46 
SEEPAGE OR RETURN WATERS FROM IRRIGATION. 
pass through small openings, which form a series of minute, tortu¬ 
ous and long tubes. It is a fact of common observation that the- 
pressure of water is much reduced by attaching a short length of hose 
or pipe. In the case of flow through sands, the openings are many 
times smaller, and the length may be very great, hence no matter 
how great the fall, the effect of the pressure is throttled by the 
friction. 
§ 36. In the lack of direct field evidence, we need to resort to 
laboratory experiments. An accomplished French engineer in 
investigating the water supply for the city of Dijon, experimented 
upon the flow through sand. He used a cast iron tube twelve feet 
long and twelve inches in diameter filled with sand, measuring the 
amount of water which passed through under different heads, and 
determined the relation between the pressure and the velocity. * 
§37. From the experiments of Darcy developed by Dupuit f, 
it is found in minute channels the velocity varies directly as the 
head, and may be expressed by the equation, 
v — k i 
in which v represents the velocity, i the inclination (being the head 
or fall in a given distance divided by the distance), and k a factor 
which varies with the kind of soil, size of interstices, etc. This fac¬ 
tor varies widely in different soils. It can be determined by exper¬ 
iment in specific soils, and the results there obtained applied to 
others of similar character. 
Table IX. is an attempt to put into tabular form, which will 
be practically useful, the value of the factor k for different cases. 
The table gives the factor by which the rate of inclination or grade 
(expressed by the fall in feet divided by the distance in feet) is to be 
multiplied to give the velocity in feet for the unit of time given in 
the corresponding column. The table is made from data obtained 
from the filters of London, Paris and Berlin, through Professor 
Nazzini, of Rome. || 
§38. Since water is more viscous at low temperature than at 
high, the formula given in §37 should evidently include a factor 
depending upon the temperature. From the experiments of 
Poiseulle X this factor would be l-\-.0018! {t-32°) -\-.00007 (t-32°} 
for any other temperature than freezing. 
* Darcy, Les eaux publiques de la ville de Dijon. 
t Traite de la conduite et de la distribution des eaux. Darcy and Dupuit 
I have not had the opportunity to consult at first hand. 
|| Idraulica pratica, 1:608. 
f Recherches experimentales sur le mouvement des liquides dans l«s; 
tubes de tres petite diametre. Quoted, Jamin et Bouty, Physique, tome 1, pt. 2* 
p. 100 ; also see Daniell’s Physics, p. 308. 
