Index
| PREFACE TO THE REVISED AND ENLARGED EDITION 1871 INTRODUCTION DIVISIONS OF THE SUBJECT OF MATTER AND ITS PROPERTIES OF GRAVITY MECHANICS, on THE LAWS OF MOTION THE MECHANICAL POWERS REGULATORS OF MOTION HYDROSTATICS HYDRAULICS PNEUMATICS ACOUSTICS |
PYRONOMICS THE STEAM-ENGINE OPTICS ELECTRICITY GALVANISM, OR VOLTAIC ELECTRICITY MAGNETISM ELECTRO MAGNETISM THE ELECTROMAGNETIC TELEGRAPH THE ELECTROTYPE PROCESS MAGNETO-ELECTRICITY THERMO-ELECTRICITY ASTRONOMY |
HYDROSTATICS
Of what does Hydrostatics treat?
- HYDROSTATICS.* Hydrostatics treats of the nature, gravity and pressure of fluids.
* The subjects of Hydraulics and Hydrostatics are sometimes described under the general name of Hydrodynamics. The three terms are from the Greek language, compounded of ὕδωρ (hýdor), signifying water, and δύναμις (dýnamis),force or power; asatzrxo~ (staticos), standing, and uveoc (aulos), a tube or pipe. Hence Hydrodynamics would imply, the science which treats of the properties and relations of water and other fluids, whether in a state of motion or rest; while the term IHydrostatics would be confined to the consideration of fluids in a state of rest, and Hydraulics to fluids in motion through tubes or channels, natural or artificial.
What is the difference between Hydraulics and Hydrostatics?
- Hydrostatics is generally confined to the consideration of fluids at rest, and Hydraulics to fluids in motion.
What is a Fluid?
- A Fluid is a substance which yields to the slightest pressure, and the particles of which, having but a slight degree of cohesion, move easily among themselves. **
** There is this remarkable difference between bodies in a fluid and bodies in a solid form, namely, that every particle of a fluid is perfectly independent of every other particle. They do not cohere in masses, like the particles of a solid, nor do they repel one another, as is the case with the particles composing a gas. They can move among one another with the least degree oy friction, and, when they press down upon one another in virtue of their own weight, the downward pressure is communicated in all directions, causing a pressure upwards, sideways, and in every possible manner. Herein the particles of a fluid differ from the particles of a solid, even when reduced to the most impalpable powder; and this it is which constitutes fluidity, namely, the power of transmitting pressure in every direction, and that, too, with the least degree of friction. The particles which compose a fluid must be very much smaller than the finest grain of an impalpable powder.
Page 109
How does a liquid differ from a (gas or a) fluid?
- A liquid differs from a fluid in its degree of compressibility and elasticity. Fluids are highly compressible and elastic. Liquids, on the contrary, have but a slight degree either of compressibility or of elasticity.*
* The celebrated experiment made at Florence, many years ago, to test the compressibility of water, led to the conclusion that water is wholly incompressible. Later experiments have proved that it may be compressed, and that it also has a slight degree of elasticity. In a voyage to the West Indies, in the year 1839, an experiment was made, at the suggestion of the author, with a bottle filled with fresh water from the tanks on the deck of the Sea Eagle. It was hermetically sealed, and let down to the depth of about seven hundred feet. On drawing it up, the bottle was still full, but the water was brackish, proving that the pressure at that great depth had forced a portion of the deep salt water into the bottle, previously compressing the water in the bottle to make room for it. As it rose to the surface, its elasticity restored it to its normal state of density.
At great depths in the sea the pressure of the superincumbent mass increases the density by compression, and it has been calculated that, at a depth of about ninety miles, water would be compressed into one-half of its volume, and at a depth of 360 miles its density would be nearly equal to that of mercury. Under a pressure of 15,000 lbs. to a square inch, Mr Perkins, of Newburyport, subsequently of London, has shown that water is reduced in bulk one part in twenty-four.
- Another difference between a liquid and a fluid arises from the propensity which fluids have to expand whenever all external pressure is removed. Thus, whenever a portion of air or gas is removed from a closed vessel, the remaining portion will expand, and, in a rarer state, will fill the whole vessel. Liquids, on the contrary, will not expand without a change of temperature. Liquids, also, have a slight degree of cohesion, in virtue of which the particles will form themselves into drops; but the particles of fluids seem to possess the opposite quality of repulsion, which causes them to expand without limit, unless confined within the bounds of some vessel, or restricted within a certain bulk by external pressure.
- The fluid form of bodies seems to be in great measure, if not wholly, attributed to heat. This subtle agent insinuates itself between the particles of bodies, and forces them asunder. Thus,,for instance, water divested of its heat becomes ice, which is a solid. In the form of water it is a liquid, having but in a very slight. degree the properties either of compressibility or elasticity. An additional supply of heat converts it into steam, endowed with a very great degree both of elasticity and compressibility. But, so soon as steam loses its heat, it is again converted into water. Again, the metals become liquid when raised to certain temperatures, and it is known that many, and supposed that all, of them would be volatilized if the required supply of heat were applied.
Page 110
The science of Geology furnishes sufficient reasons for believing that all known substances were once not only in the liquid form, but also previously existed in the form of gas.*
* The science of Chemistry unfolds the fact that all the great changes in the constitution of bodies are accompanied by the exhibition of heat either in a free or latent condition.
How do fluids gravitate?
- GRAVITATION OF FLUIDS. Fluids gravitate in a more perfect manner than solids, on account of their want of cohesive attraction. The particles of a solid body cohere so strongly that, when the centre of gravity is supported, the whole mass will be supported. But every particle of a fluid gravitates independently of every other particle.
Why cannot fluids be moulded into figures?
- On account of the independent gravitation and want of cohesion of the particles of a fluid, they cannot be formed into figures, nor preserved in heaps. Every particle makes an effort to descend, and to preserve what is called the level. or equilibrium.
What is the equilibrium of fluids?
- The level or equilibrium of fluids is the tendency of the particles so to arrange themselves that every part of the surface shall be equally distant from the centre of the earth; that is, from the point towards which gravity tends.
What is the form of the surface of all fluids?
- Hence the surface of all fluids, when in a state of rest, partakes the spherical form of the earth.
- For the same reason, a fluid immediately conforms itself to the shape of the vessel in which it is contained. The particles of a solid body being united by cohesive attraction, if any one of them be supported it will uphold those also with which it is united.
But, when any particles of a fluid is unsupported, it is attracted down to the level of the surface of the fluid; and the readiness with which fluids yield to the slightest pressure will enable the particle, by its own weight, to penetrate the surface of the fluid, and mix with it.
Page 111
What is Capillary Attraction? What are capillary Tubes?
- CAPILLARY ATTRACTION.- Capillary Attraction is that attraction which causes fluids to ascend above their level in capillary tubes. Capillary * tubes are tubes with very fine bore.
* The word capillary is derived from the Latin word capilla (hair), and it is applied to this kind of attraction because it is exhibited most prominently in tubes the bores of which are as fine as a hair, and hence called capillary tubes.
- This kind of attraction exhibits itself not only in tubes. but also between surfaces which are very near together. This may be beautifully illustrated by the following experiment. Take two pieces of flat glass, and, having previously wet them, separate their edges on one side by a thin strip of wood, card or other material tie them together, and partly immerse them perpendicularly in colored water. The water will then rise the highest on that side where the edges of the glass meet, forming a beautiful curve downwards towards the edges which are separated by the card.
- Immerse a number of tubes with fine bores in a glass of colored water, and the water will rise above its equilibrium in all, but highest in the tube with the finest bore.
- The. cause of this seems to be nothing more than the ordinary attraction of the particles of matter for each other. The sides of a small orifice are so near to each other as to attract the particles of the fluid on their opposite sides, and, as all attraction is strongest in the direction of the greatest quantity of matter, the water is raised upwards, or in the direction of the length of the tube. On the outside of the tube, the opposite surfaces cannot act on the same column of water, and, therefore, the influence of attraction is here imperceptible in raising the fluid.
- All porous substances, such as sponge, bread, linen, sugar, &c., may be considered as collections of capillary tubes; and, for this reason, water and other liquids will rise in: them when they are partly immersed.
- It is on the same principle that the wick of a lamp will carry up the oil to supply the flume, although the flame is several inches above the level of the oil. **
** The reason why well-filled lamps will sometimes fail to give light is, that the wick is too large for its tube, and, being thus compressed, the capillary attraction is impeded by the compression. The remedy is to reduce the size of the wick. Another cause, also, that prevents a clear light, is that the flame is too far from the surface of the oil. As capillary attraction acts only at short distances, the surface of the oil should always be within a short distance of the flame. But another reason, which requires particular attention, is, that all kinds of oil usually employed for lamps contain a glutinous matter, of which no treatment can wholly divest them. This matter fills the pores or capillary tubes of the wicks and prevents the ascent of the oil to feed the flame. For this reason, the wicks of lamps should be often renewed. A wick that has been long standing in a lamp will rarely afford a clear and bright light. Another thing to be noticed by those who wish the lamp to perform its duty in the best possible manner is, that the wick be n-ot of such size as, by its length, as well as its thickness, to fill the cup, and thereby leave no room for the oil. It must also be remembered that, although the wick when first adjusted may be of the proper size, the glutinous matter of the oil, filling its capillary tubes, causes the wick to swell, and thereby become too large for the tube, producing the same difficulty as has already been noticed in cases where the wick is too large to allow the free operation of capillary attraction.
Page 112
If the end of a towel happen to be left in a basin of water, it will empty the basin of its contents
On the same principle, when a dry wedge of wood is driven into the crevice of a rock, as the rain falls upon it, it will absorb the water, swell, and sometimes split the rock. In this manner millstone quarries are worked in Germany.
- ENDOSMOSE AND EXOSMOSE. In addition to the capillary attraction just noticed as peculiar to fluids, another may be mentioned, as yet but imperfectly understood, which seems to be due partly to capillary and partly to chemical attraction, known under the names endosmose and exosmose. *
* Endosmose, from endos, within, and monos, impulsion. Exosmose, from ex outward, and monos, impulsion.
These phenomena are manifested in the transmission of thin fluids, vapor and gaseous matter, through membranes and porous substances. The ascent of the sap in vegetable, and the absorption of nutritive matter by the organs of animal life, are to be ascribed to these causes.
- When two liquids of different densities are separated by a membranous substance or by porcelain unglazed, endosmose will carry a current inwards, and exosmose will force one outwards, thus causing a partial mixture of the fluids.
- Experiment. Take a glass tube, and, tying a piece of bladder or clean leather over one end for a bottom, put some sugar into it, and having poured a little water on the sugar, let it stand a few hours in a tumbler of water. It will then be found that the water has risen in the tube through the membranous substance. This is due to endosmose. If allowed to stand several days, the liquid will rise several feet.
If the experiment be reversed, and pure water be put into the tube, and the moistened sugar into the tumbler, the tube will be emptied by exosmose.
- The liquid that has the less density will generally pass to the denser liquid and dilute it.
What peculiarity is there in the gravitation of fluids of different densities?
- GRAVITATION OF FLUIDS OF DIFFERENT DENSITIES. When solid bodies are placed one above another, they will remain in the position in which they are placed so long as their respective centres of gravity are supported, without regard to their specific gravity. With fluids the case is different.
Page 113
Fluids of different specific gravity will arrange themselves in the order of their density, each preserving its own equilibrium.
- Thus, if a quantity of mercury, water, oil and air, be put into the same vessel, they will arrange themselves in the order of their specific gravity. The mercury will sink to the bottom, the water will stand above the mercury, the oil above the water, and the air above the oil; and the surface of each fi;id will partake of the spherical form of the earth, to which they. all respectively gravitate.
What is a Spirit Level, or a Water Level?
- A Water or Spirit Level is an instrument constructed on the principle of the equilibrium of fluids. It consists of a glass tube, partly filled with water, and closed at both ends. When the tube is not perfectly horizontal, that is, if one end of the tube be lower than the other, the water will run to the lower end. By this means the level of any line to which the instrument is applied may be ascertained.
Fig 61
- Fig. 61 represents a Water Level. A B is a glass tube partly filled with water. C is a bubble of air occupying the space not filled by the water. When both ends of the tube are on a level, the air-bubble will remain in the centre of the tube; but, if either end of the tube be depressed, the water will descend and the air-bubble will rise. The glass tube, when used, is generally set in a wooden or a brass box. It is an instrument much used by carpenter, masons, surveyors, &c.
[N. B. The tube is generally filled with spirit, instead of water, on account of the danger that the water will freeze and burst the glass. Hence the instrument is called indifferently the Spirit Level or the Water Level.]
Why fluids do less damage than falling solids?
- EFFECT OF THE PECULIAR GRAVITATION OF FLUIDS. Solid bodies gravitate in masses, their parts being so connected as to form a whole, and their weight may be regarded as concentrated in a point, called the centre of gravity; while each particle of a fluid may be considered as a separate mass, gravitating independently.
Page 114
It is for this reason that a body of water, in falling, does less injury than a solid body of the same weight. But, if the water be converted into ice, the particles losing their fluid form, and being united by cohesive attraction, gravitate unitedly in one mass.
In what direction do fluids press, on account of their weight?
- PRESSURE OF FLUIDS. Fluids not only press downwards like solids, but also upwards, sidewise,* and in every direction.
Fig. 62 and 63
Fig. 62. * If the particles of fluids were arranged in Fig. 63. regular columns, as in Fig. 62, there would be no lateral pressure; for when one particle is perpendicularly above the other, it can press only downwards. But, if the particles be arranged as in Fig. 63, where a particle presses between two particles beneath, these last must suffer a lateral pressure. In whatever manner the particles are arranged, if they be globular, as is supposed, there must be spaces between them, [See Fig. 1, page 22.]
- So long as the equality of pressure is undisturbed, every particle will remain at rest. If the fluid be disturbed by agitating it, the equality of‘ pressure will be disturbed, and the fluid will not rest until the equilibrium is restored.
How are the downward, lateral and upward pressure of fluids shown?
- The downward pressure of fluids is shown by making an aperture in the bottom of a vessel of water. Every particle of the fluid above the aperture will run downwards through the opening.
- The lateral pressure is shown by making the aperture at the side of the vessel. The fluid will then escape through the aperture at the side.
- The upward pressure is shown by taking a glass tube, open at both ends, inserting a cork in one end (or stopping it with the finger), and immersing the other in the water. The water will not rise in the tube. But the moment the cork is taken out (or the finger removed), the fluid will rise in the tube to a level with the surrounding water.
Page 115
What is the law of fluid pressure?
- The pressure of a fluid is in proportion to the perpendicular distance from the surface; that is, the deeper the fluid, the greater will be the pressure. This pressure is exerted in every direction, so that all the parts at the same depth press each other with equal force.
- A bladder, filled with air, being immersed in water, will be contracted in size, on account of the pressure of the water in all directions; and the deeper it is immersed, the more will it be contracted.*
* The weight of a cubic inch of water at the temperature of 620 of Fahrenheit’s thermometer is 36066 millionths of a pound avoirdupois. The pressure of a column of water of the height of one foot will therefore be twelve times this quantity, or.4328 (making allowance for the repeating decimal), and the pressure upon a square foot by a column one foot high will be found by multiplying this last quantity by 144, the number of square inches in a square foot, and is therefore 62.3332.
Hence, at the depth of lbs. lbs.
1 foot the pressure on a square inch is 4328 on a square foot 62.3232
2 feet …………….. 8656 “ “ “ “ 124.6464
3 „…………… 1.2984 “ “ “ “ 186.9696
4 „………….;. 1.7312 “ “ “ “ 249.2928
5 „…………… 2.1640 “ “ “ “ 311.6100
6’……………. 2.5968 “ “ “ “ 373.9392
7 „…….. 3.0296 “ “ “ “ 436.2624
8 „………… 3.4624 “ “ “ “ 498.5856
9 „…………… 3.8952 “ “ “ “ 560.9088
10 „……. 4.3280 “ “ “ “ 623.2320
100 „…………. 43.2800 “ “ “ “ 6232.3200
From this table, the pressure on any surface at any depth may easily be found.
It will thus be seen that there is a certain limit beyond which divers cannot plunge with impunity, nor fishes of any kind live. Wood that has been sunk to great depths in the sea will have its pores so filled with water, and its specific gravity so increased, that it will no longer float.
- An empty bottle, being corked, and, by means of a weight, let down to a certain depth in the sea, will either be broken by the pressure, or the cork will be driven into it, and the bottle be filled with water. This will take place even if the cork be secured with wire and sealed. But a bottle filled with water, or any other liquid, may be let down to any depth without damage, because, in this case, the internal pressure is equal to the external. **
** Experiments at Sea. — We are indebted to a friend, who has just arrived from Europe, says; the Baltimore Gazette, for the following experiments made on board the Charlemagne: 26th of September, 1836, the weather being calm, I corked an empty wine-bottle, and tied a piece of linen over the cork; I then sank it into the sea six hundred feet; when drawn immediately up again, the cork was inside, the linen remained as it was placed, and the bottle was filled with water.‘ I next made a noose of strong twine around the bottom of the cork, which I forced into the empty bottle, lashed the twine securely to the neck of the bottle, and sank the bottle six hundred feet. Upon drawing it up immediately, the cork was found inside, having forced its way by the twine, and in so doing had broken itself in two pieces; the bottle was filled with water.
„I then made a stopper of white pine, long enough to reach to the bottom of the bottle; after forcing this stopper into the bottle, I cut it off about half an inch above the top of the bottle, and drove two wedges, of the same wood, into the stopper. I sank it six hundred feet, and upon drawing it up immediately the stopper remained as I placed it, and there was about a gill of water in the bottle, which remained unbroken. The water must have forced its way through the pores of the wooden stopper, although wedged as aforesaid; and had the bottle remained sunk long enough, there is no doubt that it would have been filled with water.“ [See also note on page 109.]
It is the opinion of some philosophers that the pressure at very great depths of the sea is so great that the water is condensed into a solid state; %nd that at or near the centre of the earth, if the fluid could extend so deeply, this pressure would convert the whole into a solid mass of fire.
Page 116
- Questions for Solution.
(1.) What pressure is sustained by the body of a fish having a surface of 9 square feet at the depth of 150 feet. Ans. 84186.82 lb.
(2.) What is the pressure on a square yard of the banks of a canal, at the depth of four feet Ans. 2243.6852 lb.
(3.) What pressure is exerted on the body of a man, at the depth of 30 feet, supposing the surface of his body to be 21 sq. yd.? Ans. 42068.16 lb.
(4.) Suppose a whale to be at the depth of 200 feet, and that his body presents a surface of 150 yards. What is the pressure? Ans. 1682T264 lb.
(5.) How deep may a glass vessel containing 18 inches of square surface be sunk without being broken, supposing it capable of resisting an equal pressure of 1500 lbs. Ans. 192.54ft. +
(6.) What is the pressure sustained on the sides of a cubical water-tight box at the depth of 150 feet below the surface, supposing the box to rest on the bed of the sea, and each side to be 8 feet square? Ans. 299151.36 lb.
(7.) How deep can a glass vessel be sunk without breaking, supposing that it be capable of resisting a pressure of 200 pounds on a square inch! Ans. 462.1ft, +
- The lateral pressure of a fluid proceeds What causes the entirely from the pressure downwards, or, in lateral pressure of fluids? other words, from the weight of the liquid above; consequently, the lower an orifice is made in a vessel containing water or any other liquid, the greater will be the force and velocity with which the liquid will rush out.
Page 117
Fig. 64.
Explain Fig. 64
439 Fig. 64 represents a vessel of water, with orifices at the side at different distances from the surface. The different curves in the figure, described by the liquid in running out of the vessel, show the action of gravity, and the effects produced by the force of the pressure on the liquid at different depths. At A the pressure is the least, because there is less weight of fluid above. At B and C the fluid is driven outwards by the weight of that portion above, and the force will be strongest at C.
What effect has the length and the width of a body of fluid upon its lateral pressure?
- As the lateral pressure arises solely from the downward pressure, it is not affected by the width nor the length of the vessel in which it is contained, but merely by its depth; for, as every particle acts independently of the rest, it is only the column of particles above the orifice that can weigh upon and press out the water.
To what is the lateral pressure equal?
- The lateral pressure on one side of a cubical vessel will be equal only to half of the pressure downwards; for every particle at the bottom of a vessel is pressed upon by a column of the whole depth of the fluid, while the lateral pressure diminishes from the bottom upwards to the surface, where the particles have no pressure.
What causes the upward pressure of a fluid?
- The upward pressure of fluids, although apparently in opposition to the principles of gravity, is but a necessary consequence of the operation of that principle; or, in other words, the pressure upwards, as well as the pressure downwards, is caused by gravity.
Explain Fig. 65.
- When water is poured into a vessel with a spout (like a tea-pot, for instance), the water rises in the spout to a level with that in the body of the vessel. The particles of water at the bottom of the vessel are pressed upon by the particles above them, and to this pressure they will yield, if there is any mode of making way for the particles above them.
Page 118
As they cannot descend through the bottom of the vessel, they will change their direction and rise in the spout. Fig. 65 represents a tea-pot, and the columns of balls represent the particles of water magnified. From an inspection of the figure, it appears that the particle numbered 1, at the bottom, will be pressed laterally by the particle numbered 2, and by this pressure forced into the spout, where, meeting with the particle 3, it presses it upwards, and this pressure will be continued from 3 to 4, from 4 to 5, and so on, till the water in the spout has risen to a level with that in the body of the vessel. (Repeat the law of pressure) If water be poured into the spout, the water will rise in the same manner in the body of the vessel, from which it appears that the force of pressure depends entirely on the height, and not on the of fluid pressure. length or breadth, of the column of fluid. [See No. 434.]
What is the Hydrostatic Paradox?
- Any quantity of fluid, however small, may be made to balance any other quantity, however large. This is what is called the Hydrostatic Paradox. *
* A paradox is something which is seemingly absurd, but true in fact. But in what is called the Hydrostatic Paradox there is in reality no paradox at all. It is true that a small quantity of fluid will balance any quantity, however large,‘ but it is on the same principle as that with which the longer arm of the lever acts. In order to raise the larger quantity of fluid, the smaller quantity must be elevated to a height in proportion as the bulk of the larger quantity exceeds the smaller. Thus, to raise 500 lbs. of water by the descending force of one pound, the latter must descend 500 inches while the former is rising one inch; and hence, what is called the hydrostatic paradox is in strict conformity with the fundamental principle of Meehanics, that what‘ is gained in power is lost in time, or in space.
Explain Fig. 66.
- The principle of what is called the hydrostatic paradox is illustrated by the hydrostatic bellows represented in Fig. 66. A B is a long tube, one-inch square. C D E F are the bellows, consisting of two boards-, eight inches square, connected by broad pieces of leather, or india-rubber cloth, in the manner of a pair of common bellows.
Page 119
Fig. 66.
One pound of water poured into the tube will raise sixty-four pounds on the bellows. If a smaller tube be used, the same quantity of water will fill it higher, and, consequently, will raise a greater weight; but, if a larger tube be used, it will, of course, not fill it so high, and, consequently, will not raise so great a weight, because it is the height, not the quantity, which causes the pressure.
The hydrostatic bellows may be constructed in a variety of forms, the simplest of which consists, as in the figure, of two boards connected together by broad pieces of leather, or india-rubber cloth, in such a manner as to allow the upper board to rise and fall like the common bellows. A perpendicular tube is adjusted to this apparatus that water poured into the tube, passing between the boards, will separate them by its upward pressure, even although the upper board is loaded with a considerable weight.
[N. B. A small quantity of water must be poured into the bellows to separate the surfaces before they are loaded with the weight.]
How is the force of pressure on the hydrostatic bellows estimated?
- The force of pressure exerted on the bellows by the water poured into the tube is estimated by the comparative size of the tube and the bellows. Thus, if the tube be one inch square, and the top of the bellows twelve inches, thus containing 144 square inches, a pound of water poured into the tube will exert a pressure of 144 pounds on the bellows. Now, it will be clearly perceived that this pressure is caused by the height of the column of water in the tube. A pound, or a pint of water will fill the tube 144 times as high as the same quantity would fill the bellows. To raise a weight of 144 pounds on the bellows to the height of one inch, it will be necessary to pour into the tube as much water as would fill the tube were it 144 inches long.
What fundamental law of Mechanics applies also hydrostatic pressure?
It will thus be perceived that the fundamental principle of the laws of motion is
Page 120
there also in full force, namely, that what is to gained in power is lost either in time or in space; for, while the water in the bellows is rising to the height of one inch, that in the tube passes over 144 inches.
Explain Fig. 67.
- Another form of apparatus, by means of which it can be proved that fluids press in proportion to their perpendicular height, and not their quantity, is seen in Fig. 67. This apparatus unites simplicity with convenience. Instead of two boards, connected with leather, an india-rubber bag is placed between two boards, connected by crossed bars with a board below, loaded with weights, and the upper boards are made to rise or fall as the water runs into or out of the bag. It is an apparatus easily repaired, and the bag may also be used for gas, or for experiments in Pneumatics.
A and B are two vessels of unequal size, but of the same length. These may successively be screwed to the apparatus, and filled with water. Weights may then be added to the suspended scale until the pressure is counterbalanced. It will then be perceived that, although A is ten times larger than B, the water will stand at the same height in both, because they are of the same length. If C be used instead of A or B, the apparatus may be used as the hydrostatic bellows.*
* If a cask be filled with water, and a long pipe be fitted to it, by pouring water into the pipe it will exert so great a pressure as to burst the cask. In the same manner a mountain would be rent asunder by hydrostatic pressure, if a deep crevice, communicating with a small fountain below, be filled with water by the rain.
Page 121
In what manner may hydrostatic pressure be employed as a Mechanical Power
- HYDROSTATIC PRESSURE USED AS A MECHANICAL POWER. If water be confined in any vessel, and a pressure to any amount be exerted on a square inch of that water, a pressure to an equal amount will be transmitted to every square inch of the surface of the vessel in which the water is confined.
- This property of fluids seems to invest us with a power of increasing the intensity of a pressure exerted by a comparatively small force, without any other limit than that of the strength of the materials of which the engine itself is constructed. it also enables us with great facility to transmit the motion and force of one machine to another, in cases where local circumstances preclude the possibility of instituting any ordinary mechanical connexion between the two machines. Thus, merely by means of water-pipes, the force of a machine may be transmitted to any distance, and over inequalities of ground, or through any other obstructions.
On what principle is Bramah’s hydrostatic press constructed? Explain Fig.68
Fig. 68.
- It is on the principle of hydrostatic pressure that Bramah’s hydrostatic press, represented in Fig. 68, is constructed. The main features of this apparatus are as follows: a is a narrow, and A a large metallic cylinder, having communication one with the other. Water stands in both the cylinders. The piston S carries a strong head P, which works in a frame opposite to a similar plate R. Between the two plates the substance W to be compressed is placed.
Page 122
In the narrow tube, a is a piston p, worked by a lever c b d its short arm, c b driving the piston, while the power is applied at d. The pressure exerted by the small piston p on the water at a is transmitted with equal force throughout the entire mass of the fluid, while the surface at A presses up the piston S with a force proportioned to its area. For instance, if the cylinder a, of the force-pump has an area of half an inch, while the great cylinder has an area of 200 inches, then the pressure of the water in the latter on the piston S will be equal to 400 times that on p.
Next, suppose the arms of the lever to be to-each other as 1 to 50, and that at d, the extremity of the longer arm, a man works with a force of 50 pounds, the piston p will consequently descend on the water with a force of 2500 pounds. Deducting one-fourth for the loss of power caused by the different impediments to motion, and one man would still be able to exert a force of three-quarters of a million of pounds by means of this machine. This press is used in pressing paper, cloth, hay, gunpowder, &c.; also in uprooting trees, testing tiha strength of ropes, &c.
When will one fluid float on the surface of another fluid?
- A fluid specifically lighter than another fluid will float upon its surface.*
[N. B. This is but another way of stating the law mentioned in Nos. 409 and 410.]
- If an open bottle, filled with any fluid specifically lighter than water, be sunk in water, the lighter fluid will rise from the bottle, and its place will be, supplied with the heavier water.
When will a body rise, sink or float, in a fluid?
- Any substance whose specific gravity is greater than any fluid will sink to the bottom of that fluid, and a body of the same specific gravity with a fluid will neither rise nor fall in the fluid, but will remain in whatever portion of the fluid it is placed.
The slaves in the West Indies, it is said, steal rum by inserting the long neck of a bottle, full of water, through the top aperture of the rum cask. The water falls out of the bottle into the cask, while the lighten rum ascends in is stead.
Page 123
But a body whose specific gravity is less than that of a fluid will float. This is the reason why some bodies will sink and others float, and still others neither sink nor fioat.*
The bodies of birds that frequent the water, or that live in the water, are generally much lighter than the fluid in which they move. The feathers and down of water-fowl contribute much to their buoyancy, but fishes have the power of dilating and contracting their bodies by means of an internal air-vessel, which they can contract or expand at pleasure.
The reason that the bodies of persons who have been drowned first sink, and, after a number of days, will float, is, that when first drowned the air, being expelled from the lungs, makes the body specifically heavier than water, and it will of course sink; but, after decomposition has taken place, the gases generated within the body distend it, and render it lighter than water, and they will cause it to rise to the surface.
How deep will a body sink in a fluid?
- A body specifically lighter than a fluid will sink in the fluid until it has displaced a proportion of the fluid equal in weight to itself.
- If a piece of cork is placed in a vessel of water, about one third part of the cork will sink below, and the remainder will stand above, the surface of the water; thereby displacing a portion of water equal in bulk to about a third part of the cork, and this quantity of water is equal in weight to the whole of the cork, because the specific gravity of water is about three times as great as that of cork.
- It is on the same principle that boats, ships, &c., although composed of materials heavier than water, are made to float. From their peculiar shape, they are made to rest lightly on the water. The extent of the surface presented to the water counterbalances the weight of the materials, and the vessel sinks to such a depth as will cause it to displace a portion of water equal in weight to the whole weight of the vessel. From a knowledge of the specific gravity of water, and the materials of which a vessel is composed, rules have been formed by which to estimate the tonnage of vessels; that is to say, the weight which the vessel will sustain without sinking.
What is the standard of estimating the specific gravity of bodies?
- The standard which has been adopted to estimate the specific gravity of bodies is rain or distilled water,at the temperature of 60°. **
** As heat expands and cold condenses all metals, their specific gravity cannot be the same in summer that it is in winter. For this reason, they will not serve as a standard to estimate the specific gravity of other bodies The reason that distilled water is used is, that spring, well, or river water is seldom perfectly pure, and the various substances mixed with it affect its weight. The cause of the ascent of steam or vapor may be found in its specific gravity. It may here be stated that rain, snow and hail, are formed by the condensation of the particles of vapor in the upper regions of the atmosphere. Fine, watery particles, coming within the sphere of each other’s attraction, unite in the form of a drop, which, being heavier than the air, falls to the earth. Snow and hail differ from rain only in the different degrees of temperature at which the particles unite. When rain, snow, or hail falls, part of it reascends in the form of vapor and forms clouds, part is absorbed by the roots of vegetables, and part descends into the earth and forms springs. The springs form brooks, rivulets, rivers, &c., and descend to the ocean, where, being again heated by the sun, the water, rising in the form of vapor, again forms clouds, and again descends in rain, snow, hail, &c. The specific gravity of the watery particles which constitute vapor is less than that of the air near the surface of the earth; they will, therefore, ascend until they reach a portion of the atmosphere of the same specific gravity with themselves. But the constant accession of fresh vapor from the earth, and the loss of heat, cause several particles to come within the sphere of each other’s attraction, as has been stated above, and they unite in the form of a drop, the specific gravity of which being greater than that of the atmosphere, it will fall in the form of rain. Water, as it descends in rain, snow or hail, is perfectly pure; but, when it has fallen to the earth, it mixes with the various substances through which it passes, which gives it a species of flavor, without affecting its transparency.
Page 124
This is found to be a very convenient standard, because a cubic foot of water at that temperature weighs exactly one thousand ounces.
- Taking a certain quantity of rain or distilled water, we find that a quantity of gold, equal in bulk, will weigh nearly twenty times as much as the water; of lead, nearly twelve times as much; while oil, spirit, cork, &;c., will weigh less than water.*
* TABLE OF SPECIFIC GRAVITIES.
Temperature about 40° Fahrenheit
Distilled Water, 1. Palladium, 11.500
Mercury, 13.596 Iridium, 18.’650
Sulphuric Acid, 1.841 Copper, 8.850
Nitric Acid, 1.220 Lead, 11.250
Prussic Acid,. 696 Bismuth, 9.822
Alcohol (pure),. 792 Tellurium, 6.240
Ether,. 715 Antimony, 6.720
Spirits of Turpentine,. 869 Chromium, 5.900
Essence of Cinnamon, 1.010 Tungsten, 17.500
Sea Water, 1.026 Nickel, 8.270
Milk, 1.030 Cobalt, 7.810
Wine,. 993 Tin, 7.293
Olive Oil,. 915 Cadmium, 8 687
Naphtha,. 847 Zinc, 7.190
Iodine, 4.946 Steel, 7.820
Platinum, 22.050 Iron, 7.788
Gold, 19.360 Cast-iron, 7.200
Silver, 10.500 Manganese, 8.012
Rhodium, 11.000 Sodium, 972
Page 125
How is the specific gravity of a body ascertained when it is greater than that of water?
- The specific gravity of bodies that will sink in water is ascertained by weighing them first in water, and then out of the water, and dividing the weight out of the water by the loss of weight in water.
Potassium, .875 Elm, .800
Diamond, 3.530 Yew, .807
Arsenic, 5.670 Apple Tree, .733
Graphite, 2.500 Yellow Fir, .657
Phosphorus, 1.770 Cedar, .561
Sulphur, 2.086 Sassafras, .482
Lime, 3.150 Poplar, .383
Galena, 7.580 Cork Tree, .240.
Marble, 2.850 Flint Glass, 3.330
White Lead, 6.730 Pearls, 2.750
Plaster of Paris, 2.330 Coral, 2.680
Nitrate of Potash, 1.930 China-ware, 2.380
Emerald, 2.700 Porcelain Clay, 2.210
Garnet, 3.350 Flint, 2.600
Feldspar, 2.500 Granite, 2.700
Serpentine. 2.470 Slate, 2.825
Alum, 1.700 Alabaster, 2.700
Topaz, 3.500 Brass, 8.300
Bituminous Coal, 1.250 Ice, .865
Anthracite, 1.800 Common Air, .001
Pulverized Charcoal, 1.500 Hydrogen Gas, .000105
Woody Fibre, 1.500 Living Men, .891
Lignum Vits, 1.350 Brandy, .820
Boxwood, 1.320 Mahogany, 1.003
Beech, .852 Chalk, 1.733
Ash, .845 Carbonic Acid Gas, .001527
By means of this table the weight of any mass of matter can be ascertained, if we know its cubical contents. A cubic foot of water weighs exactly 1000 ounces. If we multiply this by the number annexed to any substance in this table, the product will be the weight of a cubic foot of that substance. Thus anthracite coal has a specific gravity of 1.800. A thousand ounces, multiplied by this sum, produces 1800 ounces, which is the weight of a cubic foot of anthracite coal.
The bulk of any given weight of a substance may also readily be ascertained by dividing that weight in ounces by the number of ounces there are in a cubic foot. The result will be the number of cubic feet. The cube root of the number of cubic feet will give the length, depth and breadth, of the inside of a square box that will contain it.
It is to be understood that all substances whose specific gravity is greater than water will sink when immersed in it, and that all whose specific gravity is less than that of water will float in it. Let us, then, take a quantity of water which will weigh exactly one pound; a quantity of the substances specified in the table, of the same bulk, will weigh as follows:
Platinum, 23. lbs. Silver, 11.091 lbs.
Fine Gold, 19.640 “ Copper, 9.000 “
Mercury, 14.019 “ Iron, 7.645 “
Lead, 11.525 “ Glass, 3.000 “
Marble, 2.705 lbs. Brandy, .820 lbs.
Chalk, 1.793 “ Living Men, .891 “
Coal,. 1.250 “ Ash, .800 “
Mahogany, 1.003 “ Beech, .700 “
Milk, 1.034 “ Elm, .600 “
Boxwood, 1.030 “ Fir, .500 “
Rain Water, 1.000 “ Cork, .240 “
Oil, .920 “ Common Air, .0011 “
Ice, .908 “ Hydrogen Gas, .000105 “
A cubic foot of water weighs one thousand avoirdupois ounces. By multiplying the number opposite to any substance in the above table by one thousand, we obtain the weight of a cubic foot of that substance in ounces. Thus, a cubic foot of platinum is 23,000 ounces in weight.
In the above table it appears that the specific gravity of living men is about one-ninth less than that of common water. So long, therefore, as the lungs can be kept free from water, a person, although unacquainted with. the art of swimming, will not completely sink, provided the hands and arms be kept under water.
The specific gravity of sea-water is greater than that of the water of lakes and rivers, on account of the salt contained in it. On this account, the water of lakes and rivers has less buoyancy, and it is more difficult to swim in it.
Page 126
Describe the scales used for finding the specific gravity of a body
- Fig. 69 represents the scales for ascertaining the specific gravity of bodies. One scale is shorter than the other, and a hook is attached to the bottom of the scale, to which substances whose specific gravity is sought may be attached and sunk in water.
- Suppose a cubic inch of gold weighs nineteen ounces-when weighed out of the water, and but eighteen ounces * when weighed in water, the loss in water is one ounce. The weight out of water, nineteen ounces, being divided by one (the loss in water), gives nineteen. The specific gravity of gold, then, would be nineteen or, in other words, gold is nineteen times heavier than water.
* The gold will weigh less in the water than out of it, on account of the upward pressure of the particles of water, which in some measure supports it, and, by so doing, diminishes its weight. Now, as the upward pressure of these particles is exactly sufficient to balance the downward pressure of a quantity of water of exactly the same dimensions with the gold, it follows that the gold will lose exactly as much of its weight in water as a quantity of water of the same dimensions with the gold will weigh. And this rule applies to all bodies, heavier than water, that are immersed in it. They will lose as much of their weight in water as a quantity of water of their own dimensions weighs. All bodies, therefore, of the same size, lose the same quantity of their weight in water. Hence, the specific gravity of a body is the weight of it compared with that of water. As a body loses a quantity of its weight when immersed in water, it follows that when the body is lifted from the water that portion of its weight which it had lost will be restored. This is the reason that a bucket of water, drawn from a well, is heavier when it rises above the surface of the water in the well than it is while it remains below the surface. For the same reason our limbs feel heavy in leaving a bath.
Page 127
How is the specific gravity of a body lighter than water?
- The specific gravity of a body that will not sink in water is ascertained by dividing its weight by the sum of its weight added to the found water loss of weight which it occasions in a heavy body previously balanced in water.*
* The method of ascertaining the specific gravities of bodies was discovered accidentally by Archimedes. He had been employed by the King of Syracuse to investigate the metals of a golden crown, which he suspected had been adulterated by the workmen. The philosopher labored at the problem in vain, till, going one day into the bath, he perceived that the water rose in the bath in proportion to the bulk of his body. He instantly perceived that any other substance of equal size would raise the water just as much, though one of equal weight and less bulk could not produce the same effect. lie then obtained two masses, one of gold and one of silver, each equal in weight to the crown, arid having filled a vessel very accurately with water, he first plunged the silver mass into it, and observed the quantity of water that flowed over; he then did the same with the gold, and found that a less quantity had passed over than before. Hence he inferred that, though of equal weight, the bulk of the silver was greater than that of the gold, and that the quantity of water displaced was, in each experiment, equal to the bulk of the metal. He next made trial with the crown, and found that it displaced more water than the gold, and less than the silver, which led him to conclude that it was neither pure gold nor pure silver.
- If a body lighter than water weights six ounces, and, on being attached to a heavy body, balanced in water, is found to occasion it to lose twelve ounces of its weight, its specific gravity is determined by dividing its weight (six ounces) by the sum of its weight added to the loss of weight it occasions in the heavy body; namely, 6 added to 12, which, in other words, is 6 divided by 18, or, 6/18 which is 1/3.
4G64. Questions for Solution.
(1.) A body lighter than water caused the loss of 10 lbs. to a heavier body immersed in water. In air the same body weighed 30 lbs. What was its specific gravity? Solution.- 30 lbs., its weight, divided by (30+10=) 40 (the sum of its weight added to the loss of weight which it caused in another body previously balanced in the water). Ans.75.
(2.) A body tha.t weighed 15 lbs. in air weighed but 12 in water. What was its specific gravity? Ans. 5.
(3.) If ta cubic foot of water weight 1000 ounces, what is the weight of an equal bulk of gold? Ans. 122 lb. 8 ozs.
(4.) The weight of an equal bulk of lead? Ans. 720 lb. 5 oz.
(5.) The weight of an equal bulk of cork? Ans. 15 lb.
Page 128
(6.) The weight of an equal bulk of iron? Ans. 486 lb. 12oz.
(7.) What is the weight of a cubic foot of mahogany? Ans. 66 lb. 7 oz.
(8.) The weight of a cubic foot of marble? Ans. 169 lb. 1 os.
(9.) What is the weight of an iceberg 6 miles long, 1 mile wide, and 400 feet thick 2 A1is. 949.259,520 tons.
(10.) What is the weight of a marble statue, supposing it to be exactly a yard and half of cubic measure 2 Ans. 6S47.C3 lb. +
(11.) If a cubical body of cork exactly 9 inches on each side be placed in water, how deep will it sink 2 Ans. 2.16 in.‘
(12.) Suppose that 4 boats were made each out of one of the following kinds of wood, namely, ash, beech, elm and fir, which would carry the greatest weight without sinking? Ans. That of fir.
What is an Hydrometer? and on what principle is it constructed?
- An Hydrometer is an instrument to ascertain the specific gravity of liquids.
- The Hydrometer is constructed on the principle that the greater the weight of a liquid the greater will be its buoyancy.
How is an Hydrometer constructed?
- The hydrometer is made in a variety of forms, but it generally consists of a hollow ball constructed of silver, glass, or other material, with a graduated scale rising from the upper part. A weight is attached below the ball. When the instrument thus constructed is immersed in a fluid, the specific gravity of the fluid is estimated by the portion of the scale that remains above the surface of the fluid. The greater the specific gravity of the fluid, the less will the scale sink.
Of what use is the hydrometer?
- The hydrometer is a very useful instrument for ascertaining the purity of many articles in common use. It sinks to a certain determinate depth in various fluids, and if the fluids be adulterated the hydrometer will expose the cheat. Thus, for instance, the specific gravity of sperm oil is less than that of whale oil, and of course has less buoyancy. If, therefore, the hydrometer does not sink to the proper mark of sperm oil, it will at once be seem that the article is not pure.