502 



HYDRODYNAiMICS. 



Discharge 

 of Water 



through 

 additional 



Tubes. 



.General 

 results. 



of the altitudes of the fluid above the interior orifice of 

 the vertical tube. 



It follows also from the above measurement, that 

 ivhen the height of the reservoir and the orifice are the 

 same, Ike theoretical discharge, the discharge by an ad- 

 ditional tube, and the discharge by a simple orifice, are 

 nearly as the numbers 16, 13, 10. Hence Bossut con- 

 cludes that the effect of contraction is not wholly de- 

 stroyed by the tube, as the difference between the 

 theoretical and the real discharges is too great to be 

 ascribed to friction. 



The following Table contains the effects produced by 

 tubes of different diameters, and under different alti- 

 tudes of fluid in the reservoir. 



TABLE IX. Containing the Quantities of Water dis- 

 charged by Cylindrical Tubes two inches long, ivith dif- 

 ferent Diameters and under different heads of Water. 



TABLE X. Comparison of the Theoretical with the Real 

 Discharges from an additional Tube of a cylindrical 

 form, one Inch in Diameter and two Inches long. 



From these results we may conclude, 



1. That the discharges by different additional tubes 

 under the same head of water, are nearly proportional 

 to the areas of the orifices, or to the squares of the dia- 

 meters of the orifices. 



2. That the discharges by additional tubes of the 

 same diameter under different heads of water are nearly 

 proportional to the square roots of the heads of water. 



It follows, from the two preceding corollaries, in gene- 

 ral, that the discharges during the same time, by diffe- 

 rent additional tubes, and under different heads of water 

 in the reservoir, are to one another nearly in the com- 

 pound ratio of the squares of the diameters of the lubes, 

 anil the square roots of the heads of mater. 



M. Bossut has deduced from the above experiments 

 the following Table, which contains a comparative 

 view of the theoretical discharges from a tube one inch 

 in diameter, with the real discharges by an additional 

 tube of the same diameter, under different heads of wa- 

 ter. The last column, containing -the ratio between 

 these two discharges, was computed by M. Prony. 



Discharge 

 of Water 



through 

 additional 



Tubej. 



Hence it follows, that the velocity in English inches 

 will be V = 22.47 </H for additional tubes. See p. 498. 

 col. 2. 



M. Prony has given the following formulae, as dedu- 

 ced from the preceding Table. The letters have the 

 same values as in p. 498. 



Q= 0.81 AT / 2 g H ; but since 2g is constant, and 

 is = 7.77125, we have 



Q = 4.9438 ^ 

 From which we obtain 



T = 



H = 



Y 4.9438 T ^ H' 



Q 



4.9438 d'' v/ H' 



Q 



(4.9438 & T) 2 ' 

 When the interior surface of the additional tube is 

 of a conical form, the quantities of water discharged 

 undergo considerable variations. M. Bossut made no 

 experiments whatever with tubes of this kind, but the 

 defect is fortunately supplied by those of the Marquis 

 Poleni, which are published in his work De Castellis 

 per qua derivantur Fluvium Aquae. 



On the to- 

 charge of 

 water bjr 

 conical 

 tubes. 



TABLE XI. Containing the Experiments of the Marquis Poleni, on the Quantities of Water discharged by Conical 



Tubes of different Diameters. 



