Use Dimensional Analysis to Determine the Explosive Force of a Bomb 

Find an expression for the energy of an explosion in terms of mass density, radius, and time.

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X energyExpression = DimensionalCombinations[{ QuantityVariable["MassDensity"], QuantityVariable["Radius"], QuantityVariable["Time"] }, QuantityVariable["Energy"]]

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Find the energy of an explosion for particular values of mass density, radius, and time.

In[2]:=

X energy = energyExpression /. { QuantityVariable["MassDensity"] -> Quantity[1, "Kilograms"/"Meters"^3], QuantityVariable["Radius"] -> Quantity[140, "Meters"], QuantityVariable["Time"] -> Quantity[0.025, "Seconds"]} // First

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Convert the energy to kilotons of TNT.

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X UnitConvert[energy, "KilotonsOfTNT"]

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