412 



HYDRODYNAMICS. 



Gugliel- 

 mini. 



Bcd 171o' 

 ' 



y 



History, matter of indispensable necessity among the different 



""V""' states of Italy, and hence a great number of valuable 



works were produced by the Italian engineers. 



The most eminent of these engineers was Dominic 

 Guglielmini, who was inspector of the rivers and canals 

 *" *^ e Milanese, an{ * wno obtained such eminence in 

 his profession, that a new chair on Hydrnmetry was 

 erected for him in the university of Bologna. In his 

 principal work, entitled La Misitra ddt acque Correnti, 

 he adopts the theorem of Toricelli, and founds upon 

 it a system of Hydraulics sufficiently beautiful in theory, 

 but utterly repugnant to experiment. He regards eve- 

 ry point in a mass of fluid as an orifice in the side of a 

 vessel, and as tending to move with the same velocity 

 with which it would issue from the orifice. Hence it 

 follows, that, since the velocities are as the square roots 

 of the depths of the orifices, the velocity must be greatest 

 at the bottom of a stream, and least at its surface ; and 

 that the velocity of a river must continually increase as it 

 moves. These results were so hostile to established facts, 

 that Gnglielmini himself attempted to reconcile them. 

 He had applied his theory to cases which occurred in 

 the Milanese, and to the motion of the Danube, and he 

 had seen, that the regular progress of the current was 

 often opposed by transverse motions, and by a sort of 

 boiling or tumbling motion which arises from ascending 

 masses of fluid. Hence he supposed that these causes 

 were sufficient to account for the errors of the parabo- 

 lic theory. Guglielmini had now become acquainted 

 with the labours of Mariotte, and in his work entitled 

 Delia nalura dell' Fiiimi, the first part of which appeared 

 in 1697,* and acquired great celebrity to its author, he 

 takes into account the retardation produced by friction 

 and other causes, This work consists of 1 4 chapters, the 

 three firstof which contain definition sand general notions 

 respecting the equilibrium of fluids, and the origin of 

 springs and fountains. In the 4th chapter he treats of the 

 motion of wat* falling vertically, or descending along 

 an inclined plane ; and he examines the various causes, 

 such as friction, the resistance of the air, &c. which 

 extinguish a part of its velocity, and render the theory 

 inconsistent with experiment. The 5th chapter treats 

 of the beds of rivers, their depth, their width, and their 

 declivity. The 6th chapter is an application of the 

 principles laid down in the 5th to the directions which 

 are taken by the beds of rivers. In the 7th chapter 

 he examines the various motions which are observed 

 under different circumstances in the waters of rivers, 

 and he thus follows the current from its source to its 

 embouchure. In chapter 8. he treats of the embou- 

 chure of rivers, either when they fall into one another, 

 or into the sea. In chapter 9. he considers the union 

 of several rivers, and the effects which result from it. 

 Chapter 10. treats of the increase or diminution of ri- 

 vers. Chapter 11. relates to the formation of tempo- 

 rary currents in times of rain. Chapter 12. treats of 

 regular canals, and the methods of deriving them from 

 rivers or reservoirs of water. Chapter 13. treats of the 

 drainage of wet land ; and chapter 14. of the precau- 

 tions which are necessary in changing the bed of a river. 

 In order to demonstrate the inconsistency of the Car- 

 Born 1C4?. tesian system of vortices with the laws of Hydraulics, 

 Died 1727. Sir Isaac Newton directed his particular attention to 

 the investigation of the manner in which the fluid vor- 

 tices could be produced and preserved, and he has given 

 the results of his inquiries in the 9th section of the se- 





Newton. 



cond book of the Principia, entitled, De Mutit Circultiri HUtorjr. 



Fli/i'lorum. In these elegant propositions, which are ' ~~ ' 



the 51st, 52d, and 53d, he lays down the hypothesis, ^ 



that the resistance which arises from the want of per- 



fect lubricity in fluids is ctfteris paribus proportional to 



the velocity with which the parts of the fluid are sepa- 



rated from each other ; and he demonstrates, that if a 



solid cylinder of infinite length revolves, with an uni- 



form motion, round a fixed axis in an uniform and in- 



finite fluid, the periodical times of the parts of the fluid, 



thus put into an uniform motion, will be proportional 



to their distances from the axis of the cylinder ; where- 



as, if a solid sphere is made to revolve in a similar man- 



ner, the periodical times of the fluid particles will be pro- 



portional to the squares of their distances from the cen- 



tre of the sphere. Hence it follows, from the equality 



of action and reaction, that the velocity of any stratum 



of the circulating fluid is a mean between the velocities 



of the strata by which it is bounded. In considering, 



therefore, the velocity of water in a pipe, as affected by 



viscidity and friction, it is obvious that the filaments im- 



mediately adjoining to the pipe will be greatly re- 



tarded. The contiguous filaments will be kept back 



by their adhesion to the others, and the velocity will 



thus increase towards the centre of the pipe, according 



to a law which is easily deducible from the principle ( 



that the velocity of any filament is a mean between lha 



velocities of the filaments which surround it. M. Pilot 



was the first person who took advantage of this impor. 



tant principle, and, in the Memoirs of the Academy for 



1728, he shewed, that the total diminution of velocity 



in pipes of different kinds is inversely as the diameters 



of the pipes. 



In the second book of the Principia, ( See Prop. 36. ) Newton's 

 Newton has investigated the motion of fluids when is- Cutcruit. 

 suing from an orifice made in the bottom of a vessel, 

 without limiting himself to the hypothesis of an infi- 

 nitely small orifice. Supposing the water to be al- 

 ways kept at the same height in the vessel, he consi- 

 ders the cylindrical mass of ftuid as divided into two 

 parts, one of which is in the centre of the vessel, and 

 moveable ; while the other, which is immoveable, is 

 formed by the part of the fluid in contact with the 

 sides of the vessel. The central portion, which New- 

 ton calls the Cataract, is supposed to have the form of a 

 hyperboloid, formed by the revolution of a hyperbola of 

 the 4-th degree round the axis of the cylinder. The ho- 

 rizontal strata of the cataract are always in a state of gra- 

 dual descent; while all the rest of the fluid is absolutely 

 at rest, as if it had been converted into ice. From this 

 manner of considering-the subject, it followed, that the 

 water ought to issue with a velocity equal to that which 

 it would acquire by falling through the height of the 

 fluid ; but when Newton came to investigate the sub- 

 ject experimentally, he concluded, that the velocity of 

 efflux was only that which was due to half the height 

 of the fluid. This result, however, was in direct oppo- 

 sition to the known fact, that jets of water rise to near- 

 ly the same height as their reservoir*, and the error 

 arose from his not having attended to the contrac- 

 tion of the fluid vein, (or vena eontracla) which he af- 

 terwards found to take place in such a manner, that, 

 at the distance of nearly a diameter of the orifice from 

 the orifice itself, the section of the vein of issuing fluid 

 is reduced or contracted in the ratio of 1 to the square 

 root of 2, or of 1 to 1.4142. He accordingly corrected 



* The second part of this work did net appear till after his death in 1712. The whole was published with notes by Manfredi in tbt 

 .\vvta racwlta di Biitori eke traltanu delmoto delt' arque, torn. ii. 



