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Show 2 ^ o ( 17) z' + v^ / 2g + In this equation z' is the height of the points being considered measured from a horizontal reference plane and in one and the same flow line. In addition: J v = the velocity at the point under consideration Po + S / aP' Y the pressure head, which is dependent upon the Po compressibility, above the reference pressure head, p0 p- y2 = the specific pressure at the point being considered, and at the depth z below the surface of the avalanche being subjected to the damming effect. H = the energy head, i. e., the energy per unit weight of fluid at the point under consideration. With the postulate that during an avalanche the quantity of flow per unit time must remain approximately constant, Equations ( 4) and ( 17) show that the uniform contractions of the cross section of the gullies and ravines through which avalanches run cause increases in velocity as a rule, while during expansions the velocity is reduced in proportion to the velocity of lateral spreading. B. Compressibility of Snow a) The dynamic, elastic compression of snow is limited chiefly by the compressibility of the air in the voids; the framework of ice crystals gives only slight resistance to compression, while the compressibility of the ice itself is negligible compared to that of the material in the pores. Accordingly the compressibility of snow saturated with water also can be neglected here. Air in the pores is not completely expelled from the snow by high pressure. For dry snow the maximum density Y F obtained by rapid compression will correspond approximately to that of firmly consolidated firn snow ( Y F ~ ^ 00 kg/ m3), for coarse grained dry snow the upper boundary value can decrease to Y F ~ 600 kg/ m3t while for wet snow the upper boundary value of the liquid ( y p-_ 1000 kg/ m3) can almost be reached. The density of snow can be written: ( 18> Y = Y F ( 1- VL) + v L - r L where Vr denotes the volume of air which is expellable per unit volume; it can be expressed from the foregoing equation as: ( 18') VL = ( Y F - Y ) /( YF - Y L) ~ 1- Y / YF under atmospheric pressure, p0 = 1 atmosphere - 10,000 kg/ m2^ y is set equal to 34 |