When, however, we have to deal with a physical roughness, the conditions are altered, and in order that the theory should apply, the scale of the roughness, i.e., the coarseness of the sand, must be increased as the length of the plane is increased; that is to say, the contour of the protuberances that constitute the roughness of surface becomes part of the geometrical form of the body. Thus, in the example quoted, the roughness, and so the resistance, is less on the 8 feet and 20 feet planes than it should be, and so the results are not comparable. In all probability the difference between the values of the resistance for varnish, paraffin, and tinfoil is due to some difference in the physical roughness of these bodies, and so we shall expect to find the best agreement with theory in the case of tinfoil (which shows the smallest co-efficient); this is actually the case.
§ 49. Dines' Experiments.—The most suggestive experiments of Dines are those in which wind planes of different area are balanced about a vertical axis and the relative pressure so determined. Mr. Dines found that the pressure on normal planes does not increase in proportion to their area, but is proportionately greater on small than on large planes. The actual results obtained by observations on planes 6 ft. by 7 ft., 3 ft. by 3 ft., and 1 ft. 6 in. by 1 ft. 6 in., were that the pressure per square foot on a plane 6 ft. by 7 ft. is only 78 per cent. of that on one 3 ft. square, and that on the plane 3 ft. square is 89 per cent. of that on the 1 ft. 6 in. square plane. The actual velocity of the wind in which these experiments were made is not stated.
On the other hand, Mr. Dines specifically states that he finds the wind pressure on the normal plane and on bodies generally varies strictly as the square of the velocity, a result which it is difficult, in view of dimensional theory, to harmonise with the above experiments.
It is probable that the departure from the V2 law is less than
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