Functions in the Real Functions in the Real WorldWorld

We’re now going to We’re now going to explore one of the explore one of the countless areas in countless areas in which scientists use which scientists use functions, their functions, their graphs and their graphs and their equations, to model equations, to model data and make data and make predictions that predictions that impact our lives in a impact our lives in a significant way every significant way every day. day.

Photo from Tropical Storm Allison Recovery Project

Diffusion in the Diffusion in the EnvironmentEnvironment

The area we are going to focus on is diffusion and its The area we are going to focus on is diffusion and its effects on the environment. Since these are effects on the environment. Since these are numerous and far reaching, we need to limit our numerous and far reaching, we need to limit our investigation further. What we’ll be concentrating on investigation further. What we’ll be concentrating on is diffusion’s impact on water quality when it rains – is diffusion’s impact on water quality when it rains – no - not just when it rains, but when it FLOODS! no - not just when it rains, but when it FLOODS!

Photo from Tropical Storm Allison Recovery Project

DiffusionDiffusionLet’s begin with some definitions, so everyone will Let’s begin with some definitions, so everyone will

understand exactly what is meant by the understand exactly what is meant by the particular terms that we’ll be using.particular terms that we’ll be using.

DiffusionDiffusion is defined as the process where is defined as the process where molecules move from a high concentration molecules move from a high concentration to a low concentration. Diffusion to a low concentration. Diffusion simulationsimulation

For example, spray a squirt of cologne in a room. For example, spray a squirt of cologne in a room. There will be a strong scent where you sprayed There will be a strong scent where you sprayed it, but it will diffuse and become a weaker scent it, but it will diffuse and become a weaker scent as it moves from the area where it was first as it moves from the area where it was first sprayed until it is the same concentration sprayed until it is the same concentration throughout the room. This movement of throughout the room. This movement of molecules in order to maintain an equilibrium is molecules in order to maintain an equilibrium is known as known as homeostasishomeostasis..

Diffusion in WaterDiffusion in WaterFollowing a rain, Following a rain,

runoff occurs. runoff occurs. RunoffRunoff is water from rainfall is water from rainfall which is not which is not absorbed by the soil absorbed by the soil as it flows downhill, as it flows downhill, where it eventually where it eventually drains into the local drains into the local drainage system and drainage system and ultimately into a ultimately into a creek, bayou, creek, bayou, stream, river or stream, river or other body of water.other body of water.

Photo from Tropical Storm Allison Recovery Project

Diffusion in Water Diffusion in Water ContinuedContinuedAs the water flows As the water flows

downhill, it picks up downhill, it picks up insolubleinsoluble material. This material. This is material that will not is material that will not dissolve in the water. dissolve in the water. Topsoil is an example.Topsoil is an example.

Even things like Even things like decomposing animals decomposing animals or oil that has spilled or or oil that has spilled or leaked onto streets and leaked onto streets and highways can become highways can become part of the runoff.part of the runoff.

The runoff can also pick The runoff can also pick up up contaminantscontaminants like like toxic chemical toxic chemical fertilizers and fertilizers and pesticides. pesticides. Photo from Tropical Storm Allison Recovery Project

Diffusion in Water Diffusion in Water ContinuedContinued

These contaminants These contaminants may create serious may create serious water quality water quality problems because problems because they will diffuse, they will diffuse, allowing the allowing the harmful substances harmful substances to pollute all the to pollute all the bodies of water the bodies of water the runoff empties into runoff empties into as it flows.as it flows.

Photo from Allison Tropical Storm Allison Recovery Project

Significance of Diffusion in Significance of Diffusion in RunoffRunoff

Therefore, it is extremely Therefore, it is extremely important to be able to important to be able to predict the amount of predict the amount of runoff a particular area runoff a particular area will experience during a will experience during a storm, for this can help in storm, for this can help in the prevention of major the prevention of major water pollution problems. water pollution problems.

This is especially true in This is especially true in flood prone regions flood prone regions where high levels of where high levels of contaminants exist.contaminants exist.

Photo from Tropical Storm Allison Recovery Project

WatershedsWatersheds A watershed is the total A watershed is the total

of all the land area and of all the land area and smaller bodies of water smaller bodies of water whose rainfall ultimately whose rainfall ultimately drains into a specific drains into a specific body of water.body of water.

Example: The total Example: The total region of land, creeks region of land, creeks and streams whose and streams whose runoff flows into the runoff flows into the Colorado River is called Colorado River is called The Colorado River The Colorado River WatershedWatershed

Watersheds continuedWatersheds continued

Later in our study, we will use a Later in our study, we will use a computer model to examine the computer model to examine the amount of runoff in various amount of runoff in various watersheds in Harris County, Texas watersheds in Harris County, Texas following Tropical Storm Allison following Tropical Storm Allison which hit the Houston area June 5-9, which hit the Houston area June 5-9, 2001.2001.

But before we can do that, we need But before we can do that, we need some more information. some more information.

Assignment Part I Assignment Part I Go to Go to Surface Water RunoffSurface Water Runoff and click on and click on

Background Science.Background Science. Read: Read:

““Why is it important to model runoff water?” Why is it important to model runoff water?” ““How is surface water runoff determined?” How is surface water runoff determined?” “ “What is a hydrologic soil group?”.What is a hydrologic soil group?”.

Answer the Part I questions given on the Answer the Part I questions given on the next slide on your own paper. When you next slide on your own paper. When you have completed Part II of the assignment, have completed Part II of the assignment, you will turn in your work to your teacher. you will turn in your work to your teacher. You may also choose to use Word to You may also choose to use Word to complete your assignment and email your complete your assignment and email your work to your teacher. work to your teacher.

Questions Part IQuestions Part I 1. How does the addition of fertilizers 1. How does the addition of fertilizers

affect the entire ecosystem of a body of affect the entire ecosystem of a body of water?water?

2. What is currently the most 2. What is currently the most appropriate and authentic numerical appropriate and authentic numerical model in use by soil scientists?model in use by soil scientists?

3. In the graph on Runoff Curves, 3. In the graph on Runoff Curves, a. Which axis is the independent a. Which axis is the independent

variable and what does it represent?variable and what does it represent? b. Which axis is the dependent b. Which axis is the dependent

variable and what does it represent?variable and what does it represent?

Questions Part I Questions Part I continuedcontinued

4. What is a 4. What is a predictive model?predictive model?

5. The runoff 5. The runoff curve number curve number depends on what depends on what four factors?four factors?

6. How are soil 6. How are soil groups classified?groups classified?

7. Describe the 7. Describe the four soil groups.four soil groups.

Tropical Storm Allison Recovery Project

Questions Part IIQuestions Part II

Go to Surface Water Runoff and Go to Surface Water Runoff and click on Mathematics. Read click on Mathematics. Read through this section.through this section.

Then answer the following Then answer the following questions on the same page as the questions on the same page as the responses to Questions Part I. responses to Questions Part I.

Turn the completed assignment in Turn the completed assignment in to your teacher.to your teacher.

Questions Part IIQuestions Part II 1. Give the equation used to calculate 1. Give the equation used to calculate

runoff and identify each variable. runoff and identify each variable. 2. Define initial abstraction and 2. Define initial abstraction and

infiltration of the variables.infiltration of the variables. 3. What is the runoff curve number 3. What is the runoff curve number

(CN) and its range of values?(CN) and its range of values? 4. Which equation that was specifically 4. Which equation that was specifically

formulated through the use of data formulated through the use of data compiled from the study of many small compiled from the study of many small watersheds?watersheds?

Assignment Part II Assignment Part II ContinuedContinued

0.8SP

0.2SPQ

2

SIP

IPQ

a

2a

5. Fill in the missing step.a.

b.

? ? ? ? ? ? ? ? ? ? ?

c.

Questions Part II Questions Part II ContinuedContinued

6. In the equation given above,6. In the equation given above, a. Name the type of function. a. Name the type of function. b. Write the function in functional notation.b. Write the function in functional notation. c. Identify the independent variable.c. Identify the independent variable. d. Identify the dependent variable.d. Identify the dependent variable. e. What would be a reasonable domain?e. What would be a reasonable domain? f. What would be a reasonable range?f. What would be a reasonable range?

SaI 2.0