506 



HYDRODYNAMICS. 



Exhaustion Michelotti made many experiments for determining 

 ofVessels. t ne rea i form of the vena cotracta. He constructed a 

 Michelotti'* g reat var i et y of ajutages resembling it, till he found 

 expert- one which gave the greatest discharge. This ajutage 

 menu. was formed by the revolution of a trochoid round the 

 axis of the jet. The diameter of the outer orifice was 

 S6, that of the inner orific.- 46, and the length of the 

 axis was 96. This ajutage gave.9S3l to 1000 as the 

 ratio of the real to the theoretical discharge. The fol- 

 lowing are Michelotti's results : 



Theoretical discharge 1.0000 



Trochoidal ajutage 9831 



Tube 2 diameters long 8125 



For a tube projecting into the reser- 

 voir, and flowing full .... 6814 

 For do. when the vein was contracted 5134 



SECT. V. Experiments on the Exhaustion of Vessels. 



On the ex- WE have already seen, in stating the general princi- 

 Imustioi. of pies of hydraulics, that a funnel-shaped cavity is form- 

 ed in the surface of a fluid, when, in the course of its 

 descent, it has nearly reached the orifice from which 

 the fluid is discharged. This circumstance renders it 

 impossible to determine the exact time in which a ves- 

 sel is completely emptied. The superincumbent pres- 

 sure of the head of water being removed by the for- 

 mation of the funnel-shaped cavity above the orifice, the 

 water is at last discharged in successive drops. M. Bos- 

 sut therefore abandoned the idea of attempting to mea- 

 sure the time of emptying vessels, and confined his ex- 

 periments to the determination of the time in which 

 the upper surface of the fluid descends through a cer- 

 tain vertical height in prismatic vessels, in which the 

 area of the horizontal section is constant. The follow- 

 ing Table contains the results of his experiments. 



TABLE XII. Shelving the times in which Prismatic Ves- 

 sels are partly exhausted. 



Altitude of the water in the reservoir 11.6666 Paris 



feet. 

 Constant area of a horizontal section of the vessel in 



square feet. 



vessels. 



The first column of the Table contains the diameter 

 of the circular orifice ; the second the depression of the 

 upper surface of the fluid in feet ; the third the time in 

 which the surfaces descend through this height, ac- 

 cording to experiment ; the fourth contains the time as 

 calculated from the formula in Chapter I. corrected 

 by substituting 0.62 A instead of A, in order to make 

 allowance for the effect of contraction. The numbers 

 in column fourth always err in defect, probably from 

 0.62 being taken too great. If the orifices are vertical, 

 the altitude of the fluid must be measured from their 

 centre of gravity. 



A few experiments on the partial exhaustion of ves- Exhausting 



sels were made by M. Venturi. An orifice, 4.5 lines in of y f " sel8 ' J 



diameter, was made near the bottom of a cylindrical -^". 

 i A r : i .i:_ _ TL -i*.-^ i .-.I vemurtj 



vessel 4.5 inches in diameter. The altitude of the wa- 



expen- 



ter in the vessel was 8.3 inches above the centre of the menu, 

 orifice. The Surface of the water was then depressed 

 7 inches in 27^ seconds. A cylindrical tube, of the 

 same diameter as the orifice, and 1 1 lines in length, 

 was applied to the same orifice. The vessel was filled 

 to the same height as formerly, and its surface descend- 

 ed 7 inches in 2 1 seconds of time. These experiments 

 were afterwards repeated under the receiver of an air 

 pump, in which the mercurial gauge stood only at the 

 height of 10 lines, and the surface of the fluid was de- 

 pressed 7 inches, whether the water flowed through 

 the simple orifice, or the cylindrical tube. 



SECT. VI. Experiments of Bossut on the discharge of Wa* 

 ter into a submerged Vessel. 



In order to examine the discharge of water into sub- 

 merged vessels, M. Bossut employed a vessel A BCD, 

 Fig. 1. two feet in diameter, in which a white-iron cy- 

 linder VMNT, 1 foot high, and 20 lines in diameter, 

 was immersed. This cylinder is supported on a tripod, 

 so that it can be set in a vertical line, and is furnished 

 with graduated scales for measuring the water which it 

 receives. The orifice in the cylinder VMNT being 

 shut, water is poured into the vessel till it reaches a cer- 

 tain height, and when the orifice is opened, the water 

 rushes in and fills the cylinder. The following are the 

 results of Bossut's experiments. 



On the dit- 

 ch arge of 

 water into a 

 submerged 

 vessel. 

 PLATE 

 CCCXIX. 

 Fig- 1. 



The fourth column contains the time, as calculated 

 from theory, which differs very considerably in the first 

 experiment from the observed time. M. Bossut ac- 

 counts for this, by saying, that at the first entrance of 

 the water, a jet is formed which penetrates the plate 

 of water in the cylinder VMNT, till it stands at a cer- 

 tain height, when the surface of the water becomes le 

 vel. Now as this jet will continue longer with small 

 than with large orifices, a greater quantity of water, in 

 proportion, ought to be discharged. Bassut also made 

 the following experiments. 



Exp. 1. When the water entered the cylinder by an 

 orifice one inch in diameter, it was necessary to im- 

 merse the cylinder 8 inches and 1 1 lines in the water 

 of the vessel, in order that the water might raise itself 

 to the upper margin VT of the vessel. 



Exp. 2. The bottom MN being wholly removed, the 

 cylinder required to be immersed 7 inches and 7 lines, 

 in order that the water might rise to the upper margin 

 VT. 



Exp. S. When a large plate of white-iron was put 

 round MN, it was necessary to sink the cylinder 6 

 inches 1 1 ^ lines, in order that the water might rise to 

 the upper margin VT. 



SECT. VII. Bossitt's Experiments on the Motion of Wa- Motion 'of 



ler in a Vessel crossed with Diaphragms. WM " in 



vessel with 



The experiments of Bossut on this subject were made diaphragm* 



