a Show that the products 1 , 2 , 3, 4 for the refined explosion model presented in the text are dimensionless products b Assume is essentially constant for the soil being used and restrict the explosive to a specific type, say TNT Under these conditions, is essentially constant, yielding 1 f ( 2 , ...

a To show that the products 1 2 3 4 for the refined explosion model are dimensionless products we ne ...

a. Show that the products 1 , 2 , 3, 4 for the refined explosion

Question:

a. Show that the products П₁,Π₂,Π_3,Π₄ for the refined explosion model presented in the text are dimensionless products.

b. Assume ρ is essentially constant for the soil being used and restrict the explosive to a specific type, say TNT. Under these conditions, ρ/δ=is essentially constant, yielding ∏₁= f (∏₂,∏₃) You have collected the following data with ∏₂ = 1.5 ×10^–6.

i. Construct a scatterplot of ∏₁ versus ∏₃. Does a trend exist?
ii. How accurate do you think the data are? Find an empirical model that captures the trend of the data with accuracy commensurate with your appraisal of the accuracy of the data.
iii. Use your empirical model to predict the volume of a crater using TNT in desert alluvium with (CGS system) W = 1500 g, ρ = 1.53 g/cm³, and ∏₃= 12.5.

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