Scientific American Supplement No. 275
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Various >> Scientific American Supplement No. 275
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Lastly, the difference in the methods of observation and the errors which
belong to them, must be taken into account. M. Stockalper, who experimented
on great pressures, used metallic gauges, which are instruments on whose
sensibility and correctness complete reliance cannot be placed; and
moreover the standard manometer with which they were compared was one of
the same kind. The author is not of opinion that the divergence is owing to
the fact that M. Stockalper made his observations on an air conduit, where
the pressure was much higher than in gas pipes. Indeed, it may be assumed
that gases and liquids act in the same manner; and, as will be [1]
explained later on, there is reason to believe that with the latter a rise
of pressure increases the losses of pressure instead of diminishing them.
[Transcribers note 1: corrected from 'as will we explained']
All the pipes for supplying compressed air in tunnels and in headings of
mines are left uncovered, and have flanged joints; which are advantages not
merely as regards prevention of leakage, but also for facility of laying
and of inspection. If a compressed air pipe had to be buried in the ground
the flanged joint would lose a part of its advantages; but, nevertheless,
the author considers that it would still be preferable to the ordinary
joint.
It only remains to refer to the motors fed with the compressed air.
This subject is still in its infancy from a practical point of view. In
proportion as the air becomes hot by compression, so it cools by expansion,
if the vessel containing it is impermeable to heat. Under these conditions
it gives out in expanding a power appreciably less than if it retained its
original temperature; besides which the fall of temperature may impede the
working of the machine by freezing the vapor of water contained in the air.
If it is desired to utilize to the utmost the force stored up in the
compressed air it is necessary to endeavor to supply heat to the air during
expansion so as to keep its temperature constant. It would be possible
to attain this object by the same means which prevent heating from
compression, namely, by the circulation and injection of water. It would
perhaps be necessary to employ a little larger quantity of water for
injection, as the water, instead of acting by virtue both of its heat of
vaporization and of its specific heat, can in this case act only by virtue
of the latter. These methods might be employed without difficulty for air
machines of some size. It would be more difficult to apply them to small
household machines, in which simplicity is an essential element; and we
must rest satisfied with imperfect methods, such as proximity to a stove,
or the immersion of the cylinder in a tank of water. Consequently loss of
power by cooling and by incomplete expansion cannot be avoided. The only
way to diminish the relative amount of this loss is to employ compressed
air at a pressure not exceeding three or four atmospheres.
The only real practical advance made in this matter is M. Mekarski's
compressed air engine for tramways. In this engine the air is made to pass
through a small boiler containing water at a temperature of about 120 deg.
Cent. (248 deg. Fahr.), before entering the cylinder of the engine. It must
be observed that in order to reduce the size of the reservoirs, which
are carried on the locomotive, the air inside them must be very highly
compressed; and that in going from the reservoir into the cylinder it
passes through a reducing valve or expander, which keeps the pressure of
admission at a definite figure, so that the locomotive can continue working
so long as the supply of air contained in the reservoir has not come down
to this limiting pressure. The air does not pass the expander until after
it has gone through the boiler already mentioned. Therefore, if the
temperature which it assumes in the boiler is 100 deg. Cent. (212 deg. Fahr.), and
if the limiting pressure is 5 atm., the gas which enters the engine will be
a mixture of air and water vapor at 100 deg. Cent.; and of its total pressure
the vapor of water will contribute I atm. and the air 4 atm. Thus this
contrivance, by a small expenditure of fuel, enables the air to act
expansively without injurious cooling, and even reduces the consumption of
compressed air to an extent which compensates for part of the loss of power
arising from the preliminary expansion which the air experiences before its
admission into the engine. It is clear that this same contrivance, or what
amounts to the same thing, a direct injection of steam, at a sufficient
pressure, for the purpose of maintaining the expanding air at a constant
temperature, might be tried in a fixed engine worked by compressed air with
some chance of success.
Whatever method is adopted it would be advantageous that the losses of
pressure in the pipes connecting the compressors with the motors should be
reduced as much as possible, for in this case that loss would represent
a loss of efficiency. If, on the other hand, owing to defective means of
reheating, it is necessary to remain satisfied with a small amount of
expansion, the loss of pressure in the pipe is unimportant, and has only
the effect of transferring the limited expansion to a point a little lower
on the scale of pressures. If W is the net disposable force on the shaft
of the engine which works the compressor, v1 the volume of air at the
compressor, p1. given by the compressor, and at the temperature of the
surrounding air, and p0 the atmospheric pressure, the efficiency of the
compressor, assuming the air to expand according to Boyle's law, is given
by the well-known formula--
p1 v1 log (p1 / p0)
-------------------.
W
[TEX: \frac{p_1 v_1 \log \frac{p_1}{p_0}}{W}]
Let p2 be the value to which the pressure is reduced by the loss of
pressure at the end of the conduit, and v2 the volume which the air
occupies at this pressure and at the same temperature; the force stored
up in the air at the end of its course through the conduit is p2 v2
log(p2/p0); consequently, the efficiency of the conduit is
p2 v2 log(p2/p0)
----------------
p1 v1 log(p1/p0)
[TEX: \frac{p_2 v_2 \log\frac{p_2}{p_0}}{p_2 v_2 \log\frac{p_2}{p_0}}]
a fraction that may be reduced to the simple form
log(p2/p0)
----------,
log(p1/p0)
[TEX: \frac{\log\frac{p_2}{p_0}}{\log\frac{p_2}{p_0}}]
if there is no leakage during the passage of the air, because in that cause
p2 v2 = p1 v1. Lastly, if W1 is the net disposable force on the shaft of
the compressed air motor, the efficiency of this engine will be,
W1
----------------
p2 v2 log(p2/p0)
[TEX: \frac{W_1}{p_2 v_2 \log \frac{p_2}{p_0}}]
and the product of these three partial efficiencies is equal to W1/W, the
general efficiency of the transmission.
III. _Transmission by Pressure Water_.--As transmission of power by
compressed air has been specially applied to the driving of tunnels, so
transmission by pressure water has been specially resorted to for lifting
heavy loads, or for work of a similar nature, such as the operations
connected with the manufacture of Bessemer steel or of cast-iron pipes.
The author does not propose to treat of transmissions established for this
special purpose, and depending on the use of accumulators at high pressure,
as he has no fresh matter to impart on this subject, and as he believes
that the remarkable invention of Sir William Armstrong was described for
the first time, in the "Proceedings of the Institution of Mechanical
Engineers." His object is to refer to transmissions applicable to general
purposes.
The transmission of power by water may occur in another form. The motive
force to be transmitted may be employed for working pumps which raise the
water, not to a fictitious height in an accumulator, but to a real height
in a reservoir, with a channel from this reservoir to distribute the water
so raised among several motors arranged for utilizing the pressure. The
author is not aware that works have been carried out for this purpose.
However, in many towns a part of the water from the public mains serves to
supply small motors--consequently, if the water, instead of being brought
by a natural fall, has been previously lifted artificially, it might be
said that a transmission of power is here grafted on to the ordinary
distribution of water.
Unless a positive or negative force of gravity is introduced into the
problem, independently of the force to be transmitted, the receivers of
the water pressure must be assumed to be at the same level as the forcing
pumps, or more correctly, the water discharged from the receivers to be at
the same level as the surface of the water from which the pumps draw their
supply. In this case the general efficiency of transmission is the product
of three partial efficiencies, which correspond exactly to those mentioned
with regard to compressed air. The height of lift, contained in the
numerator of the fraction which expresses the efficiency of the pumps, is
not to be taken as the difference in level between the surface of the water
in the reservoir and the surface of the water whence the pumps draw their
supply; but as this difference in level, plus the loss of pressure in the
suction pipe, which is usually very short, and plus the loss in the channel
to the reservoir, which may be very long. A similar loss of initial
pressure affects the efficiency of the discharge channel. The reservoir, if
of sufficient capacity, may become an important store of power, while the
compressed air reservoir can only do so to a very limited extent.
Omitting the subject of the pumps, and passing on at once to the discharge
main, the author may first point out that the distinction between the
ascending and descending mains of the system is of no importance, for two
reasons: first, that nothing prevents the motors being supplied direct from
the first alone; and second, that the one is not always distinct from the
other. In fact, the reservoir may be connected by a single branch pipe with
the system which goes from the pumps to the motors; it may even be placed
at the extreme end of this system beyond the motors, provided always that
the supply pipe is taken into it at the bottom. The same formula may be
adopted for the loss of initial pressure in water pipes as for compressed
air pipes, viz.,
p1 - p 64 b1
------- = --------- L Q squared +- h;
[Delta] [pi] squared D^5
[TEX: \frac{p_1 - p}{\Delta} = \frac{64 b_1}{\pi^2 D^5} L Q^2 \pm h]
h being the difference of level between the two ends of the portion of
conduit of length, L, and the sign + or - being used according as the
conduit rises or falls. The specific weight, [delta], is constant, and the
quotients, p1/[delta] and p/[delta], represent the heights, z and z1, to
which the water could rise above the pipes, in vertical tubes branching
from it, at the beginning and end of the transit. The values assigned to
the coefficient b1 in France, are those determined by D'Arcy. For new
cast-iron pipes he gives b1 - 0.0002535 + 1/D 0.000000647; and recommends
that this value should be doubled, to allow for the rust and incrustation
which more or less form inside the pipes during use. The determination of
this coefficient has been made from experiments where the pressure has
not exceeded four atmospheres; within these limits the value of the
coefficient, as is generally admitted, is independent of the pressure. The
experiments made by M. Barret, on the pressure pipes of the accumulator at
the Marseilles docks, seem to indicate that the loss of pressure would be
greater for high pressures, everything else being equal. This pipe, having
a diameter of 0.127 m. (5 in.), was subjected to an initial pressure of 52
atmospheres. The author gives below the results obtained for a straight
length 320 m. (1050 ft) long; and has placed beside them the results which
D'Arcy's formula would give.
Loss of head, in meters or ft. respectively
per 100 meters or ft. run of pipes.
+-----------------^-------------------+
| |
Calculated loss.
+-----------^-----------+
| |
Velocity of flow Actual loss
per second. observed. Old pipes. New pipes.
Meters. Feet. Met. or Ft. Met. or Ft. Met. or Ft.
0.25 0.82 1.5 0.12 0.06
0.50 1.64 2.5 0.48 0.24
0.75 2.46 3.7 1.08 0.54
1.00 3.28 5.5 1.92 0.96
1.25 4.10 6.1 3.00 1.50
1.50 4.92 7.3 4.32 2.16
1.75 5.74 8.0 5.88 2.94
2.00 6.56 10.2 7.68 3.84
2.25 7.38 11.7 9.72 4.86
2.50 8.20 14.0 12.00 6.00
Moreover, these results would appear to indicate a different law from that
which is expressed by the formula b1 u squared, as is easy to see by representing
them graphically. It would be very desirable that fresh experiments should
be made on water pipes at high pressure, and of various diameters. Of
machines worked by water pressure the author proposes to refer only to two
which appear to him in every respect the most practical and advantageous.
One is the piston machine of M. Albert Schmid, engineer at Zurich. The
cylinder is oscillating, and the distribution is effected, without an
eccentric, by the relative motion of two spherical surfaces fitted one
against the other, and having the axis of oscillation for a common axis.
The convex surface, which is movable and forms part of the cylinder, serves
as a port face, and has two ports in it communicating with the two ends of
the cylinder. The concave surface, which is fixed and plays the part of a
slide valve, contains three openings, the two outer ones serving to admit
the pressure water, and the middle one to discharge the water after it has
exerted its pressure. The piston has no packing. Its surface of contact has
two circumferential grooves, which produce a sort of water packing acting
by adhesion. A small air chamber is connected with the inlet pipe, and
serves to deaden the shocks. This engine is often made with two cylinders,
having their cranks at right angles.
The other engine, which is much less used, is a turbine on Girard's system,
with a horizontal axis and partial admission, exactly resembling in
miniature those which work in the hydraulic factory of St. Maur, near
Paris. The water is introduced by means of a distributer, which is fitted
in the interior of the turbine chamber, and occupies a certain portion
of its circumference. This turbine has a lower efficiency than Schmid's
machine, and is less suitable for high pressures; but it possesses this
advantage over it, that by regulating the amount of opening of the
distributer, and consequently the quantity of water admitted, the force can
be altered without altering the velocity of rotation. As it admits of great
speeds, it could be usefully employed direct, without the interposition of
spur wheels or belts for driving magneto-electric machines employed for the
production of light, for electrotyping, etc.
In compressed air machines the losses of pressure due to incomplete
expansion, cooling, and waste spaces, play an important part. In water
pressure machines loss does not occur from these causes, on account of the
incompressibility of the liquid, but the frictions of the parts are the
principal causes of loss of power. It would be advisable to ascertain
whether, as regards this point, high or low pressures are the most
advantageous. Theoretical considerations would lead the author to imagine
that for a piston machine low pressures are preferable. In conclusion, the
following table gives the efficiencies of a Girard turbine, constructed by
Messrs. Escher Wyss & Co., of Zurich, and of a Schmid machine, as measured
by Professor Fliegnor, in 1871:
ESCHER WYSS & CO'S TURBINE.
Effective Head of Water. Revolutions Efficiency.
per minute.
Meters. Feet. Revs. Per cent.
20.7 67.9 628 68.5
20.7 67.9 847 47.4
24.1 79.0 645 68.5
27.6 90.5 612 65.7
27.6 90.5 756 68.0
31.0 101.7 935 56.9
31.0 101.7 1,130 35.1
SCHMID MOTOR.
8.3 27.2 226 37.4
11.4 37.4 182 67.4
14.5 47.6 254 53.4
17.9 58.7 157 86.2
20.7 67.9 166 89.6
20.7 67.9 225 74.6
24.1 79.0 238 76.7
24.1 79.0 389 64.0
27.6 90.5 207 83.9
It will be observed that these experiments relate to low pressures; it
would be desirable to extend them to higher pressures.
IV. _Transmission by Electricity._--However high the efficiency of an
electric motor may be, in relation to the chemical work of the electric
battery which feeds it, force generated by an electric battery is too
expensive, on account of the nature of the materials consumed, for a
machine of this kind ever to be employed for industrial purposes. If,
however, the electric current, instead of being developed by chemical
work in a battery, is produced by ordinary mechanical power in a
magneto-electric or dynamo-electric machine, the case is different; and
the double transformation, first of the mechanical force into an electric
current, and then of that current into mechanical force, furnishes a means
for effecting the conveyance of the power to a distance.
It is this last method of transmission which remains to be discussed. The
author, however, feels himself obliged to restrict himself in this matter
to a mere summary; and, indeed, it is English physicists and engineers who
have taken the technology of electricity out of the region of empiricism
and have placed it on a scientific and rational basis. Moreover, they are
also taking the lead in the progress which is being accomplished in this
branch of knowledge, and are best qualified to determine its true bearings.
When an electric current, with an intensity, i, is produced, either by
chemical or mechanical work, in a circuit having a total resistance, R, a
quantity of heat is developed in the circuit, and this heat is the exact
equivalent of the force expended, so long as the current is not made use of
for doing any external work. The expression for this quantity of heat, per
unit of time, is Ai squaredR; A being the thermal equivalent of the unit of power
corresponding to the units of current and resistance, in which i and R are
respectively expressed. The product, i squaredR, is a certain quantity of power,
which the author proposes to call _power transformed into electricity_.
When mechanical power is employed for producing a current by means of
a magneto-electric or dynamo-electric machine--or, to use a better
expression, by means of a _mechanical generator of electricity_--it is
necessary in reality to expend a greater quantity of power than i squaredR in
order to make up for losses which result either from ordinary friction
or from certain electro magnetic reactions which occur. The ratio of the
quantity, i squaredR, to the power, W, actually expended per unit of time is
called the efficiency of the generator. Designating it by K, we obtain, W
= i squaredR/K. It is very important to ascertain the value of this efficiency,
considering that it necessarily enters as a factor into the evaluation of
all the effects to be produced by help of the generator in question. The
following table gives the results of certain experiments made early in
1879, with a Gramme machine, by an able physicist, M Hagenbach, Professor
at the University at Basle, and kindly furnished by him to the author:
Revolutions per minute 935 919.5 900.5 893
Total resistance in Siemens' units 2.55 3.82 4.94 6.06
Total resistance in absolute units 2.435 3.648 4.718 5.787
x10^9 x10^9 x10^9 x10^9
Intensity in chemical units 17.67 10.99 8.09 6.28
Intensity in absolute units 2.828 1.759 1.295 1.005
Work done i squaredR in absolute units 1948.6 1129.2 791.3 584.9
x10^7 x10^7 x10^7 x10^7
Work done i squaredR in kilogrammes 198.6 115.1 80.66 59.62
Power expended in kilogrammes 301.5 141.0 86.25 83.25
Efficiency, per cent. 65.9 81.6 93.5 71.6
M. Hagenbach's dynamometric measurements were made by the aid of a brake.
After each experiment on the electric machine, he applied the brake to the
engine which he employed, taking care to make it run at precisely the same
speed, with the same pressure of steam, and with the same expansion as
during experiment. It would certainly be better to measure the force
expended during and not after the experiment, by means of a registering
dynamometer. Moreover, M. Hagenbach writes that his measurements by means
of the brake were very much prejudiced by external circumstances; doubtless
this is the reason of the divergences between the results obtained.
About the same time Dr. Hopkinson communicated to this institution the
results of some very careful experiments made on a Siemens machine. He
measured the force expended by means of a registering dynamometer, and
obtained very high coefficients of efficiency, amounting to nearly 90 per
cent. M. Hagenbach also obtained from one machine a result only a little
less than unity. Mechanical generators of electricity are certainly
capable of being improved in several respects, especially as regards their
adaptation to certain definite classes of work. But there appears to
remain hardly any margin for further progress as regards efficiency. Force
transformed into electricity in a generator may be expressed by i [omega] M
C; [omega] being the angular velocity of rotation; M the magnetism of one
of the poles, inducing or induced, which intervenes; and C a constant
specially belonging to each apparatus, and which is independent of
the units adopted. This constant could not be determined except by
an integration practically impossible; and the product, M C, must be
considered indivisible. Even in a magneto-electric machine (with permanent
inducing magnets), and much more in a dynamo-electric machine (inducing by
means of electro-magnets excited by the very current produced) the product,
M C, is a function of the intensity. From the identity of the expressions,
i squaredR and i [omega] M C we obtain the relation M C = IR/[omega] which
indicates the course to be pursued to determine experimentally the law
which connects the variations of M C with those of i. Some experiments made
in 1876, by M. Hagenbach, on a Gramme dynamo-electric machine, appear to
indicate that the magnetism, M C, does not increase indefinitely with the
intensity, but that there is some maximum value for this quantity. If,
instead of working a generator by an external motive force, a current is
passed through its circuit in a certain given direction, the movable part
of the machine will begin to turn in an opposite direction to that in which
it would have been necessary to turn it in order to obtain a current in the
aforesaid direction. In virtue of this motion the electro-magnetic forces
which are generated may be used to overcome a resisting force. The machine
will then work as a motor or receiver. Let i be the intensity of the
external current which works the motor, when the motor is kept at rest. If
it is now allowed to move, its motion produces, in virtue of the laws of
induction, a current in the circuit of intensity, i1, in the opposite
direction to the external current; the effective intensity of the current
traversing the circuit is thus reduced to i - i1. The intensity of the
counter current is given, like that of the generating current, by the
equation, i1 squaredR = i1 [omega]1 M1 C1, or i1R = [omega]1 M1 C1, the index, 1,
denoting the quantities relating to the motor. Here M1 C1 is a function of
i - i1, not of i. As in a generator the force transformed into electricity
has a value, i [omega] M C, so in a motor the force developed by
electricity is (i - i1) [omega]1 M1 C1. On account, however, of the losses
which occur, the effective power, that is the disposable power on the shaft
of the motor, will have a smaller value, and in order to arrive at it a
coefficient of efficiency, K1, must be added. We shall then have W1 = K1
(i-i1) [omega]1 M1 C1. The author has no knowledge of any experiments
having been made for obtaining this efficiency, K1. Next let us suppose
that the current feeding the motor is furnished by a generator, so that
actual transmission by electricity is taking place. The circuit, whose
resistance is R, comprises the coils, both fixed and movable, of the
generator and motor, and of the conductors which connect them. The
intensity of the current which traverses the circuit had the value, i, when
the motor was at rest; by the working of the motor it is reduced to i - i1.
The power applied to the generator is itself reduced to W-[(i-i1)[omega]
M C]/K. The prime mover is relieved by the action of the counter current,
precisely as the consumption of zinc in the battery would be reduced by the
same cause, if the battery was the source of the current. The efficiency
of the transmission is W1/W. Calculation shows that it is expressed by the
following equations:W1/W = K K1 [([omega]11 M1 C1)/([omega]1 M C)], or = K
K1 [([omega]11 M1 C)/([omega]11 M1 C1 + (i-i1) R)]; expressions in which
it must be remembered M C and M1 C1 are really functions of (i-i1). This
efficiency is, then, the product of three distinct factors, each evidently
less than unity, namely, the efficiency belonging to the generator, the
efficiency belonging to the motor, and a third factor depending on the rate
of rotation of the motor and the resistance of the circuit. The influence
which these elements exert on the value of the third factor cannot be
estimated, unless the law is first known according to which the magnetisms,
M C, M1 C C1, vary with the intensity of the current.
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