MECHANICAL PHILOSOPHY. HYDROSTATICS. 



[FLUID 



CHAPTER IV- 

 HYDROSTATICS. 



HYDROSTATICS U the icinoe which treats of fluid*, when 

 maintaining a state of rest or eqnilibrinin under the 

 action of mechanical forces or pressures. Fluids are dm- 

 tinguiahed from solid bodies by obvious and remarkable 

 peculiarities ; and, in consequence of these differences, 

 the statics and dynamic* of the latter become only 

 partially applicable to the former ; so that the statics of 

 waU-r, ami the dynamics of water, require a distinct 

 and separate consideration. These two divisions of the 

 general science of mechanics, thus applied exclusively to 

 water, and such-like fluids, are called respectively Hydro- 

 :ind Hydrwlynamies. 



To define a/uirf would be to describe exactly what it 

 k its internal constitution, as well as the phenomena 

 peculiar to that constitution, which it presents to our 

 senses. But this U beyond our power : we know that, 

 in common with all material existences connected with 

 this earth, it has weight ; but that, unlike solid bodies, 

 it is without that entire cohesion of parts by which a 

 solid preserves its shape in whatever position it be 

 placed, and in virtue of which it is moved, as a whole, 

 by a force applied only to a part. 



It is this comparative absence of cohesion from among 

 the constituent particles of a fluid, that renders those 

 particles so freely movable among themselves, that 

 causes them so readily to yield to any impression, and 

 to obey the slightest effort to separate and detach them, 

 as also to admit of the passage of solid bodies through 

 them. It is the want of cohesion, too, that causes a fluid 

 to change the figure it is made to assume, when sup- 

 ported in a vessel, as soon as any of that support is 

 removed. A fluid presses laterally as well as vertically ; 

 and, in consequence of the lateral pressure, tends to 

 spread itself horizontally when left unconstrained. 



In all these particulars it differs entirely from a solid 

 body : in ihi* all the particles mutually cohere, and, in 

 the absence of violence, maintain their relative positions. 

 In a fluid, on the contrary, they are entirely free to inter- 

 change situations, and to move among themselves. 



In this general statement of the characteristic differ- 

 ences between a solid and a fluid, it is to be borne in 

 mind that we refer only to fluids such as we find them on 

 this earth fluids acted upon by the force of gravitation, 

 and i i vine weight. If we conceive a vessel of 



water to be suspended in space, and gravity and every 

 other force to be removed, then the fluid having no 

 weight, there would be no pressure on the vessel in any 

 direction ; so that the water would preserve the shape of 

 the Teasel even though the latter were removed. In the 

 absence of all force, there would be nothing to disturb 

 the original arrangement of the component parts of the 

 fluid mass. 



T\\n KINDS OF FLUIDS. Fluids are divided 

 into compressible fluids and incompressible fluids : the 

 former are those which by pressure may be forced to 

 contract into smaller space such a fluid is the air we 

 breathe, and every kind of gas. The incompressible 

 fluids are those which cannot by pressure be reduced to 

 mailer balk. Whether, in strictness, any such fluid 

 actually exists, is more than we can say ; because, how- 

 ever it might resist compression from the mechanical 

 forces at our command, it would be presumptuous to 

 conclude that compression was impossible. This, there 

 it reason to believe, is not the case with any fluid : water 

 wm formerly thought to bo incompressible ; but, by great 

 mechanical force, it has in a slight degree been actually 

 reduced to onallor compass. Still this, and the other 

 common liquids, are so little compressible, that no prac- 

 tical error can arise from treating them as incompresHiblu 

 fluids.* 



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 " U gnat Arptai la Ik* ocean, aaderfot* trident com- 



They are also classed under the heads of Elastic Fluids 

 and Inelastic Fluids: the former are such as yield to com- 

 pression ; and upon the pressure being removed, expand 

 to their former bulk. Air and gases are elastic fluids. 

 Water, and liquids generally, are of course regarded as 

 inelastic, as they do not admit of compression (in this 

 sense) in any degree worth notice. 



FLUID ELASTICITY. The term elasticity, as 

 applied to fluids, is not precisely the same in meaning 

 as when applied to solids. A solid body is elastic when, 

 having yielded to the force of a blow, an equal force, 

 called the force of restitution, is exerted in the opposite 

 direction, restoring the body to its original figure : there 

 is no condition as to whether or not what is called the 

 force of compression, actually causes the body to contract 

 into smaller compass. But as regards fluids, elasticity 

 refers to their contraction by pressure into smaller bulk, 

 and their subsequent expansion to the original volume 

 when the pressure is withdrawn. It is in this sense that 

 the elasticity of fluids is to be understood. But taking 

 the term with the signification attached to it in the me- 

 chanics of solid bodies, fluids may certainly bo considered 

 as elastic : a quantity of water poured down from any 

 height on a hard substance, will to a certain extent re- 

 bound, and disperse itself in spray ; and so likewise will 

 it do if poured upon water itself. A flat stone, or an 

 oyster-shell, thrown very obliquely on the surface of a 

 pool of water will also rebound ; and even a cannon-ball 

 will do the same ; but in none of these instances is the 

 fluid compressed into smaller bulk. 



TRANSMISSION OF PRESSURE. The funda- 

 mental property of water and all other fluids is, that a 

 pressure applied to any part of their surface is transmitted 

 equally in all directions throughout the entire volume of 

 the fluid : this is called the principle of equal pressure, 

 and may be proved in various ways : for instance, if a 

 vessel be perforated all round at any depth, and glass 

 tubes, however bent, be inserted in the apertures, and 

 then water or any other liquid be poured into the vessel, 

 we find that when the level of the perforations is reached, 

 the water presses into the tubes ; and however high we 

 raise the level of the water in the vessel, to the same 

 level it always rises in each tube thus showing, that on 

 the same extent of surface at the some depth, there must 

 be the same pressure. 



Again : let a vessel of any shape be filled with water, 

 (Fig. 153), and to any two equal perforations in its sides, 

 let pistons A, B, be fitted ; let the proper amount of 

 pressure bo applied to the piston 

 A to keep the fluid in its 

 and also the proper amount of 

 ]>r. -iire to the piston B. Then it 

 will be found that any additional 

 pressure applied to one of the 

 pistons is transmitted t<> tin- 

 other; so that equal additional 

 pressures must be applied to 

 both j'i.stoiis to keep the fluid 

 in its place, or to prevent one 

 of the pinions from being forced outwards. 



And if the vessel were covered with sueh pistons, the 

 same pressure would be transmitted to each of the others 

 tluit is applied to any one of tli. 



This very remarkable property of fluid* is perfectly 

 general, having place whatever be the contour or external 

 form of the vessel : if, for instance, the form be that 

 in Fig. 154 namely, ABCEF, then the downward 

 pressure at B, arising from the weight of the wat.T n: 

 the tube A B, produces an equal upward pressure upon 

 MTV portion of surface, equal to the ha.se of the tube, 

 between B and C, and Wtw I F. Also the 



pressure of the fluid upon the base I>E of the \ 



Fig. 153. 



