WATER. 



I If we were to calculate the expence or difcharge for 

 liny orifice by this table, we fhould in every inftaiice find 

 It much greater than nature really gives us. 

 [ It muit he recoUefted, that this table is not calculated 

 rom experiment, but from the theory of falling bodies, 

 jWhich makes no allowance for the lofs of velocity, which 

 ^rifes from the frittion of the particles of water againft 

 ;he edges of the aperture, and againfl: the neighbouring 

 jarticles of water which are not put in motion. 



Sir Ifaac Newton, in making experiments, found the 

 velocity thus determined to be too great, which in one cafe 

 le correfted. The friftion againft the fides of the aperture, 

 ind the oblique direftion of the particles of water before 

 ;hey reach the aperture, both tend to diminifh the velocity of 

 ;he ftream ; and if thefe caufes could be removed, efpecially 

 :he latter, the Newtonian theory would be confirmed by 

 experiment, or rather experiment would exaftly agree with 

 ;;heory. 



For, if we fuppofe water running into the top of a cy- 

 lindrical tube, and that there is no attraftion or fridlion 

 petween the particles of water and the interior of the tube, 

 the velocity of the water, or of each of the particles at the 

 bottom, would be the fame, or equal to that which they 

 would have acquired in falling through the fame fpace with- 

 )nt the tube, towards the earth. 



Hence, to obtain the true velocity, under different cir- 

 ;umftanccs, we muft correct the compnted velocity by 

 experiments. 



It is ftated in fome elementary works on hydroftatics, 

 that the velocity of the water at the orifice is only equal to 

 that which a heavy body would acquire by falling through 

 ,haif the height of the fluid above the orifice. This was firft 

 maintained by fir Ifaac Newton, who found that the dia- 

 meter of the ftream is contracted, after it has quitted the 

 (Orifice ; and at the fmalleft part, the diameter was to that 

 of the orifice as 21 to 25. The area, therefore, of the one 

 Iwas to the area of the other as 2i* to 25', which is nearly 

 Ithe ratio of i to the fquare root of 2. By meafuring 

 ithe quantity of water difcharged in a given time, and alfo 

 Ithe area of the vena contratta, fir Ifaac found, that the velo- 

 Icity at the vena contrafta was that which was due to the 

 .whole altitude of the fluid above the orifice. He, there- 

 Ifore, concluded, that fince the velocity of the orifice was to 

 jthat at the vena contraAa as i to the fquare root of 2, the 

 velocity in the vena contrafta was that which was due to the 

 whole altitude of the fluid; and that the velocity at the 

 orifice muft be that which is due to one half that altitude, 

 becaufe the velocities are as the fquare roots of the heights. 

 From this, fir Ifaac ftated the aftual velocity of flowing 

 water to be tcssj or .707 of the theoretic velocities. 



But the real quantity of the reduftion varies in different 

 cafes, according to the nature of the aperture : hence, it is 

 neceffary to confider all different forms of apertures, and 

 make a different allowance for each cafe. To do this, the 

 circumilances of the aperture muft be carefully examined. 



A, Jig. 8. PlaU II. IVater-'works, explains the manner 

 in which the filaments of water may be fuppofed to move, 

 when a ftream flows through an aperture in a thin plate. 



B fhews the motion, v.'hen a tube of about two diameters 

 in length is added to the orifice, and when the water flows 

 through the tube with a full ftream. This does not always 

 happen in fo fhort a pipe, and never in one that is fhorter ; 

 but the water will frequently detach itfelf from the fides of 

 the pipe, and flow through it with a contracted jet. 



C fhews the motion, when the pipe projetls into the in- 

 fide of the veflel. In this cafe, it is difficult to make the 

 tube flow full. 



D reprefents a mouth-piece fitted to the hole, and formed 

 agreeably to that fhape which a jet would afl'urae of itfelf. 

 In this cafe all contraftion is avoided, becaufe the mouth 

 of this pipe may be confidered as the real ca-ifice ; and no- 

 thing now diminiflies the difcharge but a trifling friftion of 

 the fides. 



When water ilfues through a hole in a thin plate, the 

 lateral columns, prefling into the hole from all fides, caufe 

 the iffuing filaments to converge to the axis of the jet, and 

 contradl us dimenfions after it has quitted the hole, and at 

 a little diftaiice from tb.e hole ; and it is in this place of 

 greateft contraftion that the water acquires that velocity 

 which we r.ffume as equal to that acquired by falling from 

 the furface : therefore, that our computed difcharge may 

 beft agree with obfervation, it muft be calculated on the 

 fuppofition that the orifice is diminifhed to the fize of 

 this fmalleft fedlion. But the contraftion is fubjeft to 

 variations, of which the reafons are not apparent. 



The following are the meafures of the contradled vein, as 

 aicertained by different authors ; the area of the aperture 

 being 1000, the area of the contrafted vein at the fmalleft 

 will be as follows : 



Sir Ifaac Newton 



Poleni - . . . . 



Greateft found by Boffut 



Mean of fix experiments by Boffut 



Loweft found by Boffut 



Bernouilli . . - . . 



Michelotti . . .- . 



Du Buat 



Venturi - . . . . 



Eytelwein - . - . . 



707 



714 

 667 

 664 

 666 

 641 

 641 

 666 

 636 

 642 



The meafures given by Boflut were taken by a pair of 

 fpherical compafles, with which he meafured direftly the 

 diameter of the contradled vein, which he found to preferve 

 the fame diameter for fome lines. The altitude of the water 

 in the refervoir which Boffut ufed was 12 feet 6 inches. 

 He meafured the vena contrafta alfo, when the water iffued 

 by vertical orifices placed 4 feet 3 inches below the furface 

 of the fluid, and he obtained the very fame refults. The 

 ratio between the area of the orifice and the area of the vena 

 contrafta appears from the above, to be by no means con- 

 ftant. It undergoes perceptible variations, by varying the 

 form and pofition of the orifice, the thicknefs of the plate 

 in which the orifice is made, the form of the veffel, and the 

 velocity of the iffuing fluid. 



The dimenfions of the fmalleft feftion of the contrafted 

 vein are at all times difficult to be afcertained with precifion. 

 It is, therefore, much more convenient to compute from the 

 real dimenfions of the orifice, and to correft this computed 

 difcharge by means of an aftual comparifon of the computed 

 and effeftive difcharges, in a feries of experiments made in 

 fituations refembling thofe cafes which moft frequently 

 occur in praftice. 



We liave made a colleftion of experiments by various 

 authors, and from them we have deduced the following rule 

 for the real velocity with which water iffues from an aper- 

 ture in a thin plate. 



Rule — Meafure the depth of the centre of the orifice be- 

 neath the furface of the water in the refervoir in inches, 

 extraft its fquare root, and multiply it by the conllant number 

 85. Sy : the produft is the velocity in feet p-r minute. 



If tlie velocity, as marked in the preceding table, is mul- 

 tiplied by .618, the fame refult will be obtained. For the 

 contraftion of the ftnam or vein of water, running out of a 

 fimple orifice in a thin plate, reduces the area of its fcdlion, 



at 



