# 3) Mixing and dispersion in the atmosphere

## Lab 3: Gaussian Mixing and Smokestack plumes

Download the lab and data files to your computer. Then, upload them to your JupyterHub [following the instructions here](/Fluid_Flows/resources/b-learning-jupyter.html#working-with-files-on-our-jupyterhub).

* [Lab 3-1: Gaussian Smokestack](lab3-1.ipynb)
* [Lab 3-2: Wind Profiles](lab3-2.ipynb)
* [Lab 3-3: Stability Classes](lab3-3.ipynb)
* [Lab 3-4: Solve an Air Quality Problem](lab3-4.ipynb)
* [Lab 3-5: BONUS, extra credit: Guassian Smokestack with an Inversion](lab3-5.ipynb)
  * Data: [Sounding Data Jan 10](../data/2022-01-10_radiosonde.csv)
  * Data: [Sounding Data Dec 26](../data/2021-12-26_radiosonde.csv)
  * Graphic: [Smokestack_gaussian_plume.png](../data/Smokestack_gaussian_plume.png)
  * Graphic: [Plume_reflection.png](../data/Plume_reflection.png)
  * Graphic: [Stability_classes.png](../data/stability_table.png)
  * BONUS Graphic: [Smokestack_oneReflection.jpg](../data/Smokestack_oneReflection.jpg)
  * BONUS Graphic: [Smokestack_2reflections.jpg](../data/Smokestack_2reflections.jpg)
  * BONUS Graphic: [Smokestacks_doublereflections.jpg](../data/Smokestacks_doublereflections.jpg)

## Homework 3: 

### Problem 1

On an overcast day with class C stability, the wind velocity at 10 m is 5 m/s.  The emission rate of an atmospheric pollutant is 70 g/s from a stack having an effective height of 100 m.  Assume rural conditions.  (You will want to use the lab python notebooks to solve this problem.)

* Estimate the center-line, ground-level concentration 25 km downwind from the stack, in micrograms per cubic meter. 
* Estimate the ground-level concentration 25 km downwind and 600 m from the stack center line, in micrograms per cubic meter.
* Calculate and plot the centerline ground level concentration versus distance from the stack (C(x)). 
* From the plot, estimate the magnitude and location of the peak ground concentration.
* How would the location and magnitude of the peak ground concentration change if the stack height was 125 𝑚? (Plot on the same axes)


### Problem 2

You are asked to assess the air quality in two cities A and B. The temperature profiles over each of the cities is shown below.  Note that a parcel rising from the surface will start with the surface temperature 25 °C. Assume dry air.

* What is the mixing height (H) over each city?
* Based on the observed temperature profiles, estimate the stability class (A-F) for each city.
* Determine the vertically averaged velocity between z=0 and z=H. You are told that the wind speed 10 𝑚 above the surface is 𝑢=6 𝑚/𝑠. Note: the velocity profile follows the power law and the vertical average is given by:

![Uavg_equation](../data/Uavg_equation.png)

* What is the Dilution Rate (or ventilation coefficient) for each city? 
* Which city is likely to have better air quality on this day?
* If both cities are 30 𝑘𝑚 across, what is the residence time over each?

![CityACityB](../data/CityACityB.png)


### Problem 3

Consider an area-source box model for air pollution above a peninsula of land (see figure below).  The length of the box is 25 km, its width is 100 km, and a radiation inversion restricts mixing to 100 m.  Wind is blowing clean air into the long dimension of the box at 1 m/s.  Between 4 and 6 pm there are 400,000 vehicles on the road, each being driven 20 km, and each emitting 5 g/km of CO. 

![BoxModel](../data/BoxModel.png)

W = 100 km, L = 25 km, H=100 m, u = 1 m/s

*  Find the average rate of CO emissions during this two-hour period (g CO/s per m^2 of land).
* Estimate the concentration of CO at 6 pm if there was no CO in the air at 4 pm.  Assume that CO is conservative (does not decay or change) and that there is instantaneous and complete mixing in the box.
* Assume the windspeed is 0, and use the basic equation (below) to derive a relationship between CO and time and use it to find the CO over the peninsula at 6 pm.

![BoxModeleqn](../data/Boxmodel_eqn.png)