5/16/11

Flooding

3D Geometry

• Memphis is located right by a bend in the Mississippi River.

• This satellite photo from Google Maps shows the Mississippi prior to the floods.

Flooding

3D Geometry

• This image shows the extensive flooding that has occurred.

• Given the two images, how can we estimate the amount of water that makes up this flood?

Flooding

3D Geometry

• In this illustration we see the portion of the Mississippi River that flows past Memphis.

Flooding

3D Geometry

• Think of this portion of the river as a curved rectangular prism, as shown.

Flooding

3D Geometry

• If we “straighten out” this rectangular prism, we get a standard-looking rectangular prism.

• The volume of a rectangular prism is length • width • height

Flooding

3D Geometry

• But this volume only provides the amount of water when the river isn’t flooding.

• What we’re interested in is a second rectangular prism that makes up the excess water.

Flooding

3D Geometry

• We can use this diagram to find the volume of flooding for different amounts of water.

• The Volume is a linear function for different values of x, the height of the flooding, in inches.

Flooding

3D Geometry

• In this graph, the x-values are the inches of flooding occurring, and the y-values are volume of flood water.

Flooding

3D Geometry

• But remember that the river is also flowing at an average speed of 2 mph.

• This means that every hour another rectangular prism’s worth of water flows through, increasing the amount of flooding.

Flooding

A Family of Linear Functions

• Because a can vary, we get a family of linear functions. In each case the y-value represents the accumulated volume of flooding for the specific number of days. 2335680000000.

Flooding

3D Geometry

• To see how massive the flooding can be. Take V = 24•f1(2)x and evaluate it for x = 20.

• This would be a situation where 2 inches of flooding occurs for 20 days.

Equivalent to the water from 10 New

Orleans Super Domes!