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MTH 252, Fall Term 2008
Group Project
Each group will submit one paper. All group members will receive the same
score for this one paper.
Due: Two copies (one hard copy and one electronic copy) at the beginning of class on
November 26, 2008. The typist must have a rough draft copy for each group
member on November 19, 2008.
Project Specifications
Groups must consist of three or four members.
Papers must be word-processed. The mathematics in the paper must be created with some
sort of math equation editor. Graphs must be created with a graphing program or be a
downloaded calculator screen. These graphs must be incorporated into the body of the paper
and not enclosed at the conclusion.
A computer generated cover sheet must be submitted along with the paper. The cover sheet
must include a title for your project and the names of each member of your group along with
their individual assignments for the project.
Papers must be written in accordance with the math 251 writing guidelines. Additionally, all
papers must include:
A clear and unambiguous introduction to the problem. This introduction must
include a diagram for the problem and clear and unambiguous definitions for all
variables used in the problem.
A clear statement of all assumptions you are making beyond those in the stated
problem.
A clear and unambiguous verbal description of the mathematics you will use to solve
the problem.
All of the algebraic steps necessary to resolve the problem. Each new algebraic
process must be motivated by a brief explanation of the purpose of the mathematics.
A clear and unambiguous conclusion to the problem.
Memo: To: Portland Community College Calculus Consultants (PC
C
From: Northwest Outdoor Organization (NOO)
Subject: Trout Reintroduction to Clover Creek
We are contracting with your organization to obtain an analysis of the suitability of two sites on
Clover Creek for the reintroduction of native cutthroat trout. The specified data for each site is
given below. The analysis for each site is similar and is based on the following requirements for
trout habitat.
- The fish prefer a stream velocity between 0.4 and 2.4 feet per second.
- Each fish requires 2.6 cubic feet per second in total stream flow through the region
where it lives, to bring sufficient food, etc.
Site 1 Data:
At this site Clover Creek flows through an artificial concrete channel whose bottom was
observed to be parabolic. The stream was 12 feet wide and had a maximum depth at the center
of 6 inches. Velocity measurements were taken at two foot intervals from one bank to the center
of the stream:
distance from bank (ft) velocity (ft/sec)
Assume the stream velocity on the other side of the stream is symmetric.
Report requirements for Site 1:
a. Plot the velocity of flow, v, as a function of distance, x, from the stream center (Note the
distances in the chart are not from the center.)
b. Find a function, v(x), to fit the data points. (You only need to go from the center to one bank,
since the other half is symmetric.)
c. Determine a function, D(x), to give the depth of the stream as a function of the distance from
the center.
d. Plot a cross-section of the stream showing the depth as a function of the distance from the
center.
e. Use the depth and velocity functions to find the total stream flow. Think of the stream as
divided into vertical strips of thickness dx. Use the functions from parts b. and c. to write an
expression for the total stream flow through each strip in terms of v(x), D(x), and dx. Then
compute the total stream flow using an integral. (Careful: does the velocity function accurately
represent stream velocity on both sides of the stream?)
f. Make recommendations regarding the introduction of cutthroat trout at the site.
