1880.] 



On the Friction of Water, fyc. 



57 



containing the fluid. Between the disk C and the outer cistern, how- 

 ever, is the light cylindrical copper chamber, AA, suspended by three 

 fine wires from a crosshead, B. EE is a diaphragm, which could be 

 moved up or down so as to alter the volume of water in the chamber 

 in which the disk rotates. K is a brake for regulating the speed of 

 the disk. W is the position of a counting arrangement for determining 

 the speed of the disk. G is a scale-pan in which weights were placed. 

 This was connected by a fine silk cord with an arc attached to the 

 chamber AA. The weight in this scale-pan exactly measures the 

 tendency of the chamber AA to rotate, in consequence of the rotation 

 of the fluid inside it. But since action and reaction are equal, the 

 tendency of the chamber AA to rotate is, when the motion is uniform, 

 exactly equal to the friction of the surface of the disk, DD. This 

 method of measuring the friction of the disk, by measuring the re- 

 action of the vessel containing it, was first used (so far as the author 

 is aware) by Professor James Thomson. A short note on some experi- 

 ments made in this way was communicated by him to the Royal 

 Society in 1855, but the details of these experiments have never been 

 published. The principle is the same as that employed by Mr. Froude, 

 in his "Fluid Dynamometer." The general results of the experi- 

 ments made with the apparatus described above are in striking 

 numerical agreement with Mr. Eroude's results, so far as the con- 

 ditions of the experiments are similar. But, from the small size of 

 the apparatus, it has been possible to vary the conditions somewhat 

 more than would be possible with the great canal of Mr. Froude. 

 The results obtained may be summarised as follows : — 



(1.) The resistance of disks of different diameters, but similar in 

 other respects, varies as the fifth power of the diameter nearly, or, 

 more exactly, as the 4* 85th power. 



(2.) The resistance varies with the roughness of the surface of the 

 disk to an extent quite as great as in the experiments of Mr. Froude. 



(3.) The friction increases in every case with the size of the 

 chamber in which the disk is rotated. This result was certainly 

 unexpected. Even if the increase of resistance is due to the increase 

 of the surface of the chamber, this result indicates another marked 

 difference between the phenomena of fluid friction at high and at low 

 speeds. At very low speeds the resistance would decrease considerably 

 as the size of the chamber increased. 



(4.) Roughening the surface of the chamber in which the disk is 

 rotated increases the resistance of the disk considerably; in some 

 cases the increase is as great as when the disk itself is roughened. 



(5.) The resistance of the disk at different speeds varies nearly as 

 the square of the speed. But the exact power of the speed to which 

 the resistance is proportional varies a little for different surfaces. The 

 indices of the powers of the speed to which the resistance is pro- 



