HYDRODYNAMICS. 



511 



Motion f irnich greater cffi ct on the fluid in the axis of the small 

 Wa-er , u O ii the fluul in the axis of the ^reat one. 



_ the six first experiments with the six 

 it will be seen that as the height of 

 reservoir i increased, the diminution 

 of discharge, and consequently of velocity, is also in- 

 creased. This fact is analogous to what takes place in 

 the friction oi solid bodies, which in general increases 

 with the velocity. Perhaps, however, it may yet be 

 found, that when a very great velocity i* given to the 

 water, its velocity may be augmented, as Coulomb 

 found it to be in some cases in solid bodies. From the 

 above experiments, M. Bossut concludes in general, 

 that the quantities of water discharged in equal times 

 General by a horizontal pipe under the same height of water in 

 -> .-. the reservoir, and for different lengths, are to one ano- 

 ther in Ike im-ersf ratio of the square root* of the 

 lengths, provided that these lengths are not very diffe- 

 rent from one another. Honce, when we know by ex- 

 periment the quantity of water discharged for a given 

 length of pipe, we may find the quantity discharged 

 for any other length. Since the diminution of velocity 

 i* greatest when the head of water is small, we may 

 conceive the head of water to be reduced to such a de- 

 gree, that the velocity with which the water enters the 

 pipe is not sufficiently powerful to overcome the resist- 

 ances arising from the friction upon the pipe, and the 

 mutual cohesion of the particles of water. In order to 

 examine this point experimentally, M. Bossut employed 

 a head of water only 16 lines, from which the water 

 flowed into the two preceding pipc-. when their length 

 was a hundred and eighty feet. In this case the water 

 was discharged in the form of a narrow fillet, and tlie 

 drops succeeded each other almost as if they were in- 

 sulated bodies. Hence it follows, that in order to have 

 perceptible and continuous discharge from conduit 

 pipes, there should be a head of water of about tf> line* 

 in 180 feet. If the current of water, however, is very 

 large, such a great declivity a* this will not be neces- 



. As the preceding experiments relate only to pipes 



placed horizontally. M.Bosaut proceeds to the considera- 

 ^p tion of vertical and inclined pipes. In the case of a 

 vertical pipe, it is obvious that lU motion will be acce- 

 lerated during it* descent through the tube, as appear* 

 in the experiment of Venturi already described. When 

 the pipe is inclined, a similar acceleration take* place 

 when the inclination i* considerable ; for if the angle of 

 inclination were only 1 degree, the reai*Unce* which 

 the fluid experiences would more than counterbalance 

 the acceleration of gravity. 



The following Table contain* Bossut's experiment* 

 with a pipe, which formed the hypothenute of a right 

 angled triangle, the hypothenuse being to the altitude 

 of the triangle a* 2184 to 241. It* diameter was 16 



TABLE II. On the Quantity of Water discharged by in. 

 ' Pipe* of different lenftAt. 



10 

 10 

 10 



PI* 



16 hues. 



M 

 16 



Length of the 



!'!'- 



Number c/osHe 

 bad 

 in a 



59 feet. 

 118 

 177 



MM 



Now, an additional tube of the tame diameter, and 

 with the same hkd / water, would have discharged 



5779 cubic inches in a minute, which is less than that Motion i 

 which is discharged, by the preceding pipes. By dimi- Water in 

 nishin}:. however, the inclination of the above pipes, 

 they would be brought to give the same discharge as 

 the additional tube. This equality of discharge will 

 take place when the inclination of the pipe is 6 31', or 

 when the depression of the lower extremity of the pipe 

 is one- eighth or one-ninth of its length. In this case 

 the velocity, arising from the relative gravity of the wa- 

 ter, is exactly counterbalanced by the resistance which 

 the water experiences in the pipe. 



On the Motion of Water in Bent Pipet. 



In order to determine the effects of flexures or 

 bendings in conduit pipes, M. Bossut made the fol- 

 lowing experiments. The pipe* were perforated with 

 sm*ll holes to facilitate the ascent of the air. At the 

 end of each pipe was soldered a tube M, about two 

 inches in diameter, which communicated with the 

 smallest of the reservoirs already m-niioned. This ad- 

 ditional tube is furnUhed with a stopcock R, perforated 

 with an aperture of more than 18 lines in diameter. 



TABLE III. Shewing the quantities of Water discharged 

 by rectilineal and curvifint 'at leaden Pipes, SO feet long, 

 1 inch in diameter, and I line thick. 



PtAT* 



CCCXIX. 

 Kiga. 6, 7, 

 8. 



It appear* from this Table, that a curvilineal pipe, 

 in which the flexures lie horizontally, discharges lesa 

 water than a rectilineal pipe of the same length, and 

 that a still greater diminution takes place when the 

 flexures are placed in a vertical plane. When there i 

 a number of contrary flexures in a large pipe, the air 

 sometimes lodges in the highest parts of the flexures, and 

 greatly retard* the motion of the water. This effect 

 may be prevented by air holes, or by stop-cocks, which 

 can be shut when the motion of the water is perfect- 

 ly established. 



A* the pipe* employed by M. Bossut were extremely 

 abort, be baa endeavoured to supply this defect bv 

 combining them with the experiments made by If. 

 Couplet at Versailles, with pipe*, several of which were 

 more than one mile, and one nearly three miles long 

 The results we shewn in the following Table. 

 1 



