# Environmental Science: Numerical Questions – Air Modelling (BOX Model)

Dr. Manishika Jain- Join online Paper 1 intensive course. Includes tests and expected questions.

## Box Model

Q1) In a city of area (8 km x 8 km) , the vehicular traffic is releasing 10 ^{− 5} g/m^{2} − s of CO during the winter season between 4 pm and 8 pm. During this period mixing height is 100 m. The wind is blowing in the city at a speed of 4.0 m/s along the side of the city. If the initial concentration of CO at 4 pm was negligible, the estimated concentration of CO after 4 hours should be:

(1) 0.2 mg/m^{3}

(2) 3.2 mg/m^{3}

(3) 2.0 mg/m^{3}

(4) 20.0 mg/m^{3}

Answer: (1) 0.2 mg/m^{3}

C (t) = 0.2 µg/m^{2}

Q2) The Box model for an airshed over a city has the following parameter values:

Length of the airshed (L) = 24 km

Average wind speed (u) = 4 m/s

If the initial concentration of a pollutant over the city is zero, estimate the time in which

the concentration of the pollutant in the airshed reaches ~63 % of its final value.

(1) 1 hr 10 minutes

(2) 1 hr. 20 minutes

(3) 2 hrs. 30 minutes

(4) 1 hr. 40 minutes

Answer: (4) 1 hr. 40 minutes

Pollutant reach 63 %

T = L/u

Where T – time

U wind speed

L length of box

T = 24 ⚹ 1000/4 = 6000 = 100 m = 1hr 40 min

Q3) Consider a box model for an airshed over a city and assume that the initial concentration of a pollutant is zero and that the air entering the box is clean. If the length of the box is 10 km and the wind speed along the length of the box is 5 m/s, what is the time taken for the pollutant concentration to reach ~95 % of its final value?

(1) 1 h 40 minutes

(2) 1 h 7 minutes

(3) 33 minutes 20 seconds

(4) 2 h 13 minutes 20 seconds

Answer: 1 h 40 minutes

Pollutant reach 95 %

T = 3 (L/u)

Where T – time

U wind speed

L length of box

T = 3 (10 ⚹ 1000/5) = 3 ⚹ 2000

= 3 ⚹ 2000

= 100 m = 1hr 40 min

-Mayank