1880.J On the Friction of Water, fyc. 55 



these cases, the motion of the fluid is complex, and the observations 

 themselves are difficult. The principal direct experiments on fluid 

 friction are those of Coulomb and of the late Mr. W. Froude. Cou- 

 lomb's experiments were made by oscillating a thin disk, suspended in 

 the fluid by a wire, in its own plane. The gradual diminution of the 

 range of the oscillations gave a measure of work lost in fluid friction, on 

 the surface of the disk. Coulomb's experiments were made at very low 

 velocities, and, indeed, the method which he employed would be quite 

 unsuitable for greater speeds of oscillation. The results at which he 

 arrived were these : — (a.) The frictional resistance to the motion of 

 the disk varied nearly as the velocity ; (b.) The friction was nearly 

 independent of the roughness of the surface ; (c.) The friction was 

 very much increased if the viscidity of the fluid was increased. 



Mr. Froude 's experiments were made in a very different way. 

 He towed boards of lengths varying from 5 to 50 feet, in a still 

 water canal, and measured by a spring dynamometer the resistance to 

 the motion. His experiments were all made at speeds much higher 

 than those employed by Coulomb. His results may be summarised 

 thus : — (a.) The friction varies nearly as the square of the velocity of 

 the board, the precise index of the speed to which the friction is pro- 

 portional depending on the nature of the surface of the board ; (b .) The 

 frictional resistance per square foot of the surface of the board is 

 greater for short than for long boards ; (c.) The frictional resistance 

 varies very greatly with the roughness of the surface of the board. 



The differences between the results of the experiments of Coulomb 

 and Froude show that the phenomena of fluid friction at very low 

 and at high speeds are essentially different. It appeared to the author 

 that it would be useful to make some experiments at speeds similar to 

 those in Mr. Froude's experiments, but with an apparatus on a smaller 

 scale, which would permit a greater variation of the conditions of the 

 experiments. A series of disks, of 10 inches to 20 inches in diameter, 

 were rotated in water by an engine, and the resistance to continuous 

 rotation at different speeds was measured. Thus the experiments 

 were virtually the same as Mr. Froude's, but with a surface of infinite 

 length substituted for surfaces of limited length. The roughness of 

 the surface of the disk was varied, the smoothest disks being of 

 turned and polished brass ; the roughest having surfaces of sand and 

 gravel cemented on to the metal disk. 



The disks were rotated in a cylindrical chamber, the size of which 

 could be varied, so that the mass of water operated on, or the thickness 

 of the layer of water in contact with the disk, could be modified at 

 will. Further, the roughness of the surface of the chamber in which 

 the disks were rotated was varied in the same way as the roughness of 

 the disks themselves. To determine the effect of the viscidity of the 

 liquid in altering the amount of friction, experiments were made with 



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