The process of atomic bomb explosion can be simplified as such a model that lots of energy has been produced at one point. Let the radius of the strong shock is R, which increases with the time. As we know, R is related to the time t, the produced energy E, the around air density ρ0 and pressure P0. So
Let us observe their units:
[R]=length, [t]=time, [E]=mass·length2·time-2,
[ρ0]=mass·length-3, [P0]=mass·length-1·time-2