q) '"

'"

0-'0 f!l 8 ~

'"

0- - cIl 1=i..c:1 ..-.:::~u

0 O~I1)~ 0 o Q) Q) u o Cl) Cl.)

:>....

...

cIl :> ~ u _{:> ........ :>} rIJ

the valve

!

the valve B(hl -hv)

Bh2 Bh. Bh2

the gate the gate Bhv

total Bh2 Bh. total Bh2 Bh.

From the aboves tablesA and B it isclearthat both when h2>hl and whenh2<hl each locking-cycleinvolvesan ingress of a volume ofsalt-water Bh, from the sea into the canal and an egressof a volume of freshwater Bh2from the canal seawards.

The difference between these volumesBh, and Bh2isthe volume of the locking water.

Consequent upon the above exchange, a quantity of chlorine B(h.C, - h2C2) enters the canal during each locking-cycle.In the Dutch sea-locks giving access to

the inland water the rise h,- h, is small with respect to the depth of the sill and since the chlorosity of the inland water (C2) is small with respect to the chlorosity of the sea-water (Cl), the quantity ofchlorine entered ismany timeslarger than the locking water might contain. Especially with large locksa large quantity of chlorine

enters the canal.

Even in the case h, > hl when locking water is drawn from the canal, a rela-tively large quantity of chlorine enters the canal per locking-cycle in consequence of the above-mentioned exchange.

It is pointed out that in each shipping-lock the exchange taking place after opening the gates will occur within a certain time, depending on the difference in density. If the gate has been opened for part of this time, no complete exchange will have taken place, sothat in that case lesschlorine will have entered. (see par. 3 under 1).

In the next section the theoretical side of the exchange discussed in this section is further elucidated.

Since during the last years many observations have been made in the North Sea canal and in the Ymuiden locks, somefigures for the duration of the exchange and the quantity of chlorine locked through will be mentioned in order to make the conception clearer. .

The North Sea canal connects the harbour of Amsterdam with the North Sea

(see fig. 11). At Ymuiden, where this canal reaches the North Sea, there are several locks.The dimensionsofthe largest one,the «Noordersluis»,are: length 400 metres, width 50 metres, depth 15 metres. The width at the entrances is the same as

between the walls of the lock-chamber. The time necessary for one exchange from

salt to fresh or vice versa in this loek is about 22 minutes. The average quantity

of chlorine entering through the Noordersluis per locking-cycle amounts to 2,1X106

kilogrammes.

The followingtable showsthe quantities ofchlorineper annum, entered through

all locks at Ymuiden in 1949,1950 and 1951.

year quantity of chlorine

in 106 kg.

1949 3404

1950 4526

1951 5591

Due to the increase in shipping thisquantity isstill growing.

§2.Theoretical treatment of the exchange in a shippinq-lock.

As said above, the vertical pressure distributions inside and outside the outer

gate are shown in fig. 17B.

Let us now suppose that the valve is about halfway between the bottom and

the water-level, so that the pressure exerted by the fresh water in the chamber on

the outside salt-water immediately below the surface, is approximately the same

as the pressure exerted by the salt-water on the fresh water near the bottom. Let

usnow suppose forthe moment that the gateswere openedsuddenly. The freshs

urface-water in the chamber would start flowing out and for the same reason the salt

bottorn-water outside the chamber would start flowing into it. Moreover, the fresh

water would acquire an upward motion and the outer water would acquire a falling

motion (see fig. 17 C). Shortly after opening the gate a current will then have

developed sweeping a layer of salt-water along the bottom into the chamber and

carrying an almost equally thick layer of fresh water out of the chamber on the

surface (fig. 17 D). In reality opening the gate takes some time and hence the

beginning of the processdiffers somewhat from that shown in figure 17 C. This is,

however, of secondary importance to the whole course of the exchange, because

,opening the gate only takes a short timein proportion to the exchange,and because

shortly after opening the gate a current as shown in fig. 17 D will develop all the

same.

If the valve is not half-way between the bottom and the water-level,but higher

up or lower, the movement during the exchange will be preceded by a slight, relati

-velyquick,horizontal shift of the interface insuch a way that the average pressure

is again balanced. Tbis shift too is entirely of secondary importance and has no

further influence on the exchange.

When opening the gate betweenthe chamber and the canal, a similar processof

exchange takes place as at the outer gate. In this case the relatively salt contents

of the chamber penetrate into the canal along the bottom through the inner entrance,

whereas the fresher canal water flows along the surface into the chamber.

-

24-Ignoring friction along the interface and the bottom, and mixing through the interface, the water would have the same velocity Vl to the right at all depths in

the salt layer, and the water in the fresh layer would, at all depths, have avelocityV2

to the left.

The front K, of the salt layer may been seen as a kind.of internal hydraulic

jump, analogousto the jump occurringwhen water runs into an originally dry canal.

Such water dispels the air as salt water does fresh. The most important difference between the two phenomena is that the dispelled air has a very much lower density than the water whereasin the loek the advancing salt-water and the dispelled fresh water are of almost equal density. Meanwhile the internal jump K, may be treated in substantially the sameway asa surface jump by applying the lawsof energy and momentum with respect to a coordinate-system moving with the velocity VI, in

fi-xed position relative to the front K,. The front of the fresh upper layer K2 may be

dealt with in the same manner.

Ignoring friction and mixing and also some entirely secondary effects, we find

~=2

From this it followsthat, if b is the width of the entrance Qo

= ~

V, b h

=

~ V2b h =

.%

bh

Y ~

gh is thedischarge ofsalt-water in one direction and also

the discharge of fresh water in the opposite direction. The exchange will persist until the whole chamber isfilled with salt-water - or with fresh water when the in

-ner gates are open.If the loek-ehamber has the same width and depth asthe·entrance of the loek, the time necessary for this complete exchange is Ta = V : Qs, if V re-presents the volume of the loek-ehamber (again ignoring friction and mixing).

In reality the movement differs considerably from the theoretical picture given here, firstly because generally the water in the chamber, the water in the canal and the outer water are not homogeneous,but laminated with a rather gradual transition

from fresher water on the surface to saltier water on the bottom. Secondly,

con-siderable turbulence develops during the exchange, resulting in a mixing of the layers, and an appreciabIe friction at the interface between the layers and along the bottom and the walls. The result of this is, firstly, a velocity distribution as

shown in fig. 17 E, differing from the theoretical distribution and secondly, a w ea-keningof the exchange consequent uponwhich the Jatter takespJace more slowlythan it wouldaccording to the elementary theory.

Let usnowconsider the exchange in two different valuesofthe density difference betweensalt and freshwater. The density distribution in the two casesare supposed to,'Je similar. The Froude number for the internal movement will then be the same in both cases,if we disregard friction and mixingfor the moment. This Froude num-ber for the internal movement may,for instance, be defined accordingto Fr _ V2

2 ~gh

inwhich ~

=

2 PI- P2 and in which PI represents the average density in the

Pl

+

P2

outer water (in the chamber respectively) before the exchange and P2 that in the

flow with a vertical density gradient, yields that the Froude-riumber stated above,

isalso indicative for the similarity of the turbulence, as long as the'Réynolds number

is large, i.e. whenturbulence is weildeveloped.Generally this will be the'case in f

ull-sized locks,but in modelson a reduced scalethis might be different.

.-From Froude's similarity rule it followsthat both the dimensionlessdischarge,

-il'

=

QQ

=

I/. Q I and the dimensionless coefficient of exchange

cp

,

i.e. o

>-4

b h} ~g.h

the exchangedvolume of salt or freshwater divided by the total volume ofthe cham

-ber, are functions of the dimensionlesstime r

=

_t_ = t , as long as

TO V : Qo

neither the geometrical proportions of the loek, nor the shape of the vertical

dis-tributions of density are altered.

The two functions -il' (T) and

cp

(T) for a loek of a given shape and given ver

-tical density distributions are not easily determined theoretically, especially owing to l.0

r---

-

---

-

--

-

---,

'f/=a

(Jo

o

0+

o

++

+

o

+

o ~---~---~---~

o

1.0 20 3.0 FIG.17 F

the complications arising in regard to friction and mixing. The knowledge that such functional relationsexist however, isimportant from a practical point of view,because this enables us to work out rationally observations of the exchange in a loek, and to compare the results with different locks, or with the same loek under different circumstances.

So, when working out the observations of salinities and veloeities during tlie locking-process, weshall calculate the dimensionlessquantities -il', cpand T from the observations and then plot -il' and cp against T.

In as much as the geometrical proportions of the loek are the same for diffe

-rent observations and the vertical density distributions are similar, the points plotted must lie on one curve in the VT - (or cpT-) diagram, but for the margin of inaccur-acy ofthe measurements. In this way a number ofobservations made in the sea loek at Terneuzen have been worked out in a lfrT-diagram(fig. 17 F.) and in a

-

26-gram (fig. 17 G). The circles and lines refer to the exchanges between the chamber

and the outer harbour, the crosses and dotted lines to the exchanges with the cana!.

The curves have been drawn such as to fit as much as possible the points plotted.

The discrepancies between the curves and some of the points plotted may be said to be entirely due to the inaccuracies of the measurements and the deviations

in the various salinity-verticals. The differences between the observations of the

ex-1.0r---; f(J 0.5

+

o

+

OL---~---~----

~

~~~

o

1.0 2.0 3.0 T~1.. 40

FIG. 17G

Ta

changes with the canal and those of the exchanges with the outer harbour may be

accounted for by the slightly different geometrical factors

§3. Ways in which the chlorine may be expelled from the canal,

The sea-water entering through the locks accumulates by its greater density at

the bottomof the canal and penetrates into the canal along the bottom.

Mixing of salt- and fresh water during the exchange of chamber as a result of

turbulence has been discussed in the previouschapter. In the canal too, mixing takes

place owing to diffusion and ships'propellers.

For efficient de-salting, the sea water that has entered must be expelled from

the canal near the locks as soon aspossible, so that mixing with the inland water is

prevented or almost prevented.

The means that may beapplied are :

1. Shorteningthe time during which the gates are open,

2. Flushing the canal withfresh water,

3. Pumping up thesalt bottom-water and discharging it into the fresher surface-w

a-ter (in combination with a sluice) (fig. 18),

4. Impelling the salt bottom-water upwards (in combination with a sluice) (fig.19),

5. Pumping up the salt bottom-water and discharging it into the sea (fig.20),

In the next sections these methods will be briefly discussed with special

re-ference to the above-mentioned North Sea canal at Ymuiden in its present condition.

1. Shortening the time dUljng which the gates are open.

It is evident that a certain space of time is necessary for the exchange of salt

and fresh water. Consequently the incoming quantity of chlorine might theoretically

be limited by opening the gate for asshort a time as possible.

In tbis case a ship should have to enter or leave the loek-ehamber during the

the exchange. Navigators are, however, of the opinion that this is not possible, a!

steering the ship, especially when entering, is very difficult, if not impossible,

be-cause ofthe currents set up during this exchange.

Moreover, the risk ofcolliding with the gate would be much greater as the ship

approaches the loek while the gate is closed. Consequently this method cannot be

applied.

2. F1ushing the canal with fresh water.

The east end of the North Sea canal near Amsterdam is connected via locks with

Lake Yssel.

De-salting has been improved by flushing the canal with fresh water from

Lake Yssel. In this way a large quantity of the chlorine that hasentered at Ymuiden

iscarried off to the sea again through sluices.

The chlorine balance drawn up for the North Sea canal per period of 4 weeks

during the years 1949, 1950 and 1951 showed that if about 100X 106mawater could

be sluiced per period.of 4 weeks, the quantity of chlorine in the canal remained

constant,

Onee an average chlorosity of less than 2.5 kg per m" was obtained after

about 170 x 106mawater had been sluiced during one period. The average chlorosity

of the canal water at the beginning of this period was3kg/ma.

The question whether better de-salting would be achieved when flushing with

larger quantities of water, if this were possible, must be answered in the affirmative.

Itmust, however,be remarked that the quantity of flushing-water must also be

li-mited in view of navigation, since the currents in the canal cannot be allowed to

become troublesome or dangerous to shipping.

When de-salting in this way, the sea-water that has been locked through still

gets the opportunity of penetrating into the canal along the bottom, whereby mixing

with the canal water takes place. This is the reason why the average chlorosity of

the canal water remains so high.

The salt water at the bottom of the canal is only partially carried off by the

fresherwater flowing over it.

However, it isnot altogether impossible that this method might be rather effi

-cient in a relatively shallowand narrow canal.

3.Pumping up the salt bottom-water and discharging it into the fresher surface

water (in combination with a sluice).

The principle ofthis method of de-salting is mixing the salt bottom-water with

the fresher surface water.

Ifgood mixing takes place,the layer ofsalt bottom-water will become thinner so

thàt the water inthis layer will penetrate lessfar into the canal. Moreover, the

sur-face water wiIl hecome saltier so that more chlorine will he carried off by the sluice,

-

28-.which discharges relatively more surface water than bottom water in virtue of the

vertical distribution of the velocity.

Experiments have been carried out with a floating pumping plant working at Ymuiden. The plant consisted of 3pumps (fig. 18) with a total capacity of 390 mS/

minute. ELEVATION G. d.... 1 ....'ne b. Vet Mlt l'ron."""IO" c. dny.nt short • ,,"p.'Ie,

FLOATING PUMPING PLANT

FIG.18

Apump ofwhich thesuction pipewith an extremely wide nozzle issuspended in

the saltier bottom-water is shown diagrammatically in fig.2.When a certain quantity

of water is drawn from the bottom-layer by this pump, the interface between the

two liquids drops as illustrated in the diagram. There is a relationship between the

velocity of the water under the rim of the nozzle, the drop of the interface and the

difference in specific gravity of the two layers. Represented simply this relationship

isasfollows :

V2

When e.g. the velocity v = 20 cm/sec, the velocity head is - 2 mmo

2g

This represents a column of water of a height of 2 mm with a density of 1,hence a

pressure of 0,2 g/cm". So if the velocity of the incomingwater under the rim of the

nozzle is 20 cm/sec, the difference in pressure between the points A and B is 0,2

g/cm-, provided the horizontal distance between A and B has been taken large en

-ough. Witb the given densities 1000 and 1010 kg/ms and a horizontal water level,

0,2

the drop of the interface will be

=

20 cm. When the velocity in the.

0,01

nozzle increases,this drop will increase. When the drop becomes so large that the

upper layer. So,if·one does not want to suck up water from the fresh upper layer, the inlet-velocity v must be kept smalI. The diameter of the circular plate under the nozzle must in a given case be made so large that the drop of the interface remains small enough.

The experiment with the floating plant at Ymuiden has taught usthat the pumps indeed only pumped up water from the bottom layer, in accordance with theory. The trouble is however, that the pumped up water only mixes with the surface w a-ter to a very slight extent, therefore this method of de-salting cannot be considered

for application. .

4. ImpeIIlng the salt bottom-water to the surface (incombination with a aluiee).

Fig. 19. Tbis method of de-sal

-ting is based on the prin-ciple that the water of the salt bottom layer if i mpel-led to the surface,will mix with the fresher surface water. The advantages of good mixing have already been stated when descri-bing the method of de-sal-ting under 3.

In figure 19 an ade-quate pump is shown dia-grammatically. From 3 abo-ve it is clear that the nozzle of the pump may be con-structed in such a way that only salt-water from the bottom layer is sucked up. Owing to the velocity- dif-ference between the water in the jet and the surroun-ding water, turbulence will be created mainly along the boundary of the jet,

causing friction and mix-ing. By this friction the jet - water is decelerated whereas at the same time the surrounding water is accelerated. The distributi-on of the velocity is as shown in fig.19.

Mixingcaused by this jet will highly depend on thedifferencein density

be-tween the bottomwater andthesurfacewater.Several research-workershave studied the behaviour of such a jet in an almost homogeneousenvironment,Le. withoutan

ap-h

IJ

ElECTRIC CA&lE

-

30-preciabIe difference in density. In the paper by Albertson and others (1) this problem

is discussed in extenso. Most likely, however, the behaviour of the jet in a highly

heterogeneous environment, i.e. with a great difference in density, will be different.

Ifapplication ofthis means were to be considered in a certain case,the efficiency of

themixing should beinvestigated carefully.

This method like the method under 3, has the disadvantage that the sea-water

that has entered ismixed up with inland water. So if one wants tosluice all the chlo

-rine that has entered, a quantity of water larger than the quantity of sea-water

en-tered will have to be discharged.

Since there is not always sufficient fresh water avaible in the Netherlands for

this purpose, the application of thismethod cannot be considered.

5. A pump whlch pumps up the salty bottom water and discharges it into the sea.

B

--1--- ---:..-==---~----==--=---~~- --_ --- -_ --

.

-~A---- SALTWATER

.

-

~~

The principle onwhich this method of de-salting works is that the layer of salt

bottom water is pumped

directly into the sea.

Such a pump is shown

infig.20.

Under 3 we have

seen that we can make

the pump such that it

only sucks the salt-water

from the bottom layer.

The pump discharges

this water into the sea

through a pressure pipe.

If this method of

de-salting were to beap

-plied at Ymuiden the

cost of the necessary

plant would amount to

capitalised according to the PUMP

nlESH WATER IOOOkQ/mJ

Fig.20.

5.000.000guilder (depreciation

+

working expenses,

prices current in December 1950).

6. A screen with a slit near the bottorn (incombination with a slulce).

This method of de-salting is based on the principle thät the screen holds back

the surface-water and only allows the salt-water from the bottom layer to flow to

the sluice.

In fig.21such ascreen and its future positionat Ymuiden isshown. The water

discharged through the sluice flows out of the canal underneath the screen. If the velocity ofthe water in the slit of the screen is smalI,the interface near the screen

willshow sucha small dropthat onlybottorn-water isdrawn from the canal. To

main-tain a small velocity of the water in the slit under the screenwhen the outflow is

large, this slit should be of a considerable cross-section.In view of this the screen

projected for Ymuiden has a length of 760 metres.

(1) «Papers» American Society of CivilEngineers December1948.

M.L. Albertson,Jun. Asce,Y.B.DaLR. A.Jensen,HunterRouse,

\

PROPOSEO

I'A

ELEVATION CROSS'SECTION A·A

r

rF':::'-;'::::

+

':_::C:::"",

y

_

'

I )

:t

c

::::_

·

·

·

::_-:~-

·

··

t

?

···

:::::~-::c·

·

+

·

~

··

·::::::·

·

·

·

··:

···

·~•••r-

t

:::

··

,'.

\

•.:.::::·

-1

c

.

:

./

'

1

_'_

·

0:=:::::::-

cr

c•_c'-=-::

l1 [

::/ I ~: . PLAN Vol

....

IJMUIDEN PLAN SECTION B-S NORTH 5EA Csoo",~ Fig. 21. N ,_. <.n.

-

32-In order to check if such a screen sufficiently retains the surface water, a full scale experiment was carried out at the Noordersluis at Ymuiden when one of the roller-gates was Iifted about 2 m so that a slit was formed.

This experiment has taught us that when a velocity of the water of appr. 0.20 m/sec. will be admittet underneath the screen shown in fig. 21, the layer of salt bottom-water will be expelled from the canaI.

For de-salting the N orth Sea canal thescreen in fig. 21 is the most efficients o-lution. Firstly, a modern sluice is already available, and the cost of the screen is estimated at 2.000.000 guilders (accordingto the prices current in December 1950),

which is much cheaper than the pump mentioned under 5; secondly, a suitable

place in the existing situation can be foundfor the screen, where it maymoreover be usedasa moorage for large sea-going vessels, which isdeemed necessaryat Ymuiden.

An expenditure of 2.000.000 guilders on such a screen is certainly justified, since the advantages for agriculture, horticulture, cattle-breeding, industry and public health that wiII accrue from de-saiting with this screen will more than offset the

expenditure.

§4.Theoretical consideration of the screenand of thepump with a wide

nozzle,

Weshall consider an under-water slit ofwhich the upper edgeliesat a distance h below the interface between salt-water and freshwater. The height of the slit be a. When sucking salt-water through the sIit, the interface wiII drop as thevelocity ofthe outflow increases. The maximum outflowat which still no fresh water is sucked up

is reached when the drop is exactly h. This maximum permissible outflow depends

on the ratio of h to a,other factors beingequaI. When a is great compared to h,and

A

_c

=1J~

-r

f

t

/ I

"-o

A /. E Fig. 22.

a slit that reaches the bottom is employed (fig. 22A), the maximum permissible

outflow may be found by reasoningas follows :

As long as the fresh water remains motionless, the movement of the salt-water

under the interface satisfies the same differential equations as does the movement

instead of g (see Craya for this proposition, for instance"). In opplying thus the law of Bemoulli to the flow towards the split, we find, when the outflow is the maxi

-PI - P2

mum permissible,v2 =vo2

+

2 ~ gh, in wbich ~ =

PI

When the accessto the slit is large,we may neglect Va and hence find forV an

approximation which is definitely not too large and consequentlyon the safe side.

The outflow per unit of width then becomes q

=

aV

=

a y2 ~ g h,

(1) or q = 1

ay2~gh .

h3

If a, however,is small with regard to h (fig. 22 B) we find : ~ g -2-= 0,43

q

according to the theory of Craya (2), satisfactorily confirmed by the experiments of Gabriel (3).

q h

From this it followsthat (2)

ay2 ~ g h 0,93a

In simular casesof movement, i.e. cases with the same volume for the

dimension-less ratio h : a, the quantity

-v

q i.e. the permissible outlow (dimens

ion-a 2 ~gh

less) will also have equal values. This means that

-v

q is a function of h

a 2 ~ gb .

a. Consequently, we plot these two quantities against each other (fig. 22 C).

The fünction sought is defined by (1) for small values of h : a. This is repres en-ted by the straight line E in fig.22C. For large values of h : a (a being small with respect to h) however, (2) holds good ; this is represented by the straight line C.

Thus the above mentioned curve must be tangent at E when h : a

=

0,and for lar-ger values of h : a it will approach C asymptotically. We do not exactly know the shape of this curve, but it should follow crudely the dotted line.

Although we do not know the exact shape, an important conclusion may be drawn: both formulae (1) (line E) and (2) (line C) give lower values for q than would really be permissible according to the unknown function (dotted line). So we are on the safe side if we apply formula (1) for h>0.93 a and formula (2) for h<0.93 a.

For the flow towards a round intake nozzle such as is shown in fig.22 D simi-lar considerations as for a slit hold good.

If the maximum permissible drop h is much smaller than the radius r of the nozzle we get an approximately redial flow towards the nozzle and then

(3) Q 1

holds good for the permissible outflow.

(1)La Houille Blanche, numéro 1, Janvier-Février 1949. Ir. A. Craya Recherches théoriques sur l'écoulement de couches superposëes de fluides de densités

dif-férentes.

(2) Sea previous page.

(3)La HouilleBlanche,numéro 1, Janvier-Février 1949.Ir. P. Gariel, Recherchesex-perimentalessur l'écoulement de couches superposées de fluides de densités

dif-férentes.