CHAP. IV., 6.] MECHANICS (OF FLUIDS.) DUBUAT VENTURI MR STOKES. 



89 



(412.) 

 Dubuat's 

 formulae 

 improved. 



(413.) 

 Viscosity 

 of fluids. 

 Venturi 

 Coulomb. 



(414.) 

 Three cases 

 Df fluid re- 

 sistance to 

 moving 

 solids. 



of induction, without any pretence whatever of pro- 

 ceeding upon the mathematical theory of fluids in 

 motion. The same views were ably expounded and 

 enlarged by Dr Robison in his excellent article on 

 Rivers and Resistance in this Encyclopaedia, through 

 which principally the theory of Dubuat became known 

 in this country. Indeed, viewed apart from the tech- 

 nical value of the enquiry, the research as to the na- 

 tural economy of rivers is a wonderful and striking 

 branch of terrestrial physics, and one which had long 

 afforded a subject of anxious and perplexing enquiries 

 to Italian engineers from the time of Leonardo da 

 Vinci, though comparatively little studied elsewhere. 

 The collected treatises of Italian authors form an 

 important body of hydraulic information. 1 The rivers 

 of the north of Italy, like those of Holland, conveying 

 vast masses of water charged with mud under very 

 feeble slopes to the sea, present a formidable difficulty 

 which compels attention, vast territories being in- 

 creasingly subject to inundation, as the beds of the 

 rivers are raised by deposition above the general level 

 of the soil. 



Dubuat's formulas have been modified, and made 

 to represent experiments better, by subsequent writers, 

 particularly by De Prony, Langsdorf, Eytelwein, and 

 Thomas Young ; and the discharge from mere orifices 

 has been discussed by numerous authors who have 

 given empirical co-efficients to represent the pheno- 

 mena. But little has been added to a philosophical 

 view of the real laws which govern the fluid motion 

 in this case. Nevertheless Savart and Magnus have 

 made some ingenious observations on the constituent 

 parts of effluent streams. 



The viscosity or imperfect fluidity of water is the 

 property most difficult to be taken into account in 

 these and other hydraulic problems. It is that which 

 causes the velocity of a stream to diminish from the 

 surface to the bottom, and from the centre to the 

 sides ; these proportions were also sought by Dubuat. 

 Each layer of water in motion exerts a dragging or 

 " tangential force" upon other layers, which from 

 any cause are comparatively quiescent ; and the ex- 

 periments of VENTURI about the end of the last cen- 

 tury, showing that a stream in motion draws towards 

 it the particles of still water with which it may be in 

 contact, with a force sufficient to overcome consider- 

 able hydrostatic pressure, attracted much attention. 

 About the same time Coulomb, with his usual ad- 

 dress, made experiments on the friction of fluids by 

 observing the rapidity with which cylinders oscillat- 

 ing by means of torsion in different fluids had their 

 original motion destroyed. 



Intimately connected with the friction, and conse- 

 quent mutual action of fluids, is the resistance which 

 they offer to the passage of solid bodies through them, 



and this favourite problem of mathematicians was 

 treated by Dubuat, in his inductive way, in an able 

 and practical manner. Three cases may be specified 

 on account of their theoretical or practical import- 

 ance : 1st, In the case of a body oscillating like a 

 pendulum, with small velocities, the body being im- 

 mersed in a resisting medium ; 2c%, The resistance 

 to vessels floating on and propelled through water ; 

 Sdly, The resistance of the air to projectiles whose 

 velocity is very great. 



Under the first head Dubuat made those ingenious (415.) 

 experiments long overlooked, but lately brought into Motion of 

 notice, which I have mentioned in the section onthe pendulum9 - 

 Pendulum in the chapter on Astronomy, Art. (246). 

 The cause of the neglect of these striking and original 

 observations has probably been correctly stated, by 

 saying that in them the pendulum was made subser- 

 vient to hydraulic experiments, and not the theory of 

 fluids to the improved use of the pendulum ; and they 

 were therefore overlooked by those whose studies were 

 connected with the pendulum and its applications. 

 The fact observed by Dubuat was, that a large mass 

 of air (or of water in the corresponding case) is car- 

 ried along with a pendulum in motion, and affects 

 in a sensible manner the time of vibration, quite in- 

 dependent of the diminution of gravity due to the 

 buoyancy of the pendulum. The moved mass of air 

 was proved by hanging a film of worsted from an 

 arm a foot long in advance of the moving sphere, 

 when it was found to be but slightly driven by the 

 inertia of the air through which the pendulum moved. 

 Dubuat significantly calls the mass of moved air " the 

 prow" of the moving body, and it is easy to antici- 

 pate the sort of effect which such a graduated con- 

 dition of the surrounding air from motion to absolute 

 rest would produce. 



But the most surprising thing is, that mathema- (416.) 

 ticians should have attempted to compute the effect, Professor 

 or should have been in any degree successful in doing Stokes's so- 



L AT. v a? j f T> 5 lutlon - De- 



so ; yet alter the preliminary ettorts ot roisson and fineg the 



Green, Professor STOKES has introduced for the first index of 

 time a correct definition of the " index of friction" of friction. 

 a fluid, and after great labour has succeeded in find- 

 ing exact expressions for the motions of a solid sphere 

 and cylinder. This investigation may be found in a 

 very elaborate paper in the Cambridge Transactions, 2 

 in which he solves the equations found by him in a 

 previous paper, 3 in the cases of pendulums having 

 the forms just mentioned. Another interesting re- 

 sult of his investigation is the immense effect of fluid 

 friction in retarding the fall of minute rain drops, 

 which he states to be such as to explain satisfactorily 

 the suspension of clouds. In the second part of the 

 paper I have first cited Mr Stokes proceeds to com- 

 pare his theory with the observations on the pen- 



1 Raccolta di Autori che trattano del moto dell' acque, 10 vols., 1822-26 ; and Nuova Raccolta, 1 vols., 1823-45. See also the 

 admirable methodized catalogue of writers on Hydraulics in the second volume of Young's Lectures on Natural Philosophy. 



2 Vol. ix. part ii. On the effect of the internal friction of Fluids on the motion of Pendulums. 



3 On the friction of Fluids in motion. Camb. Trans., vol. viii., part iii. 



