Dumping and other material-handling operations near a landfill may result in con

Question

Dumping and other material-handling operations near a landfill may result in contaminated particles being emitted into the surrounding air. To estimate such particulate emission, the following empirical formula can be used:

E(V,M)=k(0.0033)(V/5)^1.5(M/2)^-1.5

where E is the emission factor (in pounds of particles released into the air per ton of soil moved), V is the mean speed of the wind (mph), M is the moisture content of the material (given as a percentage), and k is a constant that depends on the size of the particles.

The emission factor E can be multiplied by the number of tons of material handled to obtain a measure of total emissions. Suppose 29 tons of the material in part (a) is handled. How many tons of a second kind of material with k=0.19 and moisture content 17% must be handled to achieve the same level of total emissions if the wind velocity stays the same?

tons:

Explanation / Answer

From part a, E = 0.22*0.0033*2.2^1.5*6^-1.5

Total emissions for 24 tons of material handled = 24 * (0.22*0.0033*2.2^1.5*6^-1.5)............(1)

For second material E = 0.17*0.0033*2.2^1.5*(18/2)^-1.5

Total emissions for second kind of material = m * (0.17*0.0033*2.2^1.5*(18/2)^-1.5)..........(2)

Equating (1) and (2),  24 * (0.22*0.0033*2.2^1.5*6^-1.5) = m * (0.17*0.0033*2.2^1.5*(18/2)^-1.5)

Thus m = 57.059 tons   

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