Question

A factory emits pollutants at a rate of 25 g/s. The factory is located between two mountain ranges resulting in an effective valley width of 5000 m. The height of the ceiling due to atmospheric conditions is 1000 m. During the fall and spring, a breeze that travels at a velocity of 4 m/s flows through the valley. Fortunately, the breeze coming in contains no pollutants. Based on the information given, the steady state concentration of pollutants in the valley, in micrograms per cubic meter is.

Answer 1

`1.25\ \mu\text{g/m}^3`

Step-by-step explanation:

v = Velocity of the breeze = 4 m/s

w = Width of the valley = 5000 m

h = Height of the valley = 1000 m

Volumetric flow rate is given by

`\dot{V}=vwh\\\Rightarrow \dot{V}=4* 5000* 1000\\\Rightarrow \dot{V}=2*10^(7)\ \text{m}^3/\text{s}`

`\dot{m}` = Mass flow rate of pollutant = 25 g/s =
`25* 10^6\ \mu\text{g/s}`

Concentration is given by

`C=\frac{\dot{m}}{\dot{V}}\\\Rightarrow C=(25* 10^6)/(2* 10^7)\\\Rightarrow C=1.25\ \mu\text{g/m}^3`

The steady state concentration of pollutants in the valley, is
`1.25\ \mu\text{g/m}^3`.