ENV 4001: ENVIRONMENTAL SYSTEMS ENGINEERING. University of South Florida Civil & Environmental Eng.

Transcription

1 ENV 4001: ENVIRONMENTAL SYSTEMS ENGINEERING Fall 2017 Quiz #1 Wednesday, September 27 University of South Florida Civil & Environmental Eng. Prof. J.A. Cunningham Instructions: 1. You may read these instructions, but do not turn the page or begin working until instructed. 2. This quiz contains three questions, plus a fourth extra-credit question. Answer all of the first three questions. 3. Please do not attempt the extra-credit question unless you have completed the first three problems, and you still find yourself with extra time. It is in your best interests to focus on problems 1 3, rather than being distracted by problem 4. Problem 4 is intended only for students who were not sufficiently challenged by problems Some questions might have multiple parts. In those cases, the point value of each part is indicated. The total number of points possible is Unit conversion factors and other potentially useful information is provided on the back of this page. 6. Answer each question in the space provided. If you need more space, you can attach additional pages as needed, but make sure to put your name on them. 7. Show your work and state any important assumptions you make. I cannot award partial credit if I can t follow what you did. 8. Report a reasonable number of significant digits in your answers. 9. Include units in your answers as appropriate. An answer without proper units is not correct! 10. You are allowed to use your text book, your course notes, or other printed materials. You may not receive help from another person. 11. A hand-held calculator is recommended. Other electronic devices are not permitted. 12. Time limit: 60 minutes. Stop working when asked. If you continue working after time has been called, you will be penalized at a rate of 1 point per minute. 13. Don t cheat. Cheating will result in appropriate disciplinary action according to university policy. More importantly, cheating indicates a lack of personal integrity. 14. Please print your name legibly in the space provided below, and turn in this quiz at the end of the period. 15. Hints: Read each question carefully and answer the question that is asked. Watch your units. If you take good care of your units, they will take good care of you. Work carefully and don t rush. Name: p 1/10

2 Potentially useful constants: Ideal gas constant, R: Pa m 3 mol 1 K 1 = atm m 3 mol 1 K 1 Gravitational acceleration, g: 9.81 m/s 2 Molecular weight of water, H2O: g/mole Density of water at 25 C: g/ml = 997 kg/m 3 Viscosity of water at 25 C: Pa sec Density of air at 25 C: 1.18 kg/m 3 Viscosity of air at 25 C: Pa sec Potentially useful conversion factors: Pressure: 1 atm = 760 mm Hg = 760 torr = Pa 1 Pa = 1 N/m 2 = 1 kg/(m sec 2 ) Mass: 1 kg = 1000 g = 10 6 mg = 10 9 µg 1 kg = lbmass 1 t (metric tonne) = 1000 kg = 2207 lbmass 1 ton (English ton) = 2000 lbmass Length: 1 km = 1000 m = 10 5 cm = 10 6 mm = 10 9 µm 1 ft = 12 in = cm = m Temperature: 25 C = K Volume: 1 m 3 = 1000 L = 10 6 ml = 10 6 cm 3 1 gal = L Work/Energy: 1 BTU = kj Power: 1 MW = 10 6 W = 10 6 J/s = 10 6 N m/s Area : 1 ha = 10 4 m 2 Atomic Masses: H = g/mole C = g/mole N = g/mole O = g/mole P = g/mole S = g/mole Cl = g/mole Br = g/mole Na = g/mole Mg = g/mole Al = g/mole K = g/mole Ca = g/mole Fe = g/mole Cu = g/mole p 2/10

3 This page is left blank intentionally. p 3/10

4 1. (30 pts) An important environmental problem is acid mine drainage. During mining operations, when certain minerals are exposed to air and water, sulfuric acid (H2SO4) is formed. Then, when it rains, the rainwater that flows out of the mining site is laden with sulfuric acid, which can present a number of environmental problems and hazards. H2SO4 is a diprotic acid, which means that it can donate two protons to solution: H2SO4 (aq) H + + HSO4 HSO4 H + + SO4 2 Suppose that, at a particular mining site, we know that the rainwater exiting the mine is in equilibrium with calcium sulfate (CaSO4) mineral. Also, we took some measurements and we determined that the concentration of calcium (Ca 2+ ) in the rainwater is 160 mg/l, and the concentration of bisulfate (HSO4 ) is 3400 mg/l. Based on this information, estimate/calculate the ph of the rainwater draining from the mining site. Then comment briefly (only 1 or 2 sentences) on why you think this particular site might or might not represent a significant environmental problem. Hint: you will need to look some things up to solve the problem. more space to work on problem 1 p 4/10

5 1. continued more space to work on problem 1 p 5/10

6 2. (20 pts) This problem and the next two are all based on material from Introduction to Environmental Engineering and Science, 3 rd edition, 2008, by G Masters and W Ela. A lake with constant volume 10 7 m 3 is fed by a polluted stream having a flow rate of 5.0 m 3 /s and a pollutant concentration of 10 mg/l. The lake is also fed by a sewage outfall that discharges 0.5 m 3 /s of wastewater having a pollutant concentration of 100 mg/l. There is one stream that flows out of the lake. In the lake, the pollutant decays with a first-order decay coefficient 0.20 d 1. Assuming that the pollutant is completely mixed in the lake, and ignoring evaporation or any gains/losses of water volume other than those listed above, estimate/calculate the steadystate concentration of the pollutant in the lake. Hint: you know what to do. more space to work on problem 2 p 6/10

7 2. continued more space to work on problem 2 p 7/10

8 3. (10 pts) Consider the same system as in problem 2. Now suppose that the environmental authorities have decided that the lake is too polluted. Therefore, it has been decided that the sewage outfall will be diverted to a different receiving water body. We will define t = 0 as the time at which the sewage flow to the lake is stopped. Derive a differential equation that describes how the pollutant concentration in the lake changes with time after the sewage outfall is diverted. Also write down and clearly indicate the initial condition that applies to this differential equation. You do not need to solve the differential equation. (Hint: identifying the initial condition should be easy no calculations required, assuming you did all the rest of the problem already). p 8/10

9 4. (extra credit -- up to 15 points extra credit for a perfect answer) When I wrote problems 2 and 3, what I really wanted to ask you was once the sewage outfall is turned off, how long until the pollutant concentration in the lake drops below an acceptable level of 2.0 mg/l? That would require you to solve the differential equation from problem 3, subject to the proper initial condition. I decided that 60 minutes wasn t enough time to do all the rest of problems 1 3 and still have time to answer this question too, so I took it out. But if you are really fast, and you still have time after answering questions 1 3, then I will give you extra credit for answering this question. Please do not attempt this part unless you have completed problems 1 3 to the best of your ability, and you still have extra time remaining. I do not want you to waste your time here and hurt your grade. This question is intended only for students who have completed problems 1 3 and still have extra time. more space to work on problem 4 p 9/10

10 4. continued more space to work on problem 4 END OF QUIZ p 10/10