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Thanks for watching! I originally wanted to get a full list of problems posted specifically for water and just recently started mixing in other topics instead. I should be posting another geotech problem on the 30th as long as I have time to get it done for next Monday.

Multi-step problems can sometimes feel really frustrating. Thats why practice and repetition usually help. There are other problems similar to this out there if you want to look at some of them too. Maybe those will inherently make more sense either in their wording or in what terms they give you vs what you are asked to solve for.

Sorry for the misleading choice of words in this problem. You're probably right - I've seen it written before as "primary sewage sludge" but likely not as just "primary sewage". I work in wastewater collection system modeling and so everything to me is sewage haha. Also thanks for sharing your method of solving for some terms. It seems more efficient and demonstrates that you have an inherent understanding of how these equations work and what they are for.

You're welcome! Thanks for watching and best of luck to you if you're currently studying for the exam!

You're absolutely right. My lumped math would only work if the rainfall rates were always greater than the sum of the infiltration and transpiration at each minute. I made a mistake here, thank you for pointing it out. This problem would need to be solved in 10 minute increments like you suggested.

To the best of my understanding, you are correct! I believe that 𝑃𝑠, though weight-based, effectively converts the mass of solids into a proportional volume when combined with the other factors in the equation. The moisture content impacts the total volume but is indirectly accounted for through 𝑆𝑠 and Gw (the sludge density factor, about equal to 1), ensuring the equation correctly reflects the final sludge volume. Thanks for asking such a tricky question. I will not pretend to be an expert on all of these topics and had to turn to Google for help here.

This is a great question and depending on EXACTLY how the question is worded on the test, your approach might be correct. You're keeping your wits about you and being suspicious of all the things the test might give you to trick you. In this case, my answer is simple - both commercial AND domestic flow rates are given in the units of gal/cap-day. We don't need to assume that ourselves because the problem gives it to us directly. So yeah if forced to think about what it actually means in the real world, your suggestion to think of it as commercial use per person would work. Let me know if this doesn't answer your question.

@@SolvedIn6 That makes sense! At first, I did not see it as a breakdown of per person usage. Thanks! These videos are super helpful for my PE prep

@@wadehamilton You're very welcome, thanks for watching and supporting this small channel and best of luck to you on test day!.

Thank you! I'm glad to hear that it was worthwhile to include. I wanted these problems to be solvable as often as possible just by using test-taking skills such as searching for keywords, even if the person taking the exam isn't an expert in a particular subject. I think this was more important back when the exam spanned multiple subject areas but it will hopefully still speed things up for the current format as well.

Great catch! Sorry about that and thank you for pointing it out!

Nice find. Yup, steps 1 and 2 seem like they will be the same, and then you can skip step 3 using your method and get the same answer I found in step 4. Nice job.

That's awesome, thanks for sharing! I took this exam before it became digital and so tried to rely on the Reference Manual as much as possible, and turned to some of my textbooks when I couldn't find what I needed there. I really should look into what other documents you have access to during the exam - if there is a list that you know of, I would love to see it. Thanks again~

@@SolvedIn6 You are very welcome! For the CIVIL-WATER RESOURCES AND ENVIRONMENTAL, exam takers have access to 2 documents: 1- TSS Wastewater Facilities 2014 - Recommended Standards for Wastewater Facilities, 2014, Great Lakes- Upper Mississippi River Board of State and Provincial Public Health and Environmental Managers. 2- TSS Water Works 2018 - Recommended Standards for Water Works, 2018, Great Lakes-Upper Mississippi River Board of State and Provincial Public Health and Environmental Managers.

Its my understanding that uncertainty factors are typically multiplied together to account for the margin of error possible in each factor. You can think of it as a little bit of intentional over-design. Slide 17 of the following link also mentions this: ec.europa.eu/health/ph_projects/2003/action3/docs/2003_3_09_a23_en.pdf

Thanks again for watching so many of these videos and providing such great feedback.

Great find! I might have missed that equation. Glad to know you've got at least 2 ways to solve it if you see it on the exam. Seems like you're really moving through problems!

Thanks for your note and for letting me know there might be a mistake. Can you tell me what you used to calculate an answer of 194.6 gal/cap-day? Regarding your comment about more people leading to more consumption - note how the problem is worded: the planners want their total water use to remain the same in 2012 as was used in 2005. So our goal is to figure out by how much each person needs to reduce their water use by for more people to end up using the same amount of water. Just trying to clarify in case you solved for something different than I did based on a different understanding of the problem.

​@@SolvedIn6 Hello, the math error you encountered was caused by flipping the nominator and the denominator in step 3. So, it should be 160 x 139901/ 115000 = 194.6 . At this point, we are just trying to find the consumption in 2012 that's why I said that more people mean more consumption (compared to year 2005). When we subtract, which is the final step, that's when we are calculating the usage reduction and tackling the problem in terms of how much each person needs to reduce their usage. So 194.6 - 160 = 34.6 ( 34.6 is the final answer). I hope this clarifies my comment and please feel free to reply with more questions/ concerns. Thank you again for the great content.

​@@JasmineWadie Thanks a bunch for taking the time to explain your approach! I think we might be answering slightly different questions, which seems very possible based on the poor way I worded this problem. My goal when writing this problem was to assume that "the average person uses 160 gal/day of water in 2005, and so future people would need to use less". That was what I intended to convey in the part of the problem statement that says "the city's goal is to not increase their net water usage." I'll try to explain my intended approach better below. If I multiply 160 gal/cap-day by the 2005 population (115000), I get 18400000 gal/day. Maybe this is where I should have worded the problem better and said "the max amount of water the city is allowed to use is 18400000 gal/day". Multiplying my future population (139901) by the reduced rate from my answer (160-28.5) gives me that same total water use of 18400000 gal/day. It seems like you solved for what would be the new gal/cap-day water use (194.4) if the population increased and no reduction in water use was made. Then, you subtracted the old water use (160) to get 34.6. Now, if we multiply the new population (139901) by 160-34.6 (the reduced water use in 2012), we get 17537308.1. This shows that we have reduced the water use by more than we would have needed to in order to stay within the max limit of 18400000 gal/day. Happy to continue discussing this. Thanks again for watching and discussing!

@@SolvedIn6 Hello again :) Let’s forget the question wording and set it aside for just one second. In the 2nd step, we found the population in 2012 to be 139,901 people. In the 3rd step, we need to find the corresponding water usage in 2012 when we have 139,901 people. I used cross multiply as follows: Year 2005 …. 115,000 people = 160 gal usage Year 2012 …. 139,901 people = X usage Then you solve for the unknown X (using cross multiply) X= 160 x 139901/ 115000 = 194.6 However, in your solution under step 3, you have the nominator, and the denominator flipped. Do you have a reason as to why you did that? 194.6 gal/capita-day is what we estimate the usage will be in 2012. The usage must increase from 160 to 194.6 after 7 years because people increased (it’s a direct relationship not inverse relationship). Finally, to solve for the problem to meet the city's goal to reduce usage, we subtract 194.6- 160 = 34.6 This means that in 2012, they need to reduce their usage by 34.6 gallons to stay at the 160-gallon mark. Let me know what your thoughts are. Thanks

@@JasmineWadie-j3t I apologize that I'm having trouble answering your direct question as to why my numerator and denominator are flipped. Below I will try to re-word my logic. I pasted straight from excel in case you want to copy anything into a spreadsheet. in 2005, pop was (cap): 115000 in 2005, water use was (gal/cap-day): 160 so total water use was (gal/day) 18400000 This is the critical part of the problem to me and why i focused on the wording. The way I meant to word it was that 18400000 was the max water the city could use, regardless of what each individual person's gal/cap-day's use was. in the future, they must still use only up to 18400000 gal/day, even with more people in the city. since we are asked not to exceed (gal/day): 18400000 and we now have (cap): 139901 we need to get to a gal/cap-day of 131.521576 which means that each person needs to reduce their use by (gal/cap-day): 28.48 (160-131.5) I think this is a different question than "find the new average water use" in gal/cap-day (194.6) and then subtract from the old average water use (160). in real terms, this problem is making the claim that 2012 people have to become more water efficient than 2005 people (low flow appliances, conservation, etc).

Thanks for watching!

Thanks for checking out the video!

Thanks for sharing! I recorded a number of these videos before the new handbook was published and definitely wish I had the time to keep all of these problems updated. Appreciate your thoughts on the problem.

@@SolvedIn6 your videos have been great and you exam the process perfectly. Just thought I’d leave a note for anyone taking the exam soon since the handbooks tend to change. Taking my exam in about a month and feeling more confident working through your videos

@@CG-kw5hk I really appreciate the feedback and am grateful to know that these videos are helpful. Best of luck on your exam!

Thanks for bringing this up! are you taking new PE format?

@@babakiani yes I’m taking it on Tuesday

You found a much faster way to solve this. Nice job, I'm sure the exam will be a breeze for you!

Thanks for letting me know! I'm glad these videos are reaching people and are helpful.

I think you are correct - you would just need to divide your flow rate in the beginning by the design retention time. To me, it seems like its just a matter of which step you prefer to solve for first.

Are you taking the new format exam?

Great question. In this case, it is simply because the problem gives us the amount of dry solids removed in the primary tank PER DAY as well. We are thinking about this calculation in terms of some unit length of time - in this case, sludge production PER DAY. If the problem had only told us how many pounds of dry solids were removed "in general", we could have removed "per day" on both sides of the equation.

That is a good point - and the PE will be picky about that. I should have worded the question more specifically to say something more like "from the given options, which number is most close to the maximum value that Tuesday's measurement should have been?" Thanks for pointing this out.

Thanks so much for letting me know. I'm really happy to know that these videos are actually useful.

Thanks so much! I appreciate the feedback and am glad that these videos feel worth the time to watch.

Sorry for the delay - you are one of the first people to comment on my videos and I didn't realize i wasn't getting notifications about it. So thats a good question - maybe i should have specified that the units the answer is looking for is gal/(capita-day). If I understand the way you perceived the problem, solving it in this manner would give you the net difference between old consumption and new consumption - so yes, you could still divide by the new population and get the right answer! The real trick to this problem is the concept of geometric growth for the population. if you get that part right, you can solve it based on the differences in consumption the way you described.

Hey, not sure if it helps but in the conversion section of the manual the conversion is called out as Ft of H2O= 0.433 psi, if you look at the PSI conversion in the right hand column, it says PSI = 2.307 Ft of H2O.

Thats correct! and sorry for taking 2 weeks to reply to you two. You're some of the first people who have commented on my channel and I didn't realize I wasn't getting notifications about comments.

Thanks for letting me know! I'm glad these videos are reaching people.