HYDRODYNAMICS. 



iiected by a small rod, e, at each end, to the upper 

 beam, H, of the frame, and jointed in such a manner 

 as to admit of motion in a vertical direction. 



If a single drop of water, or any liquid of a 

 like degree of fluidity, be pressed upon a solid 

 surface, it will wet that surface, and adhere to it, 

 instead of keeping together and running oft". This 

 shows that parts of the liquid are more attracted by 

 the parts of the solids than by one another. In the 

 same manner, round the glass in which a liquid is 

 contained, its surface will be seen to be higher than 

 in the centre. If the vessel be less than the twentieth 

 part of an inch in diameter, the liquid will rise in it 

 the higher in proportion to the smallness of the 

 diameter. This is called capillary attraction, and 

 tubes of this kind are called capillary tubes. See 

 Capillary Tubes ; see also Pumps, Siphons, Springs. 



Hydraulics (from vSu^, water, and at/x?, a pipe, 

 referring to the movement of water in certain musi- 

 cal instruments used by the Greeks); that branch of 

 hydrodynamics which has for its object the investiga- 

 tion of the motions of liquids, the means by which 

 they are produced, the laws by which they are regu- 

 lated, and the force or effect which they exert against 

 themselves or against solid bodies. This subject 

 naturally divides itself into three heads: 1. the 

 effects which take place in the natural flowing of 

 fluids through the various ducts or channels which 

 convey them ; 2. the artificial means of producing 

 motion in fluids, and destroying their natural equili- 

 brium by means of pumps and various hydraulic 

 engines and machines ; and 3. the force and power 

 which may be derived from fluids in motion, whether 

 that motion be produced naturally or artificially. 



The particles of fluids are found to flow over or 

 amongst each other with less friction than over solid 

 substances ; and as each particle is under the in- 

 fluence of gravitation, it follows that no quantity of 

 homogeneous fluid can be in a state of rest, unless 

 every part of its surface is on a level, that is, not a 

 level plane, but so far convex as that every part of 

 the surface may be equally distant from the centre of 

 the earth. As the particles of all liquids gravitate, 

 any vessel containing a liquid will be drawn towards 

 the earth with a power equivalent to the weight it 

 contains, and if the quantity of the fluid be doubled, 

 tripled, &c., the gravitating influence will be doubled, 

 tripled, &c. The pressure of fluids is, therefore, 

 simply as their heights, a circumstance of great im- 

 portance in the construction of pumps and engines 

 for raising water. As liquids gravitate independent- 

 ly, if a hole be made in the bottom of the vessel, the 

 liquid will flow out, those particles directly over the 

 hole being discharged first. Their motion causes a 

 momentary vacuum, into which the particles tend to 

 flow from all directions, and thus the whole mass of 

 the water, and not merely the perpendicular column 

 above the orifice, is set in motion. If the liquid falls 

 perpendicularly, its descent will be accelerated in the 

 same manner as that of falling solid bodies. (See 

 Mechanics.) When water flows in a current, as in 

 rivers, it is in consequence of the inclination of the 

 channel, and its motion is referable to that of solids 

 descending an inclined plane ; but, from want of co- 

 hesion among its particles, the motions are more 

 irregular than those of solids, and involve some diffi- 

 cult questions. The friction between a solid and the 

 surface on which it moves can be accurately ascer- 

 tained ; but this is not the case with liquids, one part 

 of which may be moving rapidly and another slowly, 

 while another is stationary. This is observable in rivers 

 and pipes, where the water in the centre moves with 

 greater rapidity than at the sides, so that a pipe 

 does not discharge as much water in a given time, 

 in proportion to its magnitude, as theoretical calcu- 



lation would lead us to suppose. As water, in 

 descending, follows the same laws as other falling 

 bodies, its motion will be accelerated ; in rivers, 

 therefore, the velocity and quantity discharged at 

 different depths would be as the square roots of those 

 depths, did not the friction against the bottom check 

 the rapidity of the flow. The same law applies to 

 the spouting of water through jets or adjutages. 

 Thus, if a hole be made in the side of a vessel of 

 water, the water at this orifice, which before was 

 only pressed by the simple weight of the perpendi- 

 cular column above it, will be pressed by ttie same 

 force as if the water were a solid body descending 

 from the surface to the orifice; that is, as the square 

 root of the distance of those two points ; and, in the 

 same way, water issuing from any other orifices, will 

 run in quantities and velocities proportionate to the 

 square root of their depths below the surface. Now, 

 the quantity of water spouting from any hole in a 

 given time, must be as the velocity with which it 

 flows: if, therefore, a hole A be four times as deep 

 below the surface as a hole B, it follows that A will 

 discharge twice as much water in a given time as B, 

 because two is the square root of four. A hole in 

 the centre of such a column of water, will project the 

 water to the greatest horizontal distance (or range), 

 which will be equal to twice the length of the column 

 of which the orifice is the centre. In like manner, 

 two jets of water, spouting from holes at equal dis- 

 tances above and below the central orifice, will be 

 thrown equal horizontal distances. The path of the 

 spouting liquid will always be a parabola, because it 

 is impelled by two forces, the one horizontal, and the 

 other (gravitation) perpendicular. 



To prove this by experiment, let two pipes of 

 equal size, m and n, be fixed into the side of 

 the vessel A, but so that the pipe n is placed four 



times deeper below the surface c than the pipe 

 m. (In this case the orifices /C g are supposed to 

 be closed.) If the surface of the water in the vessel 

 be kept at the same height by a constant supply 

 being poured in, and if two vessels, one of which 

 woula hold a pint, be placed under the pipe m, and 

 the other which would contain a quart under the 

 pipe n, both vessels will be filled in the same time 

 from their respective pipes. Wherefore the quanti- 

 ties of water passing through equal holes in the 

 same time, are as the square roots of their depths. 

 The horizontal distance to which a fluid will spout 

 from a hole made in the side of an upright vessel 

 may be determined in the following manner. Let 

 the vessel A be filled with water to the height of 

 the surface, and let d k a be a horizontal 

 plane upon which the jets fall ; on c d, as a dia- 

 meter describe a semicircle c h d, whose centre C 

 shall be the central height of the column of fluid in 

 the reservoir A ; then if holes be made in the reser- 

 voir at the points /Cg, and lines drawn from them 

 to the semicircle perpendicular to the diameter of the 

 semicircle, or the side of the vessel as at / b, C A, 

 and g i ; the distance to which water will spout from 

 the holes /C g, will be proportionate to the length 



