Vol Lecture Notes 7

Why do they move so fast and so far model of sparks

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Unformatted text preview: Sparks and others (1978) Definition of key parameters in Sparks et al. (1978) model. 9 Governing Equations C o n tin u ity ( m a s s c o n s e r v a tio n ) e q u a tio n uhr = u0 h0 r0 E n e r g y c o n s e r v a tio n ! "u "u + !u = g sin(#$! ) % 0.5 c f !u 2 h "t "r u: velocity, ρ: bulk density of flow, ∆ρ: difference between density of flow and atmosphere, α, slope, cf: between drag coefficient of surface, h: flow thickness, g: drag acceleration of gravity, r: radial distance from vent; acceleration subscript 0 denotes initial values. A s s u m e h ig h R e y n o ld s N o . ( i.e . n e g le c t v is c o u s fo r c e s ) . Ignimbrite Flow Model Flow down a volcanic slope of 15°, flattening to 1° after 8 km. Coefficient of drag 0.005 to 0.02 Initial velocities easily exceed 100 m/sec (360 km/hr) Acceleration down steep slope, Flow slows to a steady state 25-50 m/s as it reaches lower slope and spreads radially. Steady state achieved when gravitation energy matches frictional energy. 10 Ignimbrite Flow Model Init...
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