HYDRAULICS. 



Introduction. 



As Hydrostatics is that branch of Na- 

 tural Philosophy which treats of the 

 weisfht, pressure, and equilibrium of 

 water, and all such fluids as are non- 

 elastic ; so Hydraulics has for its ob- 

 ject the investigation of the motions of 

 such fluids, the means by which such 

 motions are produced, the laws by 

 which they are regulated, and the force 

 or effect they exert against themselves, 

 or against solid bodies which may op- 

 pose them. To avoid repetition, when- 

 ever fluids are mentioned in this trea- 

 tise, they must always be understood to 

 l)e inelastic, a character which not only 

 belongs to water, but to oils, spirits, 

 and all the visible and tangible fluids, 

 to such an extent that, although they 

 may vary in then* bulk by change of 

 temperature, yet they yield in so slight 

 a degree to mechanical compression, as 

 to have obtained the character of being 

 non-elastic, notwithstanding which it 

 does not perfectly apply to them, as 

 will be found explained at the com- 

 mencement of the Treatise on Hydro- 

 statics. 



Fluids are characterized by a want 

 of cohesion among their parts : hence 

 they are incapable of assuming any 

 particular form without external sup- 

 port, but always accommodate them- 

 selves to the shape of the vessel which 

 contains them. This same cause in- 

 fluences the motions of fluids, and 

 produces trje difference that exists be- 

 tween their pressure and motion and that 

 of solids : for a solid, if it moves, must 

 move altogether, and can only produce 

 a pressure downwards, which will be 

 equivalent to its weight or gravitating 

 force ; but apart of a mass of fluid may 

 be in motion while other parts of the 

 same mass may be perfectly quiescent ; 

 and although a mass of fluid can in no 

 case produce a greater downward pres- 

 sure than is equivalent to its weight, 

 yet, at the same time, its want of cohe- 

 sion among its particles will permit it 

 to exert a lateral pressure, or tendency 

 to spread horizontally, which will be 

 exerted against the sides of the vessel 

 that contains it, without altering or 

 affecting its weight; and this constitutes 

 the chief difference between the motions 



of solids and fluids. The investigation 

 of this subject very naturally divides 

 itself into three distinct heads. 1 st, The 

 effects which take place in the natural 

 flowing of fluids through the various 

 ducts or channels which convey them. 

 2ndly, The artificial means of producing 

 motion in fluids, and destroying their 

 natural equilibrium by means of pumps 

 and various hydraulic engines and ma- 

 chines ; and 3rdly, the force and power 

 which may be derived from fluids in 

 motion, whether that motion be pro- 

 duced naturally or artificially : and these 

 several subjects will accordingly be 

 separately considered in the following 

 distinct chapters. 



CHAPTER I. 



On the Motion of Fluids through vari- 

 ous Channels, Pipes, and Orifices. 



WHATEVER may be the shape or con- 

 formation which the ultimate or original 

 particles of fluids possess, they are 

 found to flow over or amongst each 

 other with less friction and impediment 

 to motion than when they have to pass 

 over solid substances. And as each in- 

 dividual particle is under the influence 

 of gravitation, so it follows that no 

 quantity of homogeneous fluid can be 

 in a state of rest and perfect equili- 

 brium, unless every part of its surface 

 is on a level, by which we are not to 

 understand a level plane, but a surface 

 that is convex upwards to such an ex- 

 tent, that every one of its points may be 

 equidistant from the earth's centre, to 

 which fluids in common with all other 

 matter gravitate. This equally applies 

 to all masses of fluid, whether they are 

 contained in a cup, in the ocean, or in 

 any number of tubes or vessels which 

 communicate with each other; for in 

 this latter case the aggregate quantity of 

 fluid must be considered as one mass. 

 If, therefore, any one part of the sur- 

 face is made higher than another, that 

 high part may be conceived to be com- 

 posed of a pillar or column of particles, 

 and of course a greater number of par- 

 ticles will be necessary to constitute this 

 hitfh column than the shorter ones 

 which surround it: consequently, the 

 high column will gravitate with greater 



