WATER. 



We have fearched in Mr. Smeaton's papers for the experi- 

 ments by which this table was made, and we find an invefti- 

 gation, from the experiments of M. Couplet, as recorded by 

 Belidor, on the flow of water through a large pipe at Ver- 

 failles. From thefe he deduced the following rule, to find 

 the height of column in inches, correfponding with the ve- 

 locities in inches per fecond, through a pipe of any diameter 

 ijiven in inches, and loo feet long. 



48 X ( velocity ) 4- velocity ^ 



depth of column ; 



52.66 X (diameter) 



jr, ftill more nearly, taking 47.873 for the conftant number 

 inftead of 48. 



It appears that he found this rule did not agree with his 

 awn obfervations ; and, in confequence, he made the foUow- 

 ,ng experiments himfelf with a pipe of i\ inch bore and 100 

 'eet in length ; and we believe he arranged them into the 

 :able, by projefting and drawing a curve, at leaft we find 

 hat was his ufual method in like cafes. 



' This is ufeful information, becaufe it (hews what part of 

 'the table may be depended upon. He aflumed, that the 

 idepth of the column in pipes of other dimenfions, was as the 

 length of the pipe direftly, and as the diameters inverfely. 



The form of this table renders it immediately applicable 

 to a great variety of purpofes ; for inftance, an engine is re- 

 quired to pump water to a height of 60 feet ; but the water 

 muft pafs through 1 800 feet of horizontal pipe of 5 inches 

 bore, and with a velocity of 140 feet per minute. The table 

 {hews, that for every 100 feet of this pipe the friftion will be 

 equal to a column of 7.6inches ; multiply this by 18.6, and 

 we find the whole friftion will be 141.36 inches, this added 

 to 60 feet makes 71.78 feet for the real column which the 

 pump muft overcome. 



Rules for meafuring the Qimntity of Water Jloiving through 

 Sluices or Apertures. — In this, like the former inftances, we 

 muft multiply the area of the aperture by the velocity with 

 which the water ruihes through it. 



Sir Ifaac Newton, in his Principia, book ii. theo. 8. 

 prob. 36. has demonftrated, that the velocity of water, 

 flowing through holes in the bottom or fide of a veflel, 

 ought to be equal to the velocity which a heavy body would 

 acquire, in falling through a fpace equal to the diftance be- 

 tween the furface of the water and the place where it is 

 difcharged. 



Hence, at the depth of i6tV feet, a ftream of 32^ feet 

 in length, ought to flow out in a fecond of time. And from 

 the laws of falling bodies, it follows, that as the fquare 

 root of I 6tV is to the velocity of the ftream flowing out at 

 that depth, fo is the fquare root of any other depth to the 

 velocity of that depth. 



Hence, the velocity of water flowing out of a horizontal 

 aperture, in the bottom of a ciftern or refervoir, is as the 

 fquare root of the height, or the depth of water above 

 the aperture. 



That is, the pren"ure, and confequently the depth, is as 

 the fquare of the velocity ; for the quantity flowing out in 

 any given time is as the velocity, and the force required to 

 produce a velocity in a certain quantity of matter in a given 

 time, is alfo as that velocity ; therefore, the force muft be 

 as the fquare of the velocity. 



The propofition is fully confirmed by Boffut's and Mi- 

 chelotti's experiment ; the proportional velocities, with a 

 preffure of i, 4, and 9 feet, being 2722, 5436, and 8135, 

 inftead of 2722, 5444, and 8166; very inconfiderable dif- 

 ferences. 



There is another mode of confidering this propofition, 

 which is a very good approximation. Suppofe a vary thin 

 cylindrical plate of water, like a wafer, fituated in the ori- 

 fice ; and fuppofe a conftant fuccelfion of fuch plates to be 

 put in motion, one at every inftant, by means of the pref- 

 fure of the whole cyhnder ftanding upon it ; let all the 

 gravitating force of the column be employed in generating 

 the velocity of each fmall cylindrical plate, (negledting the 

 motion of the cylinder itfelf,) this plate would be urged by 

 a force as much greater than its own weight, as the column 

 is higher than itfelf, and this through a fpace fliorter in the 

 fame proportion than the height of the column. But where 

 the forces are inverfely as the fpaces defcribed, the final 

 velocities are equal : therefore, the velocity of the water 

 flowing out muft be equal to that of a heavy body falling 

 from the height of the head of water. 



This velocity may be found very nearly by the rule 

 which we have before given in underfliot water-wheels, or 

 by extrafting the fquare root of the depth in feet, and mul- 

 tiplying it by 481.2 : the produft is the velocity /fr minute 

 in feet. 



In praftice it is more convenient to take the depth ii^ 

 inches, inftead of feet ; then to obtain the velocity in feet 

 per minute. 



Extract the fquare root of the depth in inches, and mul- 

 tiply it by 138.88: the produtft is the velocity in feet 

 per minute. 



As this rule is the foundation of all calculations for 

 velocities, when friftion is not confidered, it is conftantly 

 wanted : we ftiall, therefore, give a table, calculated by 

 Mr. Smeaton from the above rule, fhewing the theoretic 

 velocities correfponding with different depths. 



A Table 



