k = 0.00393 if the leathers are new or badly lubricated;
= 0.00262 if the leathers are in good condition and well lubricated.
Since the total pressure on the ram is P = ¼[pi]d²p, the fraction of
the total pressure expended in overcoming the friction of the leathers
is F/P = .005/d to .0033/d, d being in feet.
Let H be the height of the pressure column measured from the free
surface of the supply reservoir to the bottom of the ram in its lowest
position, H_b the height from the discharge reservoir to the same
point, h the height of the ram above its lowest point at any moment, S
the length of stroke, [Omega] the area of the ram, W the weight of
cage, R the weight of ram, B the weight of balance weight, w the
weight of balance chain per foot run, F the friction of the cup
leather and slides. Then, neglecting fluid friction, if the ram is
rising the accelerating force is
P1 = G(H - h)[Omega] - R - W + B - w(S - h) + wh - F,
and if the ram is descending
P2 = G(H_b - h)[Omega] + W + R - B + w(S - h) - wh - F.
If w = ½ G[Omega], P1 and P2 are constant throughout the stroke; and
the moving force in ascending and descending is the same, if
B = W + R + wS - G[Omega](H - H_b)/2.
Using the values just found for w and B,
P1 = P2 = ½G[Omega](H - H_b) - F.
Let W + R + wS + B = U, and let P be the constant accelerating force
acting on the system, then the acceleration is (P/U)g. The velocity at
the end of the stroke is (assuming the friction to be constant)
v = [root](2PgS/U);
and the mean velocity of ascent is ½v.
[Illustration: FIG. 172.]
§ 177. _Armstrong's Hydraulic Jigger._--This is simply a single-acting
hydraulic cylinder and ram, provided with sheaves so as to give motion
to a wire rope or chain. It is used in various forms of lift and crane.
Fig. 172 shows the arrangement. A hydraulic ram or plunger B works in a
stationary cylinder A. Ram and cylinder carry sets of sheaves over which
passes a chain or rope, fixed at one end to the cylinder, and at the
other connected over guide pulleys to a lift or crane. For each pair of
pulleys, one on the cylinder and one on the ram, the movement of the
free end of the rope is doubled compared with that of the ram. With
three pairs of pulleys the free end of the rope has a movement equal to
six times the stroke of the ram, the force exerted being in the inverse
proportion.
§ 178. _Rotative Hydraulic Engines._--Valve-gear mechanism similar in
principle to that of steam engines can be applied to actuate the
admission and discharge valves, and the pressure engine is then
converted into a continuously-acting motor.
Let H be the available fall to work the engine after deducting the
loss of head in the supply and discharge pipes, Q the supply of water
in cubic feet per second, and [eta] the efficiency of the engine. Then
the horse-power of the engine is
H.P. = [eta]GQH/550.
The efficiency of large slow-moving pressure engines is [eta] = .66 to
.8. In small motors of this kind probably [eta] is not greater than
.5. Let v be the mean velocity of the piston, then its diameter d is
given by the relation
Q = [pi]d²v/4 in double-acting engines,
= [pi]d²v/8 in single-acting engines.
If there are n cylinders put Q/n for Q in these equations.
Small rotative pressure engines form extremely convenient motors for
hoists, capstans or winches, and for driving small machinery. The
single-acting engine has the advantage that the pressure of the piston
on the crank pin is always in one direction; there is then no knocking
as the dead centres are passed. Generally three single-acting cylinders
are used, so that the engine will readily start in all positions, and
the driving effort on the crank pin is very uniform.
[Illustration: FIG. 173.]
_Brotherhood Hydraulic Engine._--Three cylinders at angles of 120°
with each other are formed in one casting with the frame. The
plungers are hollow trunks, and the connecting rods abut in
cylindrical recesses in them and are connected to a common crank pin.
A circular valve disk with concentric segmental ports revolves at the
same rate as the crank over ports in the valve face common to the
three cylinders. Each cylinder is always in communication with either
an admission or exhaust port. The blank parts of the circular valve
close the admission and exhaust ports alternately. The fixed valve
face is of lignum vitae in a metal recess, and the revolving valve of
gun-metal. In the case of a small capstan engine the cylinders are 3½
in. diameter and 3 in. stroke. At 40 revs. per minute, the piston
speed is 31 ft. per minute. The ports are 1 in. diameter or 1/12 of
the piston area, and the mean velocity in the ports 6.4 ft. per sec.
With 700 lb. per sq. in. water pressure and an efficiency of 50%, the
engine is about 3 h.p. A common arrangement is to have three parallel
cylinders acting on a three-throw crank shaft, the cylinders
oscillating on trunnions.
_Hastie's Engine._--Fig. 173 shows a similar engine made by Messrs
Hastie of Greenock. G, G, G are the three plungers which pass out of
the cylinders through cup leathers, and act on the same crank pin. A
is the inlet pipe which communicates with the cock B. This cock
controls the action of the engine, being so constructed that it acts
as a reversing valve when the handle C is in its extreme positions and
as a brake when in its middle position. With the handle in its middle
position, the ports of the cylinders are in communication with the
exhaust. Two passages are formed in the framing leading from the cock
B to the ends of the cylinders, one being in communication with the
supply pipe A, the other with the discharge pipe Q. These passages end
as shown at E. The oscillation of the cylinders puts them alternately
in communication with each of these passages, and thus the water is
alternately admitted and exhausted.
[Illustration: FIG. 174.]
[Illustration: FIG. 175.]
In any ordinary rotative engine the length of stroke is invariable.
Consequently the consumption of water depends simply on the speed of
the engine, irrespective of the effort overcome. If the power of the
engine must be varied without altering the number of rotations, then
the stroke must be made variable. Messrs Hastie have contrived an
exceedingly ingenious method of varying the stroke automatically, in
proportion to the amount of work to be done (fig. 174). The crank pin
I is carried in a slide H moving in a disk M. In this is a double cam
K acting on two small steel rollers J, L attached to the slide H. If
the cam rotates it moves the slide and increases or decreases the
radius of the circle in which the crank pin I rotates. The disk M is
keyed on a hollow shaft surrounding the driving shaft P, to which the
cams are attached. The hollow shaft N has two snugs to which the
chains RR are attached (fig. 175). The shaft P carries the spring case
SS to which also are attached the other ends of the chains. When the
engine is at rest the springs extend themselves, rotating the hollow
shaft N and the frame M, so as to place the crank pin I at its nearest
position to the axis of rotation. When a resistance has to be
overcome, the shaft N rotates relatively to P, compressing the
springs, till their resistance balances the pressure due to the
resistance to the rotation of P. The engine then commences to work,
the crank pin being in the position in which the turning effort just
overcomes the resistance. If the resistance diminishes, the springs
force out the chains and shorten the stroke of the plungers, and vice
versa. The following experiments, on an engine of this kind working a
hoist, show how the automatic arrangement adjusted the water used to
the work done. The lift was 22 ft. and the water pressure in the
cylinders 80 lb. per sq. in.
Weight lifted, Chain 427 633 745 857 969 1081 1193
in lb. only
Water used, in 7½ 10 14 16 17 20 21 22
gallons
§ 179. _Accumulator Machinery._--It has already been pointed out that it
is in some cases convenient to use a steam engine to create an
artificial head of water, which is afterwards employed in driving
water-pressure machinery. Where power is required intermittently, for
short periods, at a number of different points, as, for instance, in
moving the cranes, lock gates, &c., of a dockyard, a separate steam
engine and boiler at each point is very inconvenient; nor can engines
worked from a common boiler be used, because of the great loss of heat
and the difficulties which arise out of condensation in the pipes. If a
tank, into which water is continuously pumped, can be placed at a great
elevation, the water can then be used in hydraulic machinery in a very
convenient way. Each hydraulic machine is put in communication with the
tank by a pipe, and on opening a valve it commences work, using a
quantity of water directly proportional to the work done. No attendance
is required when the machine is not working.
[Illustration: FIG. 176.]
A site for such an elevated tank is, however, seldom available, and in
place of it a beautiful arrangement termed an accumulator, invented by
Lord Armstrong, is used. This consists of a tall vertical cylinder; into
this works a solid ram through cup leathers or hemp packing, and the ram
is loaded by fixed weights, so that the pressure in the cylinder is 700
lb. or 800 lb. per sq. in. In some cases the ram is fixed and the
cylinder moves on it. The pumping engines which supply the energy that
is stored in the accumulator should be a pair coupled at right angles,
so as to start in any position. The engines pump into the accumulator
cylinder till the ram is at the top of its stroke, when by a catch
arrangement acting on the engine throttle valve the engines are stopped.
If the accumulator ram descends, in consequence of water being taken to
work machinery, the engines immediately recommence working. Pipes lead
from the accumulator to each of the machines requiring to be driven, and
do not require to be of large size, as the pressure is so great.
Fig. 176 shows a diagrammatic way the scheme of a system of
accumulator machinery. A is the accumulator, with its ram carrying a
cylindrical wrought-iron tank W, in which weights are placed to load
the accumulator. At R is one of the pressure engines or jiggers,
worked from the accumulator, discharging the water after use into the
tank T. In this case the pressure engine is shown working a set of
blocks, the fixed block being on the ram cylinder, the running block
on the ram. The chain running over these blocks works a lift cage C,
the speed of which is as many times greater than that of the ram as
there are plies of chain on the block tackle. B is the balance weight
of the cage.
[Illustration: FIG. 177.]
In the use of accumulators on shipboard for working gun gear or
steering gear, the accumulator ram is loaded by springs, or by steam
pressure acting on a piston much larger than the ram.
R. H. Tweddell has used accumulators with a pressure of 2000 lb. per
sq. in. to work hydraulic riveting machinery.
The amount of energy stored in the accumulator, having a ram d in. in
diameter, a stroke of S ft., and delivering at p lb. pressure per sq.
in., is
[pi]
---- p d²S foot-pounds.
4
Thus, if the ram is 9 in., the stroke 20 ft., and the pressure 800 lb.
per sq. in., the work stored in the accumulator when the ram is at the
top of the stroke is 1,017,600 foot-pounds, that is, enough to drive a
machine requiring one horse power for about half an hour. As, however,
the pumping engine replaces water as soon as it is drawn off, the
working capacity of the accumulator is very much greater than this.
Tweddell found that an accumulator charged at 1250 lb. discharged at
1225 lb. per sq. in. Hence the friction was equivalent to 12½ lb. per
sq. in. and the efficiency 98%.
When a very great pressure is required a differential accumulator
(fig. 177) is convenient. The ram is fixed and passes through both
ends of the cylinder, but is of different diameters at the two ends, A
and B. Hence if d1, d2 are the diameters of the ram in inches and p
the required pressure in lb. per sq. in., the load required is
¼p[pi](d1² - d2²). An accumulator of this kind used with riveting
machines has d1 = 5½ in., d2 = 4¾ in. The pressure is 2000 lb. per sq.
in. and the load 5.4 tons.
[Illustration: FIG. 178.]
Sometimes an accumulator is loaded by water or steam pressure instead
of by a dead weight. Fig. 178 shows the arrangement. A piston A is
connected to a plunger B of much smaller area. Water pressure, say
from town mains, is admitted below A, and the high pressure water is
pumped into and discharged from the cylinder C in which B works. If r
is the ratio of the areas of A and B, then, neglecting friction, the
pressure in the upper cylinder is r times that under the piston A.
With a variable rate of supply and demand from the upper cylinder, the
piston A rises and falls, maintaining always a constant pressure in
the upper cylinder.
_Water Wheels._
§ 180. _Overshot and High Breast Wheels._--When a water fall ranges
between 10 and 70 ft. and the water supply is from 3 to 25 cub. ft. per
second, it is possible to construct a bucket wheel on which the water
acts chiefly by its weight. If the variation of the head-water level
does not exceed 2 ft., an overshot wheel may be used (fig. 179). The
water is then projected over the summit of the wheel, and falls in a
parabolic path into the buckets. With greater variation of head-water
level, a pitch-back or high breast wheel is better. The water falls over
the top of a sliding sluice into the wheel, on the same side as the head
race channel. By adjusting the height of the sluice, the requisite
supply is given to the wheel in all positions of the head-water level.
The wheel consists of a cast-iron or wrought-iron axle C supporting
the weight of the wheel. To this are attached two sets of arms A of
wood or iron, which support circular segmental plates, B, termed
shrouds. A cylindrical sole plate dd extends between the shrouds on
the inner side. The buckets are formed by wood planks or curved
wrought-iron plates extending from shroud to shroud, the back of the
buckets being formed by the sole plate.
[Illustration: FIG. 179.]
The efficiency may be taken at 0.75. Hence, if h.p. is the effective
horse power, H the available fall, and Q the available water supply
per second,
h.p. = 0.75 (GQH/550) = 0.085 QH.
If the peripheral velocity of the water wheel is too great, water is
thrown out of the buckets before reaching the bottom of the fall. In
practice, the circumferential velocity of water wheels of the kind now
described is from 4½ to 10 ft. per second, about 6 ft. being the usual
velocity of good iron wheels not of very small size. In order that the
water may enter the buckets easily, it must have a greater velocity
than the wheel. Usually the velocity of the water at the point where
it enters the wheel is from 9 to 12 ft. per second, and to produce
this it must enter the wheel at a point 16 to 27 in. below the
head-water level. Hence the diameter of an overshot wheel may be