canal. There was a decrease in the

T h e results of these tests are shown

in

Table 13.

This study proved that the increase

in

seepage

of

the canal was not great w h e n the third well was installed at various positions. T h e interference for well

No. 1

was Thus

the third

well can easily be located at

350

ft.

from the canal without seriously reducing the discharge of well

No. 1.

Repetition of similar tests

by

installing two wells, Nos. 3 and

4, in

line

with

wells Nos. 1 and 2 close to the canal, gave results which are'plotted in

Fig.

13.

T h e fall in discharge of wells of both the groups proved to be as shownis Table

15.

Thus

with

the wells of the second group, Nos.

3.

and

4,

as shown

in

Table 14. 015 OF WELL IIIJEII

TABLE 14.

Distance of third well from the canal bank inft.

Percentage interference of well No. 1.

150 9.25

250 5.65

350 2.6

450 0.76

200

ft. from the fist group7 the interference

is

of the order

of 5 and 7

per cent respectively.

T h e increase in the canal seepage at the position of wells of the second group w a s found to b e

15

per cent.

TABLE

15.

Percentage Percentage Distance of 2nd row interference interference in well in well of wells fiom the canal

No. 3 and 4 bank converted to

ft.

_No.₁_and₂

200 7.25 9.6

250 6.2 8.5

300 4.8 6.4

350 3.2 5.3

500 1.2 2.1

600 0.2 0.8

Thus

it seems that for sites with pervious canal bed

and having

a r o w of wells close to the bank, the installa- tion of a second r o w of wells at

300

ft. from the canal

hank would

be of advantage.

B I B L I O G R A P H Y

ANONYMOUS.

Annual reports of the Irrigation Research 10. THEIN, Guntcr. Hydrologische Methoden, Leipzig, Institute, Lahore, for the years 1938, 1939 and 1940. J. M. Gebhardt, 1906.

Statistical

&

Physics Section. 11. THEIS,

C.

V. “The relation between the lowering of the

BOULTON,

S.

“The steady flow of ground water to a piezometric surface and the rate of and duration of pumped well in vicinity of a river”, Philosophical M a g a - discharge of a well using ground-water storage”, Tran- zine, series 7, vol. 33, Jan. 1952. suctions of the American Geophysical Union, vol. 16,

GHANAN

SINGE, LUTERI, H. R. and VAIDHIANATHAN, 1935.

V. I. “On

the transmission constant of water in subsoil 12.

-

^,“The significance and nature of the cone of depres- sands”, Punjab Irrigation Research Institution, vol. 5, sion in ground water bodies”, Economic Geology, vol. 33.

no. 9, 1939. 13.

VAIDHIANATHAN,

I.

and LUTHRA, H. R. “The trans- ISRAELSEN,

O. W.

and REEVE, R.

C.

Canal lining expe- mission co-efficient of water in natural silts”, Punjab riment in the delta area, Utah. ‘(Bulletin 313 (Technical) Irrigation Research Institution, vol. 5, no. 2, Jan. 1934.

Utah Agricultural Experiment Section.” 14. WENZEL, L. K. Methods for determining permeability

?&ANGAR,

S. D.

Waterlogging in Western Punjab, Punjab of water-bearing materials, “U.S. Dept. of Interior Water Engineering Congress Paper no. 284. Supply Paper’’ no. 887.

ROZENY. Fasserkrafi und Wasserwirtschuft7 vol. 28 15.

-

^,^The^Theimmethod for determining permeability

no. 10,1933. of water-bearing materials, “U.S. Geol. Survey, Water

MUSKET,

M.

The pow of homogeneous &ids through Supply Paper” no. 679.

porous media, New York and London, McGraw

H i l l

WILSDON, B. H. and BOSE, N. R.

(‘A

gravitational survcy

Book

Co. Inc., 1937. of the sub-alluvium of the Jhalum, Chenab, Ravi Doabs ROUSE, H. Irrigation engineering, chapter on ground and its application to problems of waterlogging”, Memoirs water by C.

E.

Jacob. of the Punjab Irrigation Research Laboratory, vol. 6, TAYLOR,

E.

M. and MEHTA, M. D. %orne irrigation no. 1, 1928.

problems in the Punjab”, The Indian JournaZ of Agri- cultural Science, vol. 9, part

II,

April 1941.

16.

D I S C U S S I O N

DR, DANEL.

The lining of canals is probably the best remedy for waterlogging. It must be borne in mind that much smaller cross-sections can then be used because of better friction coeffieient and less water to convey. There is less free board if automatic control of levels and water distribution is resorted to.

DR.

NUIR

AHMAD.

Yes,

I

agree that canal lining is the best remedy but so far w e have not been able to overcome the difficulties of finding a suitable material. Our canals are very big; their width m a y vary from 150 ft. to 300 ft. and their depth from 8 ft. to 15 ft. with a discharge capacity of 5,000-15,000 CU. ft. per second,

All

these canals have to

The statics and dynamics of underground water

run throughout the year, and cannot be closed for more than a month. We are thercforc looking for a cheap and yuickly- applied material.

I

a m unable to give any opinion on automatic level control as

I

have no information.

MR.

SAYED

EL AYOUB. Dr.

Nazir Ahmad mentioned some suggested means for lowering the water-table.

I

would like to b o w if any modification of the irrigation system was ever considered; of that irrigation system which,

I

under- stand from the speaker, was the sole reason for raising the water-table.

It

is believed that modification of the irrigation system is often of invaluable help in lowering the water-table.

DR.

NAZIR

AFIMAD.

The

plains of the Indus are flat, witq a slope equivalent to approximately 1 : 50,000. The surface level of irrigation canals is deliberately set high so that they may command as large an arca of land as possible. Changing the alignment would not solve this problem. Modification of the canals to make them impervious is a solution, but it has not been undertaken because o£ practical and financial difficulties.

MR. ROBAUX wondered whether anybody had thought of using special products (bentonites, etc.), in order to try to consolidate river beds.

DE.

NAZIR AHMAD replied that such attempts had proved fruitless because the products were swept away by the rivers.

T H E M E A S U R E M E N T OF G R O U N D - W A T E R F L O W

bY

DR. P I E R R E D A N E L

Laboratoire Dauphinois d’Hydraulique Neyrpic, Grenoble (France)

B A S I C N O T I O N S

C O N C E R N I N G F L O W I N P O R O U S M E D I A

As

^is

^well

known, porous media flow is usually of the Hagen-Poiseuille type; this is the laminar régime,

in

which there is no turbulence. However, though laminar flow in a cyh&icd tube does not cause any mixing, laminar flow in a granular medium is quite different and it seems advisable to stress this important, but often neglected, aspect of the

problem.

C O N E

In Fig. 1

is shown a thin thread of liquid

fi

passing between

the

grains of a porous mass

in

laminar flow;

suppose for clearness that is coloured. This thread of liquid divides and sub-divides

in

passing through the maze of interstices formed

by

the grains; at the end of a certain distance, the numerous offshoots of

fi

are extremely fine. Considering n o w a second thread of

licpidf2

(see

Fig. 2

where, for the sake of clearness, the individual grains are no longer shown), the fine offshoots of

fi

and fi become rapidly interlaced and mixed on account of the inevitable bifurcations occurring at random throughout

the

mass of grains. Lastly, mole- cular diffusion, though very slow, will ensure a mixing as complete as that due to a thorough, turbulent shaking

up

the

whole liquid.

In

view of what has just been said, it can n o w

be

understood

why

uniform, steady flow

in

a granular medium cannot be divided up into streamlines

by

injections of colouring matter.

In

fact, a dyestuff injected at some given point tends to diffuse out along the flow

in

the shape of a cone, the angle of which varies

with

the nature of

the

grains, but which is generally about 60. T h e concentration over a plane at any given distance from the inlet point is a

bell-

shaped curve, similar to the normal (or Gaussian) probability curve (Fig.

3).

This can easily be understood from a diagrammatic explanation which, for

the

sake of simplicity, will be applied first to the two-dimensional case.

In

our diagram, the irregular1 y-shaped grains willbe replaced

by

circular discs arranged

in

a staggered pattern (Fig.

4).

It will

be

supposed that the initial stream of liquid divides into two equal streams, on accóunt of symmetry, and that this process goes on repeating itself.

If,

for each successive row, the discharge in

the

outermost threads of liquid is counted as unity,

then

the discharges passing

O F D IF F U S I O N

Fig.

The statics and dynamics of underground water

between discs are distributed according to the binomial law; our illustration is none other than the celebrated triangle of Pascal and recalls the not less famous machine of Dalton. It is known that the curve having ordinates equal to the binomial co-efficients tends toward a normal probability curve as the power of the binomial

ap-

proaches

infinity.

If

the three-dimensional cafie is studied, an analogous result is found; the shape of the initial curves is a little different but, in

the

end, the normal probability curve is once more obtained

(Fig. 5).

In Fig. 3,

the axis of the cone passes through the tops of the hell-shaped curves and corresponds to the m e a n trajectory, as considered in the usual theories of the subject. The edges of the cone, inclined at

30 to the axis, correspond to zero concentration.

Along

a straight h e drawn through the peak of the cone, the concentration falls off inversely as the square of the distance away from the summit;

in

the two-dimensional case, the falling- off

in

Concentration is inversely pro- portional to this distance.

“O‘

’ 0 ’ 0

4 0 3 0 3 0 ’

0 4 0 “ 0 4 0 4

i050400i005

0 6 ~ ~ ~ ~ 1 5 ~

0’

G ( ) I

*0702103~03502~0701

“80“~~”o”o’”o”o‘

m e a n flow trajectories are curved; it is possible to determine surfaces, which w e shall call horns of diffusion, which are similar to the cones described above but which follow the curved trajectories. It

will

then be seen that the limits of the diffusing liquid make a n angle of about 30 with the n flow paths. Similarly, w e can define curves

in

making

certain angles with the m e a n paths in the same

way

as w e formerly considered straight lines issuing from the summit of a diffusion cone.

In

particular,

if

a given flow is convergent, with an angle of convergence greater than 60, the diffusion horn, after diverging to start with, m a y thereafter converge also, but less rapidly than the general flow;

in

fact, the section of the horn would remain constant for a n angle of convergence of 60.

I

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