HYDRODYNAMICS. 



417 



have been expected from theory. M. Bossut has shewn, I! : 

 that when the height of the reservoir is increased, the ^^ 

 diminution in the discharge of the water is less sensi- 

 ble. He points oul the law, according to which the 

 rge diminishes as the pij>e becomes longer, or 

 number of its bendings is increased. In con- 

 sidering the motion of water in open canals, he first 

 examines the law, according to which the friction di- 

 minishes the velocity of the stream in rectangular ca- 

 nals ; and he shews, that in an open canal, with the 

 same height of reservoir, the same quantity of water 15 

 always discharged, whatever be it* declivity and it> 

 length ; whereas in pipes there is a very remarkable- 

 variation, by a variation in its declivity and its length. 

 He found, that the velocities in a canal are not as the 

 square roots of the declivities ; and that at an equal de- 

 clivity and an equal depth of the canal, the velocities 

 are not a* the quantities of water discharged. The sub- 

 ject of river* next occupies the attention of our author. 

 He consider* the variations which take place in the ve- 

 locity and level of the waters when two rivers unite, 

 and the manner in which rivers form and establish 

 their beds. He next treats of the formation of ban at 

 the mouths of rivers, or at the junction of two ru 

 he points out the means which may be successfully 

 employed, either in removing wholly or in part these 

 dangerous bank* ; and he concludes this pan of his 



the bottom of which he fitted different adjutages for 

 the efflux of the water. Whether this vessel was kept 



intly full, or emptied itself without any supply, 

 he observed that all the particles descended at first 

 vertically, but at a certain dUtance from the orifice the 

 lateral particles began to turn from their vertical direc- 



towards the orifice ; so that they entered the orifice 



its circumtert nee with an oblique motion, which, 

 continuing during a certain time, caused the effluent vein 

 of fluid to have the form of a truncated conoid, whose 

 greatest bate was the orifice itself, the smaller base being 

 a vertical section of the fluid, at a certain distance from 

 the orifice. Beyond thij section, which Newton called 

 the vena contracta, the fluid vein preserved its cylindri- 

 cal form. Bossut found the height of the conoid to be 

 nearly equal to the radius of the orifice, and it* bases 

 to be in the ratio of three to two. He expected to 

 have been able to employ this conoid as one of the 

 element* for determining the quantity of water dis- 

 charged ; but subsequent experiments convinced him 



this was impracticable. The contraction of the 

 fluid vein, which Bowut has so well explained, can- 

 not be removed, a* Daniel Bernoulli maintained, by 

 applying a small tube to the orifice; for though the 

 quantity of water discharged M thus increased, yet it is 

 never so great a* if all the filament* of the fluid had 

 issued in Tine* perpendicular to the plane of the orifice. 



Bowut's next object was to perform a complete set of wort, by determining the change which takes place in 

 experiment* on the quantities of water discharged by the depth of a river, when any change takes place in 



t-i in thin plates, and by additional tubes fitted to the width of it* bed, a* happen* from the construction 



these orifice*. When the orifice w* very small in com- ~* ~ * :J ' * ' : ~~ "' ' 



parison with the sise of the v case I, he found that the 

 theoretical law that the quantity of water discharged 

 was a* the product of the line by the orifice, and the 

 squ.ire root of the height of the reservoir was suffi- 

 ciently correct, and might be employed in ordinary 

 practice. Rut when the water flowed through an ori- 

 fice in a thin plate, the contraction of th vein of fluid 



>hcd the 



sixteen 'to ten; and when the fluid was discharged, 

 through an additional tube, two or three inches long, 

 so a* to follow the side* of the tube, the theor 

 discharge wa* diminished only in the ratio of sixteen 

 t . thirteen. In examining the effect* of friction and 

 contraction, Boscut found, that -mall orifices dischar- 

 ged less water in proportion linn great one*, on ac- 

 count of friction ; ana that as the height of the re- 

 servoir augments, the contraction of the fluid vein al- 

 so augment*, and consequently the quantity of water 

 discharged diminishes. . By combining these two cir- 

 cumstances, he has fiirni-lu- , the mean* of 



with precision the quantities of water 

 vered, either by simple orifice* or tube*, whether tlir 



1 i* kept constantly full, or allowed to empty itself 



it any supply. 

 Botsut next proceed* to consider the motion of jet* 



r,f -Ajter. He (lit. r, Mine- t!ie i:....t -iiiuble torn: that 



of a bridge ; and by ascertaining the depression of it-. 



level when a pert of the river iz turned aside for any 



useful purpose. 



The experiment* of Bossut, on the resistance and per- ExrCT1 - 

 tation of fluid*, were made with singular care. His m j, u of 

 rs* trials, which were published in 1771, related chief- Bossut. 



ajjajjBfj 



first trials, which were published in 1771, related chief- Bossut. 

 ly to the impulse of a vein of fluid against a plain sur- D'Alcni- 

 fice ; but he afterwards extended them to many more bwt - "<* 



theoretical discharge in the ratio of useful question*. In the year 1775, the celebrated Con ^ orK << 



Turgot, comptroller-general of the finance* of France, J^V of 



ted Bossut, D'Alembert, and Condorcet, as a faU*. 

 commission, for the purpose of executing a new set of A.D. 1771. 

 experiment* on the resistance which fluids oppose to 

 the motion of bodies of various Ion in. These experi- 

 ment* were made almost tolely by Bossut, within the 

 grounds of the I-'cole Militatrc at Paris, in a bason of 

 water 100 feet long. 53 feet wide, and (i', feet deep; 

 and the result* which they obtained were published 

 in 1777, in a separate work, entitled Ktperifncet tur It 

 rtiittaicf dri f'LiJu. According to theory, the impulse 

 upon a plane surface i* equal to the area of the surface 

 multiplied by the square of the velocity of the fluid, 

 and the square of the sine of the angle of im-id, 

 Boasut found that this measure of the resistance wa* sen- 

 sibly correct, when the fluid impinged perpendicularly 

 upon the surface ; that the deviation from the theory 



increased with the angle of incidence; but that the 



given to the adjutage*, and the best proportion theory might still be employed when this angle was 

 diameter of the adjutage and that of the not lew than 50. A* the fund* intrusted to the com- 

 pipe n which the water is conveyed. Hence we are mission had been managed with the utmost economy, 



Bossut employed the surplus in deteruiiniog the re- 

 sistance experienced by all kinds of prows, whether 

 plane, angular, or curvilineal. These experiment* were 

 performed in 1778, and were published in the Memoir* 

 of the Academy for that year. He next made a num- 



, . 



able to obtain the beet possible effect* for the decoration 

 of garden* or public building*. 



As the conducting of water i* one of the most im- 

 portant and useful branches of hydraulics, Bossut 

 made a great variety of experiment* on the motion 



of water in canal* and pipe*. The effect of friction, ber of experiment* on the effect* of undershot and 



M* or bending* in the pipes, is so re- overshot water wheels. The former he found to give 



rkable, that the quantity of water actually delivered a maximum effect when the velocity of the stream wae 



f be twenty or thirty time* lew than what might to that of the wheel a* five to two, while the elfect of 



VOL XI. PART II. 3 



