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Show The refinement which would result thereby in the solution of Equation ( 10) turns out to be negligibly small. When the avalanche front strikes the quiet air this is compressed, up to the damming pressure ps - Y _• w2/ 2g- This pressure increase produces compression waves, which precede the avalanche approximated with the velocity of sound, a. From the relationships of gas dynamics [ 10] for compression shock it follows for __ ir blasts of small intensity that: ( 13) Ap = ( YL/ g) a w In this equation a = 340 m/ sec: the velocity of sound in air w = the velocity of the air flowing behind the blast Y j - 1.25 kg/ m3 : the density of air If the reference plane is moved with the avalanche front, then the air flows toward this reference plane with the velocity of the avalanche front. If the velocity of material, w, in Equation ( 13) becomes equal to the velocity of the avalanche front, a frontal wave must form whose pressure increase is given by this equation. The frontal wave cannot be broken up into smaller pressure waves of finite size, since their material velocity would be smaller than the flow velocity, w; such waves are repulsed in the frontal wave. On the other hand waves with very small material velocity and pressure increase radiate continuously from the frontal wave with the velocity of sound. Similar phenomena are observed in the bow waves in front of ships or damming waves in front of bridge piers. The elemental pressure waves of intensity psemanating from the damming point of the avalanche front with the velocity of sound, a, accumulate in the frontal wave an average of t seconds with the result that the higher pressure A p is maintained there, that is: During this time the avalanche front has advanced approximately t • w. The distance by which the air blast precedes the avalanche is then ( 14) 1 = ( a - w) t = ( a - w) Ap/ a ps 3 2 For examples for w = 100 m/ sec and y L= 1.25 kg/ m , ps = 625 kg/ m , Ap = 4250 kg/ m2, and 1 = 5 m 2 for w = 50 m/ sec then ps = 156 kg/ m , Ap = 2125 kg/ m and 1= 12 m. The air blast precedes the avalanche farther the smaller the velocity of the avalanche, however at the same time the intensity of the blast decreases proportionally with the velocity. Experimental data for the verification of this simple attempt at calculation of complicated phenomena are lacking at the present time. On the other hand the effect of the air blast preceding the avalanche certainly has 30 |