a. Use dimensional analysis to establish the cube-root law: for scaling of explosions, where r is the

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a. Use dimensional analysis to establish the cube-root law:

1/3 r ( 2 ) / = constant

for scaling of explosions, where r is the radius or depth of the craterρ, is the density of the soil medium, and W the mass of the explosive.

b. Use dimensional analysis to establish the one-fourth-root law:

1/4 T (PE)" pg r  = constant

for scaling of explosions, where r is the radius or depth of the crater ρ is the density of the soil medium, g is gravity, and E is the charge energy of the explosive.

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A First Course In Mathematical Modeling

ISBN: 9781285050904

5th Edition

Authors: Frank R. Giordano, William P. Fox, Steven B. Horton

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