AN IMPROVED METHOD OF AND APPARATUS FOR PRODUCING AND UTILIZING A FALL OF WATER
Year: 1870

page_text: PROVISIONAL SPECIFICATION left by William Robert Lake at the
Office of the Commissioners of Patents, with his Petition, on the
25th February 1870.-A communication from abroad by Doctor
Heiman Sanders-Ezn, Assistant in the Physiological Laboratory
of Amsterdam, at present residing at Paris, in the Empire of
France.
I, WILLIAM ROBERT LAKE, of the "International Patent Office,"
Southampton Buildings, London, Consulting Engineer, do hereby declare
the nature of the said Invention for "AN IMPROVED METHOD OF AND
APPARATUS FOR PRODUCING AND UTILIZING A FALL OF WATER," a communication,
to be as follows:-
.
It is an acknowledged fact that a body floating or immersed in water
exercises a certain pressure whose intensity is determined by the displaced
volume of water. There are shown in this phenomenon two forces in
equilibrium, one being the weight of the displaced water and the other
the weight of the floating body. If these two forces are suddenly
liberated there will be a controllable force equal to the pressure of a
column of water double the height of that which has been displaced, and
it is the object of this Invention to make a mechanical application of

page_text: these forces. There is however in the commencement this difficulty to
be overcome, namely, to renew or replace the column of water which
has acted and whose pressure has been used, for without this renewal
the work will quickly come to an end. This problem may be solved by
using for such renewal the inexhaustible forces furnished by the water
in which the body is immersed. One example will be sufficient to show
how this idea may be carried into practice.
Figure 1 of the accompanying Drawing represents a section D, A, E,
of a vessel which draws three meters. All parts of the bottom arc
subjected to the pressure of a column of water 3 meters in height. If
it be supposed that the part A of the bottom has a surface of 1 square
meter it will be subjected to an upward pressure equal to the weight of
three cubic metres of water, the height of the displaced column, while a
downward pressure of 3 meters of water arising from the weight of the
vessel holds the force in equilibrium. If it be supposed that the part A
is opened the external pressure will cause the water to enter the interior
of the tube A, C, in the vessel to the height of the exterior level, that is
to say, to 3 meters, but this force being exhausted the other force;
namely, that due to the weight of the vessel, causes the latter to descend.
Then another 3 meters of water will enter the tube A, C; as soon as the
height of the column of water in the tube A, C, is equal to 6 metres the
equilibrium will be established. If the opening A remains open the column
of water will descend quickly to the exterior level, but if the opening A
is closed at the moment when the column of water A, C, arrives at its
greatest height the vessel will have a load of 6 cubic meters of water, that
is to say, I have utilized the acquired speed with which the water is elevated
by converting it into weight; the weight of the vessel is therefore
increased to the extent of 6,000 kilograms, and it will be immersed to
such a depth that 6 cubic meters of the external water will be displaced.
Let it be supposed that as soon as A is closed another lateral aperture B
in tube A, C, is opened at the height of the exterior level; then the
column B, C, of 3 cubic meters will flow through the said aperture and
will give a cubic meter of water falling through an mean height of 2
meters, a second cubic meter falling through an mean height of 1½ meters,
and a third cubic meter falling through a height of 1 meter.
The sum
of the mechanical work done will equal one cubic meter of water falling
from the height of 2% + 1½ + ½ = 4½, that is to say, an effect will be
produced equal to about 60 theoretical horses' power. After this flow
Π
m

page_text: and the production of this, mechanical effect the water in the tube is at
the height of the external level. If two cubic meters overflow from the.
vessel the latter will be diminished proportionally in weight and will rise
till the volume of water displaced by it is diminished to the extent of 3
cubic meters, that is to say; by the pressure of the external water a new.
quantity of latent force is produced equivalent to that already expended.
If at this moment A is again opened a column of water of 3 cubic meters.
will be obtained in the tube A, C, and the actions herein-above described
will be repeated. The 3 cubic meters which overflow from the interior
have expended all their force usefully, and they regain their latent power
by contact with the surrounding water and by atmospheric pressure.
It therefore follows that these forces cost nothing, and upon the principal
of their origin are based the two examples of motive-power apparatus,
which I will now describe, and which I call "archimedo-motors."
The first apparatus is illustrated in Figure 2. The floating vessel or
ship A, A, draws 3 meters of water: Above an opening made in the.
bottom of about one square meter in area there rises a tube C to a
height of 7 meters, having in all parts the same sectional area of one.
square meter; this tube is partly open at the top, at the bottom it
communicates with the horizontal tube B, also having a sectional area
of one square meter. A tube D of the same sectional area extends
from the tube C at such a position that its upper side lies at the same
level as the external water. B and D are closed and opened by the
valves E and F. There is in a column of water 3 meters in height:
When E. is opened and F closed another column of 3-meters rises in C;
as soon as this column is obtained Ę is closed- and F is opened. The 3
meters of water-enter at D- with a velocity proportionate to the diameter
of D, and to the height of the said column of water. As soon as the
column has descended the first pressure is produced by opening E and
closing F, and so on. In order that the valves may operate with the
required precision and rapidity the tube C may be provided with a float
jointed to a lever attached to the side of the tube. As soon as the
column of water has fallen below the highest point to which the float G`
can rise (such point being determined by the arrangement of its joint)
the said float will also fall. By this limited movement of the float it
is very easy by the aid of any suitable mechanism to regulate the
opening and closing of the valves.

page_text: . If the vessel is furnished with a second apparatus similar to that
above described, but acting inversely, it will be readily understood that
the effect of the propelling forces may be continued and the force
obtained from the current of water or rather the fall of water aforesaid
may be utilized for turbine or any other hydraulic motor.
3
3,456
The calculation of the force which may be produced is as follows:
The column of water having a height of 3 meters has at the commence-
ment of its fall a pressure of 3 meters, and at the end of 0, that is to
say, it has an average pressure of 1 meters according to the formula
for the quantity of flowing water M=cf √2g s. in which c co-efficient=
0-64-f-surface--1-square-meter, 8-height of fall =1.50". I can obtain
in one second about 3 cubic meters 456 cubic decimeters. The 3 cubic
meters will run out in or 0.87 of a second, and will naturally rise
in the same time; there will therefore be a theoretical effect of 60 horses*
power of steam in a period of 0.87 of a second when the whole column
is caused to fall, and for an entire second of time there will be obtained
67.4 horses' power. If the level of the water is maintained in the upper
part of the tube C by means of the float at a mean height of two meters
there will be obtained in a second 4,006 cubic meters; when this result
is desired only 2 cubic meters are caused to run out, which requires a
period of half a second. The lower cubic meter falls then from a mean
height of 0.5 meters, the second of 1 meters, the 3rd of 2 meters,
producing together an effect of 106/rds theoretical horses' power in a
second. But as 0-7 second is required to replace the two cubic meters
which have run out whilst the second motor cannot furnish in half a
second enough water there would be some irregularity, and in order to
avoid this difficulty it is necessary to diminish the section of the tube D
in order that the 2cm may only run out in a period of about 0.7 of a
second. There will then be obtained per second about 742/3rds theoretical
horses' power. The tube D therefore instead of a section of a cubic meter
will have a section of only 0.7cm; or a diameter of nearly 0·944”. In
cases where the elevation of the tube C above the level of the external
water may not be convenient it may be reduced to the height of the
same level and even below, as shewn in Figure 3, but then it will be
necessary to close it at the top. The side tube will rise in this case
directly from the bottom C as shewn, whilst B will always be filled with
water to the height of the float G. Above this colunin of water is

page_text: 9.5
placed a closed air receiver. If E is open and F closed the air in the
receiver will be compressed by a pressure equal to 6000 kilogramms and
the water will enter the tube C; if now E is closed and F opened this
water will be expelled by the same pressure and produce a useful effect.
By the movement of the float the irregularities of the pressure are here
also controlled, and two similar apparatus working alternately will give
a constant current of water. By these arrangements of the archimedo-
motors I produce falls of water which may be utilised as desired.
According as the ship draws more or less water the length of the tube
C will be varied and also the place of outlet of the tubes. When the
ship draws much water the effect will be great, as there will be a greater.
fall, it is evident also that for different applications the dimensions will
be varied. When I employ for the production of a continued effect two,
elevating tubes the discharging pipes D will be connected and form one
pipe, whose aperture may be turned towards the stern of the ship. The
tubes B, as in Figure 4, have their mouths turned towards the bows of
the ship.