660 WIND WINDERMERE able practical interests (such as the construc- tion of windmills, the art of gunnery, the the- ory of the pendulum, the driving of railroad trains, and the sailing of vessels), the twin ques- tions of the force of the wind and the resis- tance of air or water to moving bodies have been studied by very many eminent philoso- phers and experimenters. The results thus far obtained are almost entirely empirical. As re- gards the connection between pressure and velocity, the law announced by Newton, that the resistance should be as the square of the velocity of the moving body, is, for ordinary winds, sufficiently exact. The resistances or pressures vary directly as the density of the medium ; they even vary slightly in the air for the ordinary ranges of the temperature and barometer; but they vary in a remarkable manner with every change in the form and the dimensions of the resisting body. The laws of the variation of the resistance as depending on velocities and forms and dimensions can only be satisfactorily given in the shape of an abstract of the numerical results deduced from each experiment. In general, it may be said that a concave surface exposed to the wind offers greater resistance than an equal sectional area of plane surface, and that a convex surface offers less resistance than a plane. The resis- tance offered by any body depends quite as much on the configuration of its hinder as of its front portions. The resistance offered by a plane surface which is not normal to the wind is less than when it is normal; and it diminishes in proportion to the cosine of the angle of incidence. For normal incidence the resistance is not to any great extent dependent on the nature of the surface, /. ., whether it be rough or smooth. The determination by experiment of the actual pressure exerted by the wind is a very delicate matter. That which has been most widely adopted is known as the Smoaton or Rouse formula ("Philosophical Transactions," 1759), according to which the pressure in pounds avoirdupois on a surface of one square English foot is equal to 0*00492 mul- tiplied by the square of the velocity expressed in miles per hour; the pressures calculated by this formula are given in the following ta- ble. A more trustworthy formula was deduced by Muncke (1842) from the observations of Borda, Hutton, and Woltmann, according to which the above constant coefficient should be 0*00499 ; but the difference between the two is insignificant in consideration of the extreme variations which depend on the size and shape of the resisting object. In very recent times this important subject has received further elucidation by both theoretical and experi- mental methods. (See the works of Stokes, Rankine, Thomson, Duchemin, Russell, Robin- son, Saint- Venant, Oavallero, Dohrandt, &c.) Maxwell ("Proceedings of the Mathematical Society," 1870) has given theoretical formulas and curves showing the movements of the particles of an incompressible fluid streaming past a moving obstacle ; while Hagen (Berlin, 1872) has experimentally investigated these motions. Helmholtz (Berlin Monattbericht, 1878) has shown that for moderate velocities it is very approximately proper to consider the air as an incompressible fluid, free from fric- tion. Finally, Thiesen ( Wind-Repertorium, 1875) has made a careful theoretical study of the experiments of Hagen and Dohrandt, and established the rule that the pressure of the wind against an inclined rectangular plate is really very nearly proportional to the square of the velocity and the cosine of the angle of incidence of the wind, while the absolute value of the normal pressure is as given by Hagen's observations. The latter physicist (Berlin, 1874) has embodied the results of very care- ful observations at moderate velocities in a for- mula which, converted into English measures, is as follows : P=(0*0028934 + (KKX>14080)A* ; where the velocity v is expresed in miles per hour, the area A of the surface is in square feet, the perimeter p of the surface in linear feet, and the resulting pressure P is in pounds avoirdupois per square foot. By introducing the term p Hagen has expressed the fact that the pressure depends to a considerable extent on the shape aa well as the surface of the re- sisting body. The formula applies to piano surfaces placed normal to the incident wind, and assumes that the density of the air is that belonging to the barometric pressure, 29*84 in., and the temperature 59 F. For the resistance to shot at high velocities, see GUNNKKY. PRESSURE OF THE WIND. VELOCITY. ME88UEE PER SQUARE FOOT, POUNDS. MilM pr hour. Ft p MCOOd. Root* and SmwtoB, per (q. foot. H*cn. Circular platM Sqoan of on* tquan TrianguUr foot. 1 a 8 1*47 2-98 4-40 0*005 0-020 044 O-IXIM 0-014 0-080 0-008 0-014 0-081 n-oiii 0-014 0-082 4 6 10 i:, 20 25 80
- ,
M 40 CO 60 6-87 7-88 14-67 0-079 0-128 0-41)2 0-054 0-OS5 0-889 0-055 on,,; 845 0-057 0-OS-* B'M 22-00 29-84 89-67 1-107 1-968
- .,;.-,
-7fi8 1-856 2-119 ('777 1-882 2-159 0-795 1-418 2-208 44-01 61*84 68-68 4*429 6-027 7-878 8-053 4-154 5-426 8-109 4-282 6-527 8-180 4-828 5-658 66-01 78-85 88*02 '.i-<ir,:i 12-800 17*715 6>8M --IT, 12-208 Ml - ,;:;7 12*437 7-155 8-SN 12-719 80 100 117 ::>-, 146-70
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49-200 21-701 83-903 22-110 84*546 _'-' -r,i;i tt-M V l DKKMKKi:. an English lake, in Lancashire and Westmoreland, surrounded by gentle wood- ed eminences. It is about 11 in. long, and from a third of a mile to a mile wide, and its depth varies from 80 to 240 ft. Its outlet is the river Leven, discharging into Morecambe bay. It is abundantly stocked with fish.
