HYDRAULICS.] tions ; DS is a graduated disk serving to measure the angles through which the apparatus oscillates. To this the friction disk is rigidly attached hanging in a vessel of water. The friction disks were from 47 to 77 inches diameter, and they generally made one oscillation in from 20 to 30 seconds, through angles varying from 360 to 6. When the velocity of the circumference of the disk was less than 6 inches per second, the resistance was sensibly proportional to the velocity. Bcaufoy s Experiments. Towards the end of the last century Colonel Beaufoy made an immense mass of experiments on the resist ance of bodies moved through water (Nautical and Hydraulic Experiments, London, 1834). Of these the only ones directly bearing on surface friction were some made in 1796 and 1798. Smooth painted planks were drawn through water and the resistance measured. For two planks differing in area by 46 square feet, at a velocity of 10 feet per second, the difference of resistance, measured on the difference of area, was 339 lt> per square foot. Also the resistance varied as the 1 949th power of the velocity. 66. Mr Fronde s Experiments. The most important direct ex periments on fluid friction at ordinary velocities are those made by Mr Froude at Torquay. The method adopted in these experiments was to tow a board in a still water canal, the velocity and the resist ance being registered by very ingenious recording arrangements. The general arrangement of the apparatus is shown in fig. 79. AA is the board the resistance of which is to be determined. B is a cut water giving a fine entrance to the plane surfaces of the board. CC is a bar to which the board AA is attached, and which is suspended by a parallel motion from a carriage running on rails above the still water canal. G is a link by which the resistance of the board is transmitted to a spiral spring H. A bar I rigidly connects the other end of the spring to the carriage. The dotted lines K, L indicate the position of a couple of levers by which the extension of the spring is caused to move a pen M, which records the extensions on a greatly increased scale, by a line drawn on the paper cylinder N. This cylinder revolves at a speed proportionate to that of the carriage, its motion being obtained from the axle of the carriage wheels. A second pen 0, receiving jerks at every second and a quarter from a clock P, records time on the paper cylinder. The scale for the line of resistance is ascertained by stretching the spiral spring by known weights. The boards used for the experiment were -jV inch thick, 19 inches deep, and from 1 to 50 feet in length, cutwater included. A lead keel counteracted the buoyancy of the board. The boards were covered with various substances, such as paint, varnish, Hay s composition, tinfoil, &c., so as to try the effect of different degrees 483 (3) The average resistance per square foot of surface was much greater for short than for long boards ; or, what is the same thing, the resistance per square foot at the forward part of the board was greater than the friction per square foot of portions more stern- ward. Thus, Varnished surface 2 ft. lon< 50 Fine sand surface 2 ,, 50 Mean UcMstance in lt> per sq. ft. 41 0-25 0-81 0-405 This remarkable result is explained thus by Mr Froude : "The portion of surface that goes first in the line of motion, in experiencing resistance from the water, must in turn communicate motion to the water, in the direction in which it is itself travelling. Consequently the portion of surface which succeeds the first will be rubbing, not against stationary water, but against water partially moving in its own direction, and cannot therefore experience so much resistance from it." 67. The following table gives a general statement of Ivlr Froude s results. In all the experiments in this table, the boards had a fine cutwater and a fine stern end or run, so that the resistance was entirely due to the surface. The table gives the resistances per square foot in pounds, at the standard speed of 600 feet per minute, and the power of the speed to which the friction is proportional, so that the resistance at other speeds is easily calculated. Length of Surface, or distance from Cutwater, in feet. 2 feet. 8 feet. 20 feet. 50 feet, A B c A B C A B C A B C 2-00 41 38 30 87 81 90 1-10 390 370 295 725 G90 730 880 1-85 1-94 1-99 1-92 2-00 2-00 2-00 325 314 278 626 583 625 714 26-1 2CC 263 504 450 488 520 1-85 1-93 1-90 1-89 2-00 2-00 2-00 278 271 262 531 480 534 588 240 237 244 447 384 465 490 1-83 1-83 1-87 2-00 2-00 250 246 474 405 488 226 232 423 337 456 Tinfoil 2-16 1-93 2-00 2-00 2-00 Calico Fine sand Medium sand Coarse sand Fig. 79. of roughness of surface. The results obtained by Mr Froude may be summarized as follows : (1) The friction per square foot of surface varies very greatly for different surfaces, being generally greater as the sensible roughness of the surface is greater. Thus, when the surface of the board was covered as mentioned below, the resistance for boards 50 feet long, at 10 feet per second, was Tinfoil or varnish 25 lb per sq. ft. Calico 47 Fine sand 405 Coarser sand 488 (2) The power of the velocity to which the friction is proportional varies for different surfaces. Thus, with short boards 2 feet long, For tinfoil the resistance varied as i> 2 16 For other surfaces ,, ,, r 2 00 With boards 50 feet long, For varnish or tinfoil the resistance varied as v l 8 * For sand r a-oo Columns A give the power of the speed to which the resistance is approximately proportional. Columns B give the mean resistance per square foot of the whole surface of a board of the lengths stated in the table. Columns C give the resistance in pounds of a square foot of surface at the dis tance stcrnward from the cutwater stated in the heading. Although these experiments do not directly deal with sur faces of greater length than 50 feet, they indicate what would be the resistances of longer sur faces. For at 50 feet the de crease of resistance for an increase of length is so small that it will make no very great difference in the estimate of the friction whether we suppose it to continue to diminish at the same rate or not to diminish at all. For a varnished surface the friction at 10 feet per second [5 diminishes from 41 to 32 per square foot when the " length is increased from 2 to 8 r^inn_r^injr_l feet, but it only diminishes ^nnnTTJTZ fVoni 0-278 to 0-250 Ib per - square foot for an increase from r_~ ~J~J~_T1- _ 20 feet to 50 feet. If the decrease of friction .sternwards is due to the genera tion of a current accompanying the moving plane, there is not at first sight any reason why the decrease should not be greater than that shown by the experiments. The current accompanying the board might be assumed to gain in volume and velocity sternwards, till the velocity was nearly the same as that of the moving plane and the friction per square foot nearly zero. That this does not happen appears to be due to the mixing up of the current with the still water surrounding it. Part of the water in contact with the board at any point, and receiving energy of motion from it, passes afterwards to distant regions of still water, and portions of still water are fed in to wards the board to take its place. In the forward part of the board more kinetic energy is given to the current than is diffused into sur rounding space, and the current gains in velocity. At a greater distance back there is an approximate balance between the energy communicated to the water and that diffused. The velocity of the current accompanying the board becomes constant or nearly con stant, and the friction per square foot is therefore nearly constant
also.
