HYDRODYNAMICS, 



509 



the principle that the squares of the diameters of the 

 cor.duit tubes are as the squares of the diameters of the 

 ajutages multiplied by the square roots of the altitude 

 of water in the reservoir. 



It appear j from a comparison of columns 5th and 6th 

 of Table XIII. that the jets never reach the height of the 

 reservoir, and that a small inclination of the jet causes it 

 to rise higher than when it is projected vertically, a fact 

 which was long ago observed by Wolfius. (See Ele- 

 neula Maiheteos Lnicerite, torn. i. p. 802. schol. 4.) 

 The diminution of the height of the jet has been very 

 properly ascribed by Wolfius principally to the gravity 

 of the falling waters, which obstruct the ascent of the 

 water which is rUing. When the velocity of the fore- 

 most particles of water is spent, the particles imme- 

 diately behind strike against them, and loe their ve- 

 locity, and in consequence of this constant collision 

 between the ascending and descending particles, the 

 jet continues at an altitude less than that of the reser- 

 voir. This consideration also afford* a reason why the 

 height of the jet is increased, by giving it a slight in- 

 clination; for the descending fluid falling a little to one 

 side, no longer opposes the ascent of the rising fluid. 

 In proof i;f the opinion that the diminution of the jet is 

 produced by the gravity of the falling water, Wolfius 

 fates that he has found that mercury rises to a still 

 Its* altitude than watr-. This, however, is not owing 

 to the greater specific poi* ity of mercury ; for though the 

 particle* of mercury r>- heavier than those of water, 

 yet the momentum with which they ascend is propor- 

 tionally greater, and therefore there is the same ratio 

 between the momentum and the resistance which op- 

 poses their accent, as there is in the case of water. 



Toricelliui t seems to nave been the first who ob- 

 served, that when the water is first projected from the 

 orifice it generally springs higher than the height at 

 which it permanently settles, which no doubt arises 

 from there being at first no descending fluid to retard 

 its vertical ascent. Another phenomenon however, 

 more remarkable, has been noticed by other authors. 

 When the water first escape* from the orifice, it gene- 

 rally springs higher than the reservoir from which it 

 flows, but the elevation is momentary, and the water 

 speedily settles at a constant height This fact has 

 l>ecn ascribed to the elasticity of the air which follows 

 the water in its passage through the orifice : but it 

 is manifest that thii would only diminish its spe- 

 cific gravity, as in the hydreoles of M. Mannoury 

 Uectot, (see page 485,) and would never give an addi- 

 tional impulse to the ascending fluid. In order to ex- 

 plain this phenomenon, Dumit suppose* the ajutage 

 to be stopped, and that the air which follow* the wa- 

 ter accumulates near the orifice in a condensed state ; 

 as soon therefore a* the orifice is opened, the elasticity 

 of the included air causes it to escape with rapidity, and 

 the water rushing into the space which it leave*, ac- 

 quires by this short fall in the tube a certain velocity, 

 which increase* at the orifice in the ratio of the section 

 of the orifice to the section of the tube. 



In Chap. I. of HYDRAULIC*, we have considered the 

 theory of oblique jets. The following experiments 

 were made by Boatot 



Hence it follows, that the real amplitudes, which are 

 always less than those deduced from theory, are nearly 

 as the square roots of the altitudes of the water in the 

 reservoirs. In order to find the amplitude of any other 

 jet, when the height of the water in the reservoir is 25 

 feet, we have +/9 : ^5=11 feet 3 inches 3 lines : 

 18 feet 9 inches 5 lines. 



The following experiments on oblique jeU were made Ventun'* 

 by M. Venturi and M. Michelotti. 



Height of Height of the Amplitude 



the water Nature ajutage above of 



in the of the a horizontal projection. 

 reservoir, orifice. plane. 



Inche*. Inches. Inchea. 



32.5 A simple orifice 54 81.5 



S8.5 Additional tube 54 69 

 PlateCCCXVIII.Fig.5. 



A simple orifice 19.33 23.2 



Additional tube 19.33 20 



expenmenw 

 on oblique 

 jttj. 



PLATE 

 CCCXVIIi. 



Fig. 4. 



M. Boarat took a tube, and having filled it with wa- 

 ter, he allowed it to empty itself by orifices of different 

 size*. When no orifice was added, but when the tube 

 was allowed to empty itself, the water did not issue 

 with the greatest velocity when the tube was fullest, 

 but when a certain Quantity of the water had run out. 

 In the case of small ajutage*, the greatest velocity, 

 and the greatest amplitude of projection, is always that 

 which U due to the corresponding height of water in 

 the reservoir ; but, in very large orifices, this relation 

 does not exist. 



CHAP. IV. 



ON THE MOTION or WATER IN PIPES AND OPEN 

 CANALS. 



THERE i* perhaps no branch of science so highly Mou<m of 

 important a* that part of Hydrodynamics which relates "*** J". 

 to the conveyance of water in pipes and canals, and j" 

 there i* none in which theory affords the engineer so 

 tittie assistance. 



When it is required to supply a town with water, 

 the first step of the engineer is Co discover one or more 

 springs situated above the level of that part of the town 

 from which the water is to be distributed to private 

 houses, and to the public fountains. Tire water dis- 

 charged by the springs is then to be collected into one 

 or more reservoirs, and conduit pipes of load, or wood, 

 or iron, are then to be laid to convey the water to the 

 principal reservoirs in the town. The quantity of wa- 

 ter which is necessary for the supply of the inhabitants 

 having been previously ascertained, an additional al- 

 lowance being made for the probable extension of the 



" Ego quidem multum triboo gnvitati aquas aacendentia, quia obacnrati quod argentum vivum ad minorem altitudinern elevatur 

 qnam aqua. Nlmlnim guHarui anteriorom metua ti languaadt, poaMriota to raa iDcurrente* retardantor : id quod Ipainnet ocu- 

 lia i* vidcre pourit, qui aquas asHaalea attnHhueeoUMplart votaark. Atque Inde cat quod >i lumen angulo quantolibet exiguo 

 Imtlmlm at aqua aaKeaa a paipaadliulu mum adaaodoaa Vdlnaia vHaalnr, ultus altitude Maum major evadat." Wolfii Blcmeut* 



f^if'i L'mntTH,. torn. l.p.HOS. SchoL 4. 



.W0 fnjtttjrvm, lib. ifc at hi* Chwa C<MM<nc, p. 19*. 



