Question

ACME Incorporated has built a factory 1 kilometer upwind of your home. It is a coal power plant that emits carbon monoxide (CO) at a rate of 500 kilograms per second.

Discussion Question 1

What will the concentration of CO be outside your home be if the factory emits CO at the rate given above, your home is 1 km downwind of the factory, the wind speed is 3 meters per second, and the atmospheric stability is slightly stable? Report in units of kg/ m³. To calculate this concentration, use the simplified Gaussian Plume Equation:

C= QU    ×   12πσyσz

Where:

• C is concentration (mg/m³)
• Q is emission rate (kg/second)
• U is wind speed (m/s)
• p is a constant = 3.14159
• s_y is the horizontal dispersion coefficient (m)
• s_z is the vertical dispersion coefficient (m)

We can estimate s_y and s_z as:

s_y = ax^0.893                     s_z = cx^d – f

Where:

• x is the distance downwind (m)
• a, c, d, and f are dependent on atmospheric stability and are given in the table below

	a	c	d	f
Very unstable	213	440.8	1.941	-9.27
Unstable	156	106.6	1.149	-3.3
Slightly unstable	104	61	0.911	0.0
Neutral	68	33.2	0.725	1.7
Slightly stable	50.5	22.8	0.678	1.3
stable	34	14.35	0.741	0.35

Discussion Question 2

Does this concentration violate the 8-hour NAAQS standard for CO (9 ppm)? Note that you need to convert units from kg/m³ to ppm to answer this.

***Hints***

1 kg = 1000 g

The molar mass of CO is 22.01 g/mol

Avogadro’s number is 6.02*10²³ molecules/mol

Assuming standard conditions of T=298 Kelvins and P = 1 atm, there are 2.46 *10²² molecules/L of air

1000L = 1 m³

To get units in ppm, do: (# of molecules of CO)/(# of molecules of air) *10⁶

Answer 1

Given information in the problem:

Here to find the concentration of CO outside the home and CO emits by a coal power plant that is located one km away from home.

----------------------------------------------------------------------------------------------------------------------------------------------------------

Concentration is calculated by simplified Gaussian Plume Equation as shown below:

----------------------------------------------------------------------------------------------------------------------------------------------------------

Here need find the y and z to solve above equation

For slightly stable atmosphere the value for a, c, d, f are 50.5, 22.8, 0.678, 1.3 respectively

----------------------------------------------------------------------------------------------------------------------------------------------------------

Putting the values of each term to find concentration: