HYDRODYNAMICS. 



it is called has a specific gravity of "796, water 

 being i. The stronger any spirit is, then that 

 is, the less the proportion of water it contains 

 the lighter it is ; and in this way the hydrometer 

 becomes the means of measuring the strength of 

 spirits. The hydrometer used by the officers of 

 excise is of the kind known as Sikes's Hydrometer. 

 What is called ' proof-spirit ' consists of equal 

 weights of alcohol and water, and has a specific 

 gravity of '92. When placed in this liquor, the 

 exciseman's hydrometer sinks to a point on the 

 scale marked proof. In a stronger, and, therefore, 

 lighter spirit, it will sink farther, and the spirit 

 will be so many degrees ' above proof.' The con- 

 trary takes place with a weaker spirit. The 

 <legrees are so contrived that a spirit that is, we 

 shall say, 1 1 overproof, would require 1 1 measures 

 of water added to every 100 measures of the spirit, j 

 in order to reduce it to proof. 



As heat expands liquids, rendering them specif- 

 ically lighter, great attention must be paid to the 

 temperature of those experimented upon, as other- 

 wise wrong results will be obtained. The standard 

 temperature is 60, and observations taken at any 

 other temperature have to be reduced to the , 

 standard by certain rules. 



HYDRODYNAMICS. 



Hydrodynamics treats of the laws of the motion 

 of liquids ; the flow of water from orifices and in 

 pipes, canals, and rivers ; its oscillations or waves ; 

 and its resistance to bodies moving through it. 

 The term Hydraulics is sometimes applied to this 

 part of the subject, from the Greek word aulos, 

 a pipe. The application of water as a moving 

 power forms the practical part of the subject. 

 Efflux. If three apertures. A, B, C, are made 

 at different heights in the side of a 

 vessel (fig. 22) filled with water, 

 'the liquid will pour out with greater 

 impetuosity from B than from A, 

 and from C than from B. The 

 velocity does not increase in the 

 simple ratio of the depth. The : 

 exact law of dependence is known j 

 as the theorem of Torricelli ; the j 

 demonstration is too abstruse for 

 introduction here, but the law 

 itself is as follows : 



' Particles of fluid, on issuing, 

 from an aperture, possess the same ; 

 degree of velocity as if they had \ 

 fallen freely, in vacuo, from a Jieight equal to j 

 the distance of the surface of the fluid above the : 

 centre of the apertiire! The jet from B, for in- 

 stance, has the same velocity as if the particles 

 composing it had fallen in vacuo from H to B. , 

 Now, the velocity acquired by a body in falling ; 

 is as the time of the fall ; but the space fallen 

 through being as the square of the time, it follows 

 that the velocity acquired is as the square root of 

 the space fallen through. In the first second, a 

 body falls sixteen feet, and acquires a velocity of 

 thirty-two feet. If C, then, is sixteen feet below 

 H, a jet from C flows at the rate of thirty-two 

 feet ; and if A is at a depth of four feet, or one- 

 fourth that of C, the velocity of the jet at A will 

 bo half the velocity of that at C, or sixteen feet. 



Fig. 22. 



In general, to find the velocity for any given 

 height, multiply the height by 2 X 32, and extract 

 the square root of the product. 



The area of the orifice and the velocity of the 

 flow being known, it is easy to calculate the 

 quantity of water discharged in a given time. 

 Thus, suppose the area to be one square inch, and 

 the velocity twenty feet a second, it is evident 

 that there issues in a second a cylinder or a prism 

 of water one square inch in section and twenty 

 feet long, the content of which is I X 240 = 240 

 cubic inches. This is true only on the supposi- 

 tion that the water in the vessel or reservoir is 

 kept constantly at the same height. 



The ' Contraction of the Vein! When, by 

 means of the area of the opening and the velocity 

 thus determined, we calculate the number of cubic 

 feet or of gallons that ought to flow out in a given 

 time, and then measure the quantity that actually 

 does flow, we find that the actual flow falls 

 short of the theoretical by at least a third. In 

 fact, it is only the central part of the jet, which 

 approaches the opening directly, that has the 

 velocity above stated. The outer particles approach 

 from all sides with less velocity ; they jostle one 

 another, as it were, and thus the flow is retarded. 

 In consequence of this want of uniformity in 

 velocity and direction among the component layers 

 of the jet, as they enter the orifice, there takes 

 place what is called a 'contraction of the vein' 

 (vena contracta) ; that is, the jet, after leaving the 

 orifice, tapers, and becomes narrower. The great- 

 est contraction is at a distance from the orifice 

 equal to half its diameter ; and there the section 

 of the stream is about two-thirds the area of the 

 opening. It is, in fact, the section of the con- 

 tracted vein that is to be taken as the real area of 

 the orifice, in calculating by the theory the quan- 

 tity of water discharged. 



Adjutages, It has as yet been supposed that 

 the issue is by means of a simple opening or hole 

 in the side or bottom of the vessel ; but if the flow 

 takes place through a short tube, the rate of dis- 

 charge is remarkably affected. Through a simple 

 opening, in a thin plate, the actual discharge is 

 only about 64 per cent, of the theoretical ; through 

 a cylindrical conducting-tube, or adjutage, as it is 

 called, of like diameter, and whose length is four 

 times its diameter, the discharge is 84 per cent. 

 The effect is still greater if the discharge-tube is 

 made conical both ways, first contracting like the 

 contracted vein, and then widening. The effect 

 of a conducting-tube in increasing the discharge 

 is accounted for by the adhesion of the water to 

 its sides, which widens out the column to a greater 

 area than it would naturally have. It has thus a 

 tendency to form a vacuum in the tube, which acts 

 like suction on the water in the reservoir, and 

 increases the quantity discharged. 



Pipes. When a conduit-pipe is of any consider- 

 able length, the water issues from it at a velocity 

 less than that due to the head of water in the 

 reservoir, owing to the resistance of friction. With 

 a pipe, for instance, of one and a third inch in 

 diameter, and thirty feet long, the discharge is only 

 one half what it would be from a simple orifice of 

 the same diameter. The rate of reduction depends 

 upon the diameter of the tube, its length, the 

 bendings it undergoes, &c. The resistance in- 

 creases greatly with the narrowness of the pipes. 



Rivers. The natural tendency in the water 



233 



