This is a Hydraulic Press in its simplest form. Practically it is requisite to have a reservoir from which more water can be obtained by a pump, and we therefore defer the description of a complete Hydrostatic Press until the principle of the Pump has been explained.

The Safety-Valve.

15. In many machines, and especially in steam engines, a very great fluid pressure may be produced, and the strength of the machine may be very severely tried: in order to guard against accidents arising from the bursting of the machine a safety-valve is employed, which serves to indicate the existence of too large a pressure.

Various forms may be used, but the principle of the safety-valve is simply that

of the uniform transmission of pressure in a fluid.

Thus if BC be one of the connecting tubes through which the fluid passes, and

B

A

ᏁᎳ

Da small tube opening out of BC, the pressure on a lid at the end of D will measure the fluid pressure within, and if the lid be of a suitable weight, it will be lifted when the pressure is greater than the machine is intended to bear. Suppose, for instance, the greatest permissible pressure of the fluid to be 500 lbs. on a square inch, and the sectional area of the tube D to beth of a square inch, then a weight of 500 or 31 lbs. will be lifted when the pressure exceeds 500 lbs. The weight employed may be diminished if the lid be moveable about a hinge at A, and a weight w be placed at some little distance from A.

Ex. The tube D is circular, its diameter is one-fourth of an inch, and a weight of 4 lbs. is attached to the lid at a distance of two inches from the hinge; it is required to determine the greatest fluid pressure which will not lift the lid.

The resultant fluid pressure will evidently act at the centre of the circle, and therefore at a distance of th of an inch from A: hence if p be the greatest pressure

Taking π=3, we obtain roughly p=1365 lbs.

Ex. 2. If the diameter be of an inch, and the distance AW 2 inches, find the weight which will indicate a pressure of 1000 lbs. on the square inch.

Answer. 5 lbs. approximately.

16. It will be seen that in Hydrostatic presses, as in all machines, the principle holds that what is gained in power is lost in motion.

Thus, if there be two apertures in a closed vessel, fig. art. 5, and the piston B be forced down through any given space, the piston A is forced upwards, if the fluid be incompressible, through a space which is less as the area of A is greater.

This is a simple case of the principle of virtual velocities which we proceed to demonstrate, as applied to incompressible fluids.

Let A, B, C,... be the areas of a number of pistons working in cylindrical pipes fitted into the sides of a closed vessel which is filled with fluid. Let the pistons be moved in any manner so that the fluid remains in contact with them, and a, b, c,..... be the spaces through which they are moved, these quantities being positive or negative, as the pistons are pushed inwards or forced outwards.

Then, since the volume of fluid is the same as before, it follows that

Aa+Bb+Cc+...=0,

the positive portions, that is, the volumes forced in, being balanced by the negative portions, or the volumes forced out.

But if P, Q, R,... be the forces on each piston,

PQR ...=.
=A: B: C:...

:. Pa+Qb+ Rc + ... = 0;

or the sum of the products of each force into the space through which its point of application is moved is equal to

zero.

Observing that a, b, c,... are proportional to the virtual velocities of the pistons, this is the equation of virtual velocities.

17. It is not to be imagined that there exists any substance in nature exactly fulfilling the definition which has been given of a fluid. Just as the ideas of a perfectly smooth surface and a perfectly rigid body are formed from observations of bodies of different degrees of rigidity, and surfaces of different degrees of smoothness, so the idea of perfect fluidity is suggested. Nevertheless in the cases of fluids at rest the theoretical properties of fluids derived from this definition will be found to agree with facts, and it is in cases of fluid motion that sensible discrepancies will be found. Thus, a cup of tea set rotating will gradually come to rest, proving the existence of a friction between the liquid and the tea-cup, and also between the particles of the liquid, since the dragging force is gradually communicated from the outer to the inner portions. The motion of water in inclined tubes also indicates the existence of a frictional action amongst the particles of water.

18. It should be observed that the proofs which have been given of the equality in all directions of the pressure at any point, and of the transmission of pressure, apply to gases as well as to incompressible fluids. When, however, an additional pressure is applied to a gaseous fluid, the immediate effect will be a compression of the fluid, and after the equilibrium is established, the additional pressure will have been communicated to every portion of the fluid.

1.

EXAMINATION UPON CHAPTER I.

DISTINGUISH between elastic and inelastic fluids. Are any liquids absolutely inelastic?

2. State the property which is assumed as the basis of all reasonings upon fluid action.

3. Define the measure of fluid pressure.

4. It is found that the pressure is uniform over the whole of a square yard of a plane area in contact with fluid, and that the pressure on the area is 13608 lbs.; find the measure of the pressure at any point, 1st, when the unit of length is an inch, 2nd, when it is two inches.

5. The plane of a rectangle, in contact with fluid, is vertical, two of its sides are horizontal, and it is known that at all points of the same horizontal line the pressure is the same. The pressure on the rectangle, for all values of h, is wbh (a+h) where b is the width and h the height of the rectangle; find the pressure at any point of the upper side. (Art. 4.)

6. A cylindrical pipe which is filled with water opens into another pipe the diameter of which is three times its own diameter: if a force of 20 lbs. be applied to the water in the smaller pipe, find the force on the open end of the larger pipe, which is necessary to keep the water at rest.

7. Account for the fact of the transmission of pressure through a liquid.

Mention any direct practical application of this principle.

8. In a Hydrostatic Bellows (Art. 12), the tube A is 4th of an inch in diameter, and the area B is a circle, the diameter of which is a yard. Find the weight which can be supported by a pressure of 1 lb. on the water in A.

9. A safety-valve consists of a heavy rectangular lid which is horizontal when it closes the aperture beneath it, and is moveable about one side. The aperture being a square which has one side coincident with the fixed side of the lid, find the maximum pressure marked by the valve.

10. Prove the principle of virtual velocities in the case of the sixth question.

11. A triangular area ABC is exposed to fluid pressure, and it is found that if any straight line PQ be drawn parallel to BC, and at a distance x from A, the pressure on the area APQ is px2; find the pressure at A, and also at any point of the line BC.

12. A strong cylindrical tube, one foot in diameter inside, and ten feet in length, is filled with distilled water, and closed with a piston to which a pressure of 10000 lbs. is applied; shew that the resulting compression of the water will be nearly 7th of an inch,

CHAPTER II.

Density and Specific Gravity.

19. IN the classification of fluids the most prominent

division is between gases and liquids, or elastic

and non-elastic fluids, as they are sometimes termed, and under these two heads all fluids are naturally ranged. It has been remarked already that the term non-elastic is inaccurate, but no confusion will be produced by its use, as the compressibility of liquids is practically insensible, and for all ordinary purposes unimportant.

It will be found, however, that the theory of sound is partly dependent on this compressibility, and it is therefore of importance at once to recognize its existence.

There are many other characteristics which distinguish fluids from each other, such as colour, degree of transparency, chemical qualities, viscosity, &c., but in the theory of Hydrostatics and Hydrodynamics the only characteristic which it is necessary to consider is the density or specific gravity of a fluid.

It is not meant that density and specific gravity are synonymous terms, but that these terms have reference to the substance of a fluid.

Thus, a cubic inch of mercury and a cubic inch of water have different weights, the former being more than 13 times the latter, and it is inferred that the quantity of matter in the mercury is greater than in the water, or that the density of mercury is greater than that of water.

These remarks apply to both fluid and solid bodies, and the density and specific gravity of a fluid or solid must be measured respectively by reference to the density and specific gravity of some standard substance.

B. E. H.

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