y MB a 



-r in 



, tmti 



HYDRODYNAMICS. 



TABLE II. 



Containing the Feloatut ofWultr in Canah, at obtened in lairlif-me Experiments, compared irilh 

 I fie Velocities calculated by Prony' f Formula. 



M 



ia 

 dnit 



; . - 



In comparing the calculated with the observed re- 

 mits in the preceding Table, it appears that the abso- 

 lute positive differences- are O.O27*. and the absolute ne- 

 e differences 0.0260, which shews that the anoma- 

 lin have been divided with great etjualitv, and that the 

 calculated results hold a just medium between those 

 which were observed. The preceding formula may 

 therefore be adopted in practice with much confidence. 



M. Prony next proceed* to the investigation of. a for- 

 mula for the motion of water in conduit pipes. In this 



case we have = J D, D being the -diameter of the 



tube ; and if Z it the difference of level between the 

 surface of water in the superior reservoir, and that of 

 the water in the lower basin, or the height of the head 

 of water, the equation will be 



Motion 01 



Water in 



Pipes ar.il 



CanaU. 



In order to find and f, M. Prony selected fifty-one 

 of the best experiments made by Couplet, Bossut, and 

 l).i Kujt, and by the application of the methods ef cor- 

 '' , be obtained 



m = 0.00017, / = 0,003416. 



From which we obtain 

 ZD 



= 0.00017 U + 0,003416 f*. 



/* 



which, after reduction, gives 



L = 0,0246829 + ,/(o.0006l9l59 -f 



By means of this formula, the numbers in column ft 

 of the follow inp Table have been calculated, which agree 

 most surprisingly with the observed results. Thisagree- 

 snent is the more remarkable, as tin- experiments were 

 made by different observers, and with different appara- 

 tus, anil upon pipes whose lengths varied from 1 1 A feet 

 to 7020, and their diameters from 1 inch to 1 8 inches. 



The differences between the calculated and observed 

 results amount only to or ,',.. 



The preceding formula should always be used in its 

 present state when the velocities are very 1.111. ill ; but 

 when the velocities are considerable, we may in ordi- 

 nary oases use the following very simple formula, 



Us 



