An ethylene storage tank in your plant explodes. The distance that the blast wave travels from the blast site $(R)$ depends upon the energy released in the blast $(E)$, the density of the air $(ho)$, and time $(t)$. Use dimensional analysis to determine:

(a) The dimensionless group(s) that can be used to describe the relationship between the variables in the problem;

(b) The ratio of the velocity of the blast wave at a distance of $2000 \mathrm{ft}$ from the blast site to the velocity at a distance of $500 \mathrm{ft}$ from the sites;

The pressure difference across the blast wave $(\Delta P)$ also depends upon the blast energy $(E)$, the air density $(ho)$, and time $(t)$. Use this information to determine:

(c) The ratio of the blast pressure at a distance of $500 \mathrm{ft}$ from the blast site to that at a distance of $2000 \mathrm{ft}$ from the site.