HVDKODYNAMICS. 



HYDRODYNAMICS. 





Again. if two jeta meet obliquely, but not centrally, the liquid plate 

 U rtill formed, but it IB no longer flat, being twisted by iU cohesion 

 with the unimpaired parts of the jeU. 



From these two laat cases especially, Prof. Magnus ban shown the 

 formation of a single jet from an orifice to be due to the clashing of 

 several jets at the ma contracts, thus throwing out between them a 

 plate of an elliptic form, and so on throughout the whole liquid vein. 

 The chain mortmenl of the jet thus produced is easily converted into a 

 iptral one by any alight impediment at the orifice, or by currents, even 

 very slight, in the cistern, since all motion whatever of water in a 

 cistern neceturily resolves itself into rotatory motion ; because all other 

 motions are destroyed by the sides of the vessel Besides this, even 

 when there is perfect stillness in the water of the cistern, rotation will 

 take place at an orifice, by reason of the motion of the earth. This is 

 well illustrated by Foucault's pendulum experiment. [OTBOSCOPK.] 

 It is evident from this, that everything on the earth's surface has too 

 motions rtlatirely to the earth namely : one round the earth's axis in 

 24 hours ; and another round an axis in itself, and parallel to the 

 former, in the same period. The latter, in the case of a vessel of water, 

 U resolved into two, one parallel to the liquid surface, the other per- 

 pendicular to it ; neither being visible, because the vessel and every- 

 thing else have the same motion. The horizontal rotation, in the 

 latitude of Great Britain, will be about J J per minute, so that the 

 liquid has the rotation about its rertical axis. This will be abundantly 

 sufficient to show the cause of the rpiral motion of the issuing jet. 



Prof. Magnus, by introducing a tranquilliter, that is, a fan con- 

 sisting of four radiating plates, in order to destroy the effect of this 

 rotatory motion on the jet, succeeded in showing that, in this case, no 

 ventral_segment8 or any other irregularities were produced, perhaps 

 not even the rena contracta; but the issuing column was perfectly 

 smooth and uniform. U. Plateau, however (' Phil. Mag.,' Oct., 1856), 

 denies this statement, and shows, by reference to his celebrated method 

 of destroying the action of gravity on fluid veins, that a liquid cylinder 

 U in stable equilibrium when its length and diameter do not exceed 

 the limit of 3 and 3'G, being in unstable equilibrium beyond this limit, 

 so that it is ruptured spontaneously into a series of isolated spheres 

 with alternating spherules. This effect of the formation of various- 

 sized spheres is well shown in the fusion of a platinum wire by a strong 

 electric current. The wire is first elongated, and then, by the rupture 

 of equilibrium of the parts, resolves itself, just as a liquid jet, into 

 spheroidal particles. 



Lastly, with regard to the formation of the vena contracta in such 

 cimm, we Khali see that it must be formed, if we consider the theorem 

 of Torricelli, as correctly representing the approximate velocity of any 

 affluent jet. By this theorem, as before shown, we have the velocity 

 at the orifice given by the equation v*=Sjjw, where < is the distance 

 from the surface to the orifice. Now, <j is about 32'2 feet for the 

 latitude of London : hence r s = C4'4 x $ 



:. v = 8-026 x vT 



But it U shown by experiment, that this theoretic velocity (given by 

 substituting any value for s proper for the vessel in question) is 

 14 times the actual velocity, or this latter is ] of the former ; so that 

 we must reckon the actual height of the surface, not from the orifice, 

 but from the into contracta itself, in which case TomcclU's theorem 

 is in accordance with experiment. 



The distances, measured on a plane passing through the base of a 

 vessel, to which fluids will be projected from orifices at different 

 depths in its side, may be easily determined (the resistance of the air 

 being neglected) by combining the action of gravity on the particles of 

 fluid after they have left the orifice with the velocity communicated 

 to them in consequence of the pressure arising from the depth of the 

 orifice below the top of the column ; and the path of the filament may 



U' .-I... -.111. . . 1M til'- tlsi IV i if ^'l lllll. -I \ . 1" IT .1 p.ir.llinli,- rnrvi'. 



The results of experiments tend to show that, when the height of a 

 head of water in a vessel and the diameter of an orifice in its base or 

 side are given, the discharge of water through an ajutage, or tube 

 inserted in the orifice (its length not exceeding three or four times its 

 diameter), is to that through the simple orifice, nearly in the ratio of 

 12 to 11 ; and it is observed that, with a given diameter at its farthest 

 extremity, the tube which is formed to coincide as nearly as possible 

 with the natural figure of the vena contracta affords the greatest 

 discharge. When the tube is fixed vertically in the base of a vessel, 

 the effect is increased in proportion nearly to the length of the tube ; 

 since the velocity at the lower extremity of the tube is that which i 

 due not merely to the height of the fluid above the base of the vessel, 

 but to the height above the extremity of the tube. Again, if a short 

 tube be applied horizontally to an orifice in the side of a vessel, the 

 part nearest to the vessel having the form of the vena contracta, and, 

 from the narrow part of the tube, diverging conically to the opposite 

 end, the discharge of water is found to be more abundant than from a 

 tube whose form beyond the vena contracta is cylindrical. For when 

 the water has filled the tube, the cylindrical stream through the 

 contracted part communicates its motion laterally to the rest of the 

 water, till it causes the whole to acquire the same velocity. The 

 quantity discharged in this case, compared with that discharged from 

 a cylindrical tube, is considered to be nearly in the ratio that the 

 diameter of the conical tube at its extremity bears to that of the vena 



contracta. The following U the remit of some experiments on this 

 subject, showing the use of an ajutage : 



A ventl with a ilmple bole . 



A vend with a pipe whose length**! 



dlunetcn of the hole . 

 A VMKl with the ramp pipe inserted 



only half way in the hole . 

 When the bottom of the vr*Kl the 



parabolic curve described by the 



particles ..... 

 With * bell-mouth added to thin . 



discharged 62 quart* In 100 tec. 



61 



a maximum. 



It is customary to express the slope, or inclination, of a pipe or canal, 

 when uniform, by the quotient arising from the division of the vertical 

 height of one end above the other by the whole length. But, in the 

 case of a reservoir, as A u, having a conduit-pipe r> K ; let A A' be the 

 surface of the water, and E, in the horizontal line r K. be the lower 

 orifice of the pipe. Then, if A'O express the height due to the observed 

 velocity at E, o F will be the height necessary to overcome the friction in 



the pipe, and is considered as the effective slope. 

 DE 



The passage of water through long pipes is greatly retarded by 

 adhesion and friction in the interior, by the resistance experienced 

 where bends take place, and by the disengagement of air, which 

 remaining stationary in the pipes when the latter are laid along a level 

 surface, or rising to the higher parts of any vertical bends, opposes an 

 obstacle and sometimes entirely arrests the motion of the water. 

 Experiments alone can, at present, .afford information concerning the 

 amount of the retardation in pipes of given lengths and diameters ; and 

 those which were conducted by the Abbe* Bossut at Mezie'res in 1779 

 are the most complete of any which have yet been made. The water 

 was allowed to flow through pipes whose diameters were 1J inch and 

 2 inches, and whose lengths varied from 30 to 180 feet. They were 

 chiefly of tin, and were inserted in the side of a reservoir in which the 

 water during any experiment was always kept at one height ; which 

 was either 1 foot or 2 feet above the axis of the pipe. The general 

 rules deduced from the experiments are, that the discharges in given 

 tunes, with pipes of the same length and with the same head of water, 

 are proportional to the squares of the diameters; and, when the 

 diameters are equal, the discharges are inversely proportional to the 

 square roots of the lengths of the pipes. In order to afford the means 

 of obtaining by calculation the supply which may be expected from a 

 pipe of given dimensions, it may be assumed that when a pipe is 30 

 feet long and 1J inch in diameter, the discharge at its extremity is 

 about one-half of that which would be obtained from a simple orifice, 

 or short tube, of the same diameter. The experiments made by M. 

 Couplet at Versailles, in 1730, were with pipes whose lengths varied 

 from 280 to 2340 fathoms, and the diameters from 4 to 12 inches. 

 The pipes were of iron or stone, or of both combined, and they were 

 bent in various directions both horizontally and vertically. A pipe 

 whose length was 600 fathoms, and which was 12 inches in diameter, 

 when the head of water was 12 feet, afforded a discharge amounting to 

 about ^jth ; and a pipe of equal diameter, whose length was 2340 

 fathoms, when the head of water was 20 feet, discharged only Ath, of 

 that which would have been obtained from a simple orifice. Bossut 

 found that, in order to produce a continued discharge in a pipe, the 

 head of water should be about 1J inches in 180 feet. 



The motion of water in the bed of a river depends on the action of 

 gravity, by which the particles endeavour constantly to descend, and on 

 the mobility of the particles, by which they are enabled to assume a 

 level surface when at rest. The descent by gravity takes place in con- 

 sequence of the difference, in a longitudinal section of the river, 

 between the levels of any two points on its surface, whatever be the 

 form of its bed ; since the molecules of water, which are in every part 

 of a transverse section, have equal facilities of moving in the direction 

 in which, from the general slope, the motion can take place. Ami. by 

 the nature of an inclined plane, the accelerative force by which a 

 particle is moved is to that of gravity as the difference of level between 

 any two points at the surface in a longitudinal section is to the 

 distance between those points on the surface. .That the motive force 

 of the molecules composing a river depends on the upper surface nl\ 

 may be easily admitted, when it is considered that the bed may have 

 any inclination and any degree of irregularity, yet if the upper surface 

 be horizontal the water wiO be at rest. 



If the water of a river experienced no resistance from the sides and 

 bed, its motion would go on continually accelerating from its source to 

 its mouth, like a solid body falling by the action of gravity ; and the 

 consequence would be, that besides the destruction ensuing from the 

 violence of the torrents in the lower lands, the moisture would be 

 drawn from the soils in the upper regions, which would thus become 

 incapable of supporting vegetable and animal life. The adherence of 

 the particles of water to each other, and the friction against the beds, 

 produce together a resistance which increases with the velocity of the 

 current, and becomes at length equal to the accelerative force of the 

 descent ; and then a uniform motion is established. 



But when a current is in a state of equilibrium, the velocities in 

 different transverse sections of the river may lie very unequal,- on 

 account of the variations in the areas of those sections, through all nf 



