Environmental Engineering Reference
In-Depth Information
5. Touch or place your hand near a 100 W incandescent lightbulb and a 20-40 W fluores-
cent lightbulb. Qualitatively describe the amount of light output and heat output for the
two bulbs.
ORDER OF MAGNITUDE ESTIMATES
In terms of energy consumption, production, supply, and demand, estimates are needed and an
order of magnitude calculation will suffice. By order of magnitude, we mean an answer (one or at
most two significant digits) to a power of 10.
EXAMPLE
How many seconds in a year? With a calculator it is easy.
365 days * 24 h/day * 60 min/h * 60 s/h 31,536,000 s, an answer to ive signiicant digits
When you round to one significant digit, this becomes 3 * 10 7 s. For two significant digits, the
answer is 3.2 * 10 7 s.
Order of magnitude estimate: Round all input to one number with a power of 10, then multiply
the numbers and add the powers of 10. So without a calculator, the above becomes:
4 * 10 2 * 2 * 10 1 * 6 * 10 1 * 6 * 10 1 4 * 2 * 6 * 6 * 10 5 288 * 10 5 3 * 10 2 * 10 5 3 * 10 7
If you have trouble with powers of ten, please consult the instructor.
PROBLEMS
OM means order of magnitude problem.
1. A snowball, mass 0.5 kg, is thrown at 10 m/s. How much kinetic energy does it possess?
What happens to that energy after you are hit with that snowball?
2. OM: The Chamber of Commerce and the Board of Development are always promoting
their city as the place for new industry. If a city has a population of 100,000 and a growth
rate of 10% per year, what is the population after five doubling times? How many years
is that?
3. What is the doubling time if the growth rate is 0.5%? The world population in 2008 was
around 6.7 * 10 9 .
4. OM: If world population is 7 * 10 9 , estimate how many years before the population
reaches 28 * 10 9 .
5. OM: How many people will there be on the earth by the year 2100? Assume present rate
of growth of world population.
6. OM: If the growth rate of population could be reduced to 0.5% per year, how many years
would it take to reach 24 * 10 9 people?
7. OM: The population of the world is predicted to reach 11 * 10 9 . Mexico City is one of the
largest cities in the world at 2 * 10 7 people. How many new cities the size of Mexico City
will have to be built to accommodate this increase in population?
8. OM: The most economical size of nuclear power plants is around 1,000 MW. How many
nuclear power plants would have to be built in the United States over the next 50 years to
meet the U.S. long-term historical growth of 7% per year in demand for electricity?
9. OM: Assume electricity demand increases by 10% per year over the next 30 years for the
world. To meet all that increased demand, how many 1,000 MW nuclear plants would
have to be installed by the end of 30 years? What is the total cost for those nuclear plants
at $5,000/kW?
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