544 



HYDRODYNAMICS. 



Resistance 

 of Fluids. 



Resistances 

 in a narrow 

 canal. 



On the re- 

 sistances of 

 prows of 



different 



ioims. 



TI.ATJ: 

 e:ccxix. 



Fig. 10. 



a greater resistance when the waters of the canal were 

 low ; but no precise measure of this increase of resist- 

 ance, nor any explanation of its cause, were given till 

 Bossut published his experiments. The following were 

 the general results which he obtained. 



1. That in narrow canals the resistances are propor- 

 tional to the squares of the velocities, following the 

 same law as in a fluid of indefinite extent. 



2. That the resistances in narrow canals, and canals 

 which have little depth, is greater than in fluids of 

 indefinite extent. 



The cause of this is obvious. When the velocity of 

 the body is considerable, the fluid which that body 

 pushes before it has not liberty to expand itself on every 

 side, but forms a current more or less rapid as the ve- 

 locity of the body is more or less great. If the body 

 entirely filled the canal, it would push all the water 

 before it like the piston of a pump ; but as, in narrow 

 canals, there is always some room for the water to run 

 both below the boat and at its sides, a part of the fluid 

 escapes in this way, while another part is driven back ; 

 and in this way a variety of contrary currents are form, 

 ed, by which the resistance is increased. This aug- 

 mentation of resistance is produced, not only by the 

 heaping up of the fluid on its anterior part, but also by 

 the want of hydrostatical support behind. 



The preceding results furnish an excellent lesson to 

 the engineer, in so far as they point out the advantage 

 of making all canals of navigation as wide and deep as 

 is consistent with a proper economy. 



In 1778, M. Bossut undertook, in conjunction with 

 Pondorcet, a series of experiments, the object of which 

 was to determine the law according to which the resist- 

 ance varied in an indefinite fluid like the sea, by vary- 

 ing the angle of the prow of a vessel from a straight 

 line, or 180, to an angle of 12. These experiments 

 were made in the great reservoir, now destroyed, which 

 formerly existed on the north side of the Boulevards of 

 Paris. This reservoir was 200 long, 100 wide, and 

 8 1 deep. The form of the apparatus employed is 

 shewn in Plate CCCXIX. Fig. 10. where MQNOP 

 is the small vessel. The prow, MQN, had various 

 angles, from 180 to 12. The vessel was drawn along 

 by a cord C attached to its centre of gravity, which 

 passing below a pulley on the same level with c, rises 

 nearly in a vertical line, and passing again over a pul- 

 ley descends and is attached to the weights, by the 

 descent of which the motion of the vessel is produ- 

 ced. A rope QR stretching across the whole length 

 of the reservoir, serves to regulate the motion of the 

 vessel. The vessel was then brought, by another 

 rope fixed at o, to one end of the reservoir, and the 

 time in which it described 96 feet uniformly by dif- 

 ferent weights suspended to the end of the rope, was 

 carefully measured by an excellent seconds watch. 

 Each experiment was repeated five times, and the mean 

 of these times was adopted as the true measure. The 

 general results of these experiments are given in the 

 following Table, and compared with those given by the 

 ordinary theory. The Table contains the resistances 

 for fifteen different kinds of prows, The base MN 

 Fig. 10. remains always the same, while the angle 

 MQN of the prow, formed into an isosceles triangle, 

 ia made variable. 



Comparative Table of the Resistances experienced by 15 

 Angular Proms, as deduced by Bossut from his Ex- of Fluid! 

 periments. ""/* 



I hi Bust 



The results in column third, as given by the ordina- 

 ry theory, are calculated by the formula 1000 Cos. 2 x, 

 x being the angle of the prow. In order to obtain a 

 formula which will express the law of the experimen- 

 tal resistances, Bossut observes, that when the angle x 

 undergoes a variation of 12, each of the angles at the 

 base of the isosceles prow will vary 6. Calling this va- 

 riation q, Bossut finds that the experimental resistance 

 may be expressed by the formula 



( v \3.25 

 ) 



This formula, however, though it answers well for 

 prows with large angles, yet when the angle is small, 

 it errs considerably in excess. In a prow of 12, for 



example, the term 3.153 ( \ becomes 4766 in- 

 etead of 3631. 



2. Account ofDu Buat's Experiments. 

 The attention of Du Buat was first directed to the de- 

 termination of the resistance experienced by an immove- experime 

 able surface, when struck by an insulated vein of fluid, on the hi 

 whose area is either greater than, or equal to, the area pulse of i 

 of the surface. In order to measure this resistance, he vein of fit 

 balanced it by a column of fluid, the height of which 

 measured the height due to the impulse. A tube of 

 glass, about 1^ lines of interior diameter, was bent into 

 a right angle at its lower extremity. Into this bent 

 part were fitted different surfaces for receiving the im- 

 pulse of the fluid vein, which was to be balanced by 

 the weight of column which ascended in the tube. 



The result of these experiments was, that the height 

 due to the impulse is the same as the height due to the 

 velocity of the vein ; whereas Bossut made it equal to 

 the height due to twice the velocity. Du Buat accounts 

 for this difference with great success. The vertical 

 vein of fluid in Bossut's experiments, enlarged itself in 

 striking the surface upon the balance ; and the fluid fila- 

 ments took a horizontal direction, after they had given 

 the shock to the surface. The resistance, therefore, 

 measured by Bossut was not merely the impulse of a 

 vein whose diameter was that of the orifice, but also the 

 additional pressure of a ring of fluid of a certain extent, 

 I 



