508 



HYDRODYNAMICS. 



menu on 

 Jets d'eau. 



large ones having a greater momentum, are more able 

 to overcome the obstacles which are opposed to them. 

 This, however, is true only of high jets. For when 

 they do not exceed two or three feet in height, and 

 when the ajutages are not below one line in diameter, 

 small jets rise to the same height as large ones. This 

 conclusion must also be limited to the case where the 

 conduit pipe OE aflbrds a sufficient supply of water ; 

 for it appears from the three last experiments, when the 

 conduit tube OE is very narrow, that the small jets rise 

 to a greater height than large ones. Hence there is ob- 

 viously a certain ratio which must exist between the 

 diameter of the horizontal tube and that of the ajutage, 

 to produce a maximum height in the jet. 



In order to find this ratio, Bossut has given the fol- 

 lowing method. Let D be the diameter of the tube, 

 d that of the orifice, v the velocity of the water in the 

 tube, and h the altitude of the fluid in the reservoir, 

 Now t/h may be taken as the constant velocity at 

 the ajutage. But by HYDRAULICS, Chap. I. Prop. 1. 



Jh : v = T)' : rP, and v = -==r /h. In like manner, in 



any other tube, in which D' d', h' and v' represent the 



d's 

 same quantities as before, we have v ' = -j^- */h'. But 



upon the hypothesis, whicli is conformable to experi- 

 ment, that two jets will each rise to the greatest possi- 

 ble height when the velocities of the water in the two 



cl- 

 cenduit tubes are equal, -we have v v' and /h = 



~ 



h'; consequently, D : D' 1 = d '^/h : d" ,/h'; that 



is, Ike squares of the diameters of the horizontal lubes ought 

 to be to each other in the compound ratio of the squares of 

 the diameters of the ajutages, and the square roots of the 

 heights of mater in the reservoir. 



Hence, if we know from one direct experiment the 

 diameter which a tube ought to have to supply a given 

 ajutage under a given height of fluid in the reservoir, 

 we may find the diameter of every other tube which is 

 necessary to supply any other ajutage under a given 

 height of fluid in the reservoir. 



. With this view, M. Bossut made the following expe- 

 riments. He applied a tin tube one inch in diameter 

 to a reservoir. The point of the tube, bent upwards 

 in order to project the water vertically, was made of 

 lead, and was a little more than an inch long, and to 

 the extremity of it seven different orifices were succes- 

 sively applied. The following were the results. 



TABLE XIV. Containing the Experiments of Bossut on 

 the Height of Jets viith different Orifices, 



From these results it follows, that for a height of wa- 

 ter in the reservoir of 3 feet 2 inches and 1 1 lines, and 

 a conduit tube which has a diameter of 1 inch, the dia- 

 meter of the orifice should be about 3f lines. Now 

 Mariotte found from experiment, that for a head of 

 water of 52 feet, and an ajutage 6 lines in diameter, 



the diameter of the conduit tube should be 3G lines; r> 

 whereas the preceding rule will give 38, agreeing very ment! on 

 nearly with the experimental result. Jets ' 



It appears, from a comparison of the experiments of " 

 Bossut and Mariotte, that the differences between the 

 height of vertical jets and the height of l/ie reservoir 

 arc nearly as lite square of the heights of the jets them- 

 selves. Hence, if we know this difference in once case, 

 the difference in any other will be found by simple 

 proportion. If the height of the reservoir of the second 

 jet is given, and if it is required to determine the height 

 of the jet, we must resolve a quadratic equation. 

 Thus, let a be the height of the reservoir of the ex- 

 perimental jet, b the height of the same jet, c the height 

 of the reservoir of the proposed jet, a: the height of the 

 proposed jet; then by the rule a b:c jr=6 2 :a- z , 

 we obtain 



,_b>(c x) 



or x = 



62 + 6,^(4 a c 46 c + 4*) 



a b ' 2(ad) 



In order to facilitate the application of the preceding 

 principles to practice, Bossut has computed the follow- 

 ing Table: 



TABLE XV. Containing the Altitudes of Reservoirs, the 

 Diameters of the Horizontal Tubes, 8fc. for Jets of 

 different heights. 



The two first columns, containing the heights of 

 the jets and the corresponding altitudes of the reser- 

 voirs, are taken from Mariotte. The heights of the 

 jets and of the reservoirs not included in the Table, 

 may be found from the preceding formula. The third 

 column contains, in Paris pints, of which 36 form a cu- 

 bic foot, the water discharged in a minute by an ajutage 

 six lines in diameter ; and the fourth column contains 

 the diameter which ought to be given to the conduit 

 tubes for an ajutage of six lines relatively to the alti- 

 tudes in column 2. This column is computed on the 

 hypothesis, that for an ajutage six lines in diameter, 

 and an altitude of 16 feet of water in the reservoir, the 

 conduit tube must be 28^ lines in diameter, and upon 



