| OCR Text |
Show everywhere to the static pressure at the wave front, if this curves in such a way that its inclination, a , to the flow direction everywhere fulfills the condition sin a = z/ h where z denotes the depth of the point observed below the undisturbed surface of flow. As an example, for Y 0 = 10° kg/ m3 , y . = 1.25 kg/ m3, g = 10 m/ sec » £= 500 m/ sec2, h= 3m, ty = 30° , according to Equation ( 10): y = 15.6 kg/ m , according to Equation ( 9) with m = 1: h = 39 m, and from Equation ( 4'): v - 100 m/ sec. By disintegration and aereation, that is by increasing the height and proportionally reducing the flow resistance, powder avalanches reach astonishingly high velocities, whose origin until now remained unexp-plainableto most observers. Quantitative data were given for this for the first time by the very valuable measurements of Canton Forester Dr. M. Oechslin L4 J. Ing. A. Roch, SLF, Davos, made possible their evaluation, on the basis of meteorological statistics, by later determining the snow heights existing at the time of the avalanche falls described by Dr. Oechslin. The first impression which one obtains from Figure 23 had almost lead to the rejection of any theory, especially the fundamental Equation ( 4). However, when the value for Y from Equation ( 10) is introduced into Equation ( 4T), the following astonishing consequence results: ( 11) v2 = 2 g h ( Y J Y L> ( 1 + m) that is, if the slope inclination permits a disintegration of the snow, the velocity of powder avalanches is actually not dependent upon the slope inclination and the results of the evaluation of the measurements, incomprehensible at first ( Figure 23), furnish real evidence for the essential correctness of the preceding theory. On the other hand according to Equation ( 4') for all other kinds of avalanches the square of their velocities is proportional to the height of the naturally deposited snow. This the evaluation of the available measurements clearly confirms ( Figures 23 to 25), although these measurements correspond to very variable situations and therefore ( especially because of the variability of the densities) give rise to considerable scatter. The velocity, w, of the avalanche front is at any given time somewhat smaller than the flow of velocity, v, of its central part given by Equation ( 11), since the damming pressure at the avalanche front causes back eddying of the snow similar to that which the airstream shows during the intrusion of cold air into a valley. At a reference plane moving with the avalanche front the air strikes with a velocity, w, while behind it the snow flows with the velocity v - w. The continuity of the pressure distribution through the avalanche front is maintained according to from which ( 12) 2 2 ( y/ 2q) ( v - w) = ( y / 2g) w = v/( l +[ Y L/ Y ] 1/ 2) 29 |
