HYDRODYNAMICS. 



15 



indefinitely condensed by pressure. The fundamental 

 truth, on which the whole science of hydrostatics rests, 

 is equality of pressure. A 11 the particles of fluids are 

 so connected together, that they press equally in 

 every direction, and are continually pressed upon; 

 each particle presses equally on all the particles that 

 surround it, and is equally pressed upon by them ; it 

 equally presses upon the solid bodies which it touches, 

 and is equally pressed by those bodies. From this, 

 and from their gravity, it follows, that when a fluid 

 is at rest, and left to itself, all its parts rise or fall so 

 as to settle at the same level, no part standing above 

 or sinking below the rest. Hence, if we pour water 

 or any other liquid into a tube bent like the letter U, 

 it will stand at the same height in both limbs, whether 

 they are of the same diameter or not, and thus a por- 

 tion of the liquid, however small, will resist the pres- 

 sure of a portion however large, and balance it. In 

 a common tea-kettle, for instance, water poured into 

 the body of the vessel will rise to the same level in 

 the nose as in the vessel; and if poured into the nose, 

 the same will also be true, and the small column of 

 water in the nose balances the whole column in the 

 body of the vessel, and will continue to do so, how- 

 ever large the one, and however small the other may 

 be. From this fact two important conclusions follow, 

 derived both from reasoning and from daily expe- 

 rience. The one is, that water, though, when uncon- 

 iined, it can never rise above its level at any point, 

 and can never move upwards, will, on being confined 

 in close channels, rise to the height from which it 

 came, that is, as high as its source; and upon this 

 principle depend all the useful contrivances for con- 

 veying water by pipes, in a way far more easy, cheap, 

 and effectual than by those vast buildings, called 

 aqueducts, by which the ancients carried their sup- 

 plies of water in artificial rivers overarches for many 

 miles. In this case, the stream must have been run- 

 ning down all the way, and consequently a fountain 

 fed from it at its termination, could not furnish the 

 water at the same height as its source. The other 

 conclusion is not less true, but far more extraordinary, 

 and, indeed, startling to belief, if we did not consider 

 the reasoning upon which it is founded; it is that 

 the pressure of the water upon any object against 

 which it comes, is not in proportion to tiie body or 

 bulk of the water, but only to the size of the surface, 

 on or against which it presses, and its own height 

 above that surface. Thus, in a tunnel-shaped vessel, 

 the pressure on the bottom is not proportioned to the 

 whole body of water in the vessel, but only to a 

 column of the fluid equal in diameter to the bottom. 

 The general rule for estimating the pressure of any 

 fluid, is to multiply the height of the fluid by the ex- 

 tent of the surface on which it stands. If any portion 

 of the fluid is supported by a tube above the remainder, 

 the pressure on the bottom of the vessel will be the 

 same as if the water was throughout at the same height 

 as that in the tube, so that the height of the tube is pro- 

 perly multiplied by the extent of the bottom of the ves- 

 sel, to determine the whole pressure. '1 his principle of 

 equal pressure has been called the hydrostatic paradox, 

 though there is nolhing in reality more paradoxical 

 in it than that one pound at the long end of a lever 

 should balance ten pounds at the short end; it is, 

 indeed, but another means, like the contrivances 

 called mechanical powers, of balancing different 

 intensities of force by applying them to parts of an 

 apparatus which move with different velocities. This 

 law of pressure is rendered very striking in the 

 experiment of bursting a strong cask by the action 

 of a few ounces of water. Suppose a cask already 

 filled with water, and let a long tube be screwed 

 tightly into its top, which tube will contain 'inly a 

 few ounces of water ; by filling this tube the ca^k will 



be burst. The explanation of the experiment is this ; 

 if the tube have an area of a fortieth of an inch, and 

 contain half a pound of water, this will produce a pres- 

 sure of half a pound upon every fortieth of an inch 

 over all the interior of the cask. The same effect is 

 produced in what is called the hydrostatic bellows. 

 The tube is made to communicate with an apparatus 

 constructed like a common bellows, but without s 

 valve. If the tube holds an ounce of water, and has 

 an area equal only to one thousandth of that of the 

 top board of the bellows, an ounce of water in the 

 tube will balance weights of a thousand ounces rest- 

 ing on the bellows. The hydrostatic or hydraulic 

 press of Mr Bramah, (See Bramah's press), is con- 

 structed on this principle ; a prodigious force is thus 

 obtained with great ease, and in a small compass, so 

 that, with a machine the size of a common teapot, a 

 bar of iron may be as easily cut as a slip of paste- 

 board. A small forcing pump takes the place of the 

 tube in the instrument above described, and a pump 

 barrel and piston is substituted for the bellows ; 

 water is then driven from the small pump into the 

 large barrel under the piston, and the piston is thus 

 pressed against the object to be operated upon. If 

 the small pump have one thousandth of the area of 

 the large barrel, and the force of 500 pounds be 

 applied to its piston by its lever handle, the great 

 piston will rise with a force equal to one thousand 

 times 500 pounds, or more than two hundred tons. 

 The uses to which this power may be applied, are of 

 great variety and extent, but this branch of art seems 

 to be yet in its infancy. Upon the tendency of all the 

 parts of fluids to dispose themselves in a plain or 

 level surface, depends the making of levelling instru- 

 ments, or instruments for ascertaining whether any 

 surface is level, or any line horizontal ; for finding 

 what point is on the same level with any given point, 

 and how much any point is above or below the level 

 of any other point. 



We have thus far spoken of the pressure of liquids 

 upon a horizontal or level surface, in which case it is 

 only necessary to multiply the height of the fluid by 

 the extent of the surface, and the weight of the bulk 

 is equal to the pressure upon the surface. But if the 

 surface is not horizontal, a different rule must be 

 applied ; for then the pressure is equal to the weight 

 of the bulk, found by multiplying the extent of the 

 surface into the depth of the centre of gravity of the 

 surface. In this manner we can find the pressure 

 upon a dam ; we must take half the depth of the 

 water, and multiply it by the superficial extent of the 

 dam ; this gives the bulk of water whose weight is 

 the pressure on the dam. The pressure against the 

 upright sides of a cylinder filled with water, may be 

 found by multiplying the curve surface under water 

 by the depth of its centre of gravity, which is halt the 

 depth of the water. The increase of pressure in pro- 

 portion to the depth of the fluid, shows the necessity 

 of making the sides of pipes or masonry, in which 

 fluids are to be contained, stronger in proportion to 

 their depth. It is therefore needless to make them 

 equally thick and strong from the top downwards. 

 If they are thick enough for the great pressure be- 

 low, they will be thicker than is required for the 

 smaller pressure above. The same is true in regard 

 to flood-gates, dams, and banks. 



When a solid body is plunged in any liquid, it must 

 displace a quantity of that liquid exactly equal to its 

 own bulk. Hence by measuring the bulk of the 

 liquid so displaced, we can ascertain, precisely the 

 bulk of the body ; for the liquid can be put into any 

 shape, as that of cubic feet or inches, by being poured 

 into a vessel of that shape divided into equal parts. 

 This is the easiest way of measuring the solid contents 

 of irregular bodies, when a body is plunged into a 



