Transcript Calculus and the Environment: Like Bread and Butter

Calculus and Engineering:
Like Bread and Butter
AP Calculus
Bell 2 rocks!!!
October 30, 2008
What do Engineers Do?
Engineers use their knowledge of science,
mathematics, and appropriate experience
to find suitable solutions to a problem.
What types of Engineers are there?
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Mechanical engineers research, develop, design, manufacture, and test tools,
engines, machines, and other mechanical devices.
•
Biomedical engineers develop devices and procedures that solve medical and
health-related problems.
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Electrical engineers design, develop, test, and supervise the production of
electrical and electronic equipment.
•
Nuclear engineers who research and develop the processes, instruments, and
systems used to derive benefits from nuclear energy and radiation.
What types of Engineers are there?
• Civil Engineers design, construct and manage physical facilities,
including roadways, dams, buildings and pipelines.
• Environmental Engineers design solutions for environmental
problems. They provide safe drinking water, manage wastes,
maintain air quality, control water pollution, and clean sites
contaminated by spills or improper disposal of hazardous wastes.
• Chemical Engineers apply of physical science and mathematics, to
the process of converting raw materials or chemicals into more
useful or valuable forms.
How can I become an Engineer?
• A bachelor’s degree from a four or five-year accredited college or
university program (ABET)
• Completion of the Fundamentals of Engineering (FE) examination.
• Engineer-In-Training (EIT) for 4-5 years under a profession engineer.
• Pass the Professional Engineering Examination.
• Passage of this exam leads to licensure as a Professional Engineer.
• Median engineering salaries range from 60,000-90,000$ (Not too
bad!)
What is Calculus?
• Calculus is the study of how things change. It
provides a framework for modeling systems in which
there is change, and a way to deduce the predictions
of such models.
• It provides a way for us to construct relatively simple
quantitative models of change
• With this you get the ability to find the effects of
changing conditions on the system being
investigated.
How do Engineers Use Calculus?
• Engineers often develop mathematical models of the devices, systems, or
processes they seek to create.
• These models allow the engineer to estimate the cost of different designs
and to compare their probable behavior under various conditions of operation.
• These models are based on the fundamentals of calculus!!!
• Chemical engineers use derivatives describe the behavior of how a
compound degrades over time.
• Electrical engineers use derivatives to calculate how magnetic and electric
field changes certain circuits.
• Environmental engineers use derivatives to describe how chlorine residual
changes over time in a distribution system.
Problem in the Greater Cincinnati
Area
Problems with Combined Sewer
Overflows
• CSOs
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storm water
untreated human waste
industrial waste
toxic materials
• Contact with discharges from CSOs can have adverse
effects on human health
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Hepatitis
gastric disorders
dysentery
cholera
Swimmer’s ear
Problem in the Greater Cincinnati
Area
Help be part of the Solution
• It would be helpful to know rate of change
in stormwater runoff within different
watershedsID problematic watersheds.
• This information could also help inform
environmental scientists and engineers
decide where management practices
need to be implemented first, and if
management practices are working.
Storm Water Management Model
(SWMM)
Storm Water Activity
• Three different watershed scenarios (Downtown
Cincinnati, Norwood, and Batavia)
• Simulate an identical rain event over three different
watersheds.
• How do physical differences within each watershed
affect the rate of storm water runoff within each
watershed?
– Generate a graph representing storm water runoff data
– Create a graph representing the derivative of that function.
– Compare instantaneous rates of change in runoff across three
different graphs, representing different watershed scenarios and
relate these different values to watershed characteristics.
– Recommend appropriate storm water management technologies
for watershed with high rates of storm water runoff
Combined Sewer Overflow Video
• http://www.youtube.com/watch?v=MJMtUa
8i4Jc
Re-Cap of Yesterday
• Simulated a rain event over three different
watershed scenarios.
• How do physical differences within each
watershed affect the rate of storm water
runoff within each watershed?
• Measured cumulative volume of storm
water runoff for several minutes following
a rain storm
Objectives
– Generate a graph representing storm water runoff
data.
– Create a graph representing the derivative of that
function.
– Compare rates of change in runoff across three
different graphs, representing different watershed
scenarios and relate these different values to
watershed characteristics.
– Recommend appropriate storm water management
technologies for watershed with highest rates of storm
water runoff
Trip to Sanitation District 1
• Leave Norwood at 8:30am Thursday,
November 13.
• Arrive at SD1 before 9:30am
• Tour of Storm Water Management
Technologies. (9:30am-11:30am)
• Lunch
• 12:30-1:30 (Meet with Engineers and
Scientist that work for SD1)
Review and Extension