ENDY 6013 - ENVIRONMENTAL DYNAMICS

HOMEWORK ASSIGNMENT #2 - PRACTICE MAKES PERFECT (PART 1)

DUE FRIDAY 23 SEPTEMBER 2005

We are still just getting started, and reviewing very basic principles, refreshing our memories, and learning (again) to do those little tasks we all ignored when we first took algebra because the instructors weren't able to convey to us why these tasks were relevant. Well, I'm not certain that I can convey their relevance either, but I hope that as we move through the semester and see the applications of these principles, their relevance will make itself apparent!

Your assignment this week is to simply work through the problems below, taking care to arrive at the appropriate conversions, etc. Some of the numbers we generate will, in fact, have some usefulness throughout the semester, so it is not a bad idea to become familiar with them (especially those relating to various dimensional aspects of Earth).

I don't expect that you will be able to recall the appropriate formulae from memory, but I do expect you will be able to locate them in appropriate reference material will a little bit of effort.

1. Assuming Earth is a sphere with radius 6,378 km, calculate the volume of planet Earth in a) cubic kilometers (km³), b) cubic meters (m³), and c) cubic centimeters (cm³).

2. Geophysicists (like me) have estimated the Moon's average density is about 3.34 g/cm³. Calculate the total mass of the moon in a) grams (g), b) kilograms (kg), c) metric tonnes (T), d) megatonnes (MT), e) gigatonnes (GT), f) petagrams (10¹⁵ g).

3. Find an equation for the acceleration of gravity on the moon. Provide a full reference for this source of information. How does this value compare to the value for acceleration due to gravity on Earth?

4. The ocean covers approximately 70% of Earth's surface. What is the area (in km²) of the ocean?

5. The ocean has an average depth of 4,000 meters. Calculate the volume of the ocean in a) cubic meters (m³), b) cubic kilometers (km³), c) cubic centimeters (cm³), d) liters (l), e) milliliters (ml).

6. The average salinity of the the Great Salt lake is s 120 parts parts per thousand (ppt). How many parts per million (ppm) is this?

7. What is the total mass of salt in the Great Salt Lake when it is at its typical elevation of 4,200 ft (1,280 m) above sea-level? in a) grams (g), b) kilograms (kg), c) metric tonnes (T), d) megatonnes (MT), e) gigatonnes (GT), f) petagrams (10¹⁵ g).

8. If you remove all of the "salt" from the Great Salt Lake, what would the volume of the "salt" block be?

9. Find a source of information that yields an estimate of the annual flux of "salt" to the Great Salt Lake and provide a full reference for this source of information. a) What is the annual flux of "salt" to the Great Salt Lake in grams? b) in kg? c) in T?

10. Assuming the Great Salt Lake is a steady state system, what is the residence time of "salt" in the Great Salt Lake?

11. Geologist often descibe the magnitude of volcanic eruptions in terms of the total volume of material erupted (in cubic kilometers). Some well known volcanic eruptions produced the volumes of erupted material listed below:

Arkansas occupies 137,539 km². If the erupted material from each of the volcanoes above were to fall across the Natural State, how deep (in meters) would the accumulations be if we assume the density of this material is 2.67g/cm³ at 0% porosity? How deep would these deposits be at 50% porosity? 70% porosity?

12. A recent report in northwest Arkansas indicated that the West Fork of the White River delivers 28,000 'tons' of sediment to Beaver Lake annually. Assuming the 'tons' mentioned in this report are metric tonnes, what is the total mass of sediment delivered to Beaver Lake annually in a) kilograms, b) grams, c) petagrams, d) gigatonnes?

13. According to the U.S. Army Corps of Engineers, Beaver Lake has a surface area of 28,000 acres. Assume sediment delivered to Beaver Lake has a density of 2.65 g/cm³. a) If all 28,000 tonnes of sediment delivered annually to Beaver Lake were to be deposited as a uniform layer of sediment on the lake bottom, how thick would that layer be in meters? b) Is the quantity of sediment delivered to Beaver Lake annually by the West Fork of the White River a large quantity or a small quantity? c) Assume a sediment density of 1.0 g/cm³. How thick is the sediment layer now?

14. In 2003, Dr. Boss generated a map of the upper 7,000 acres of Beaver Lake showing a total volume of sediment accumulated since impoundment in 1966 of 5,647 acre feet. Assuming these values are representative of the entire lake basin, what is the average annual accumulation rate of sediment in Beaver Lake in a) acre feet, b) cubic meters. c) Assuming a sediment density of 1.0 g/cm³, what is the average thickness of sediment in Beaver Lake in meters? d) How does this value compare to that you calculated for #14 above? e) What percentage of sediment in Beaver Lake can be attributed to the West Fork of the White River using these values?