Need help with evaporation question

[utilityeng]

This seems like a pretty straightforward problem, but I can't seem to get the same answer as the solution manual.

Evaporation from the surface of a pond is 2 gpd/ft^2. The surface area of the pond is 1.4 acres. How much water evaporates in one hr?

The solution is: 

Total volume of water lost to evap in 1 hr: 2gpd/ft^2 x (1/24) x 1.4 x 43560 = 122,000 gallons

I get 5,082 gallons. Where am I going wrong?

I thought at first I was missing a unit conversion but since you are multiplying the evap rate by the surface area of the pond in ft^2, the answer should come out as gallons, yes?

 

[ptatohed]

I get what you get: 5082 gal/hr.

The solution you posted mathematically comes out to 5082 gal as well, not 122,000.  

Maybe the book's solution is correct but the answer is a typo?  Are there A - D choices?  Have you checked the publisher's errata?  

 

[utilityeng]

It's from a Goswami practice exam: https://www.amazon.com/Practice-Exam-Civil-PE-RESOURCES/dp/1517333822

The evap question is actually just a sub-part of a larger hydrology question. Basically you have run-off from a 60 acre tract going into a pond, evap happening at the pond's surface, and a weir draining the pond. You have to find the elevation of the pond's surface after one hr. I would post the question/answer in its entirety but don't want to violate any copyrights. Several of the Amazon reviews do mention errors - I've found a few others. Not sure where I can find concrete errata for Goswami's publications, other than here?

As for the answer choices, when you use 5082 gallons lost to evap to solve for the larger answer - you don't get what the author considers to be the correct answer.

 

[matt267 PE]

I also get 5,082 gallons lost to evaporation. I suspect there's an error in the book's solution. I found many errors while I was studying. Very frustrating.

 

[Jbone27 PE]

What answer is author giving for evaporation?

Are all of the variables above given or are you solving for them?

 

[ptatohed]

Let's ask the man himself.  @civilized_naah ?

 

[youngmotivatedengineer]

It looks like the issue is the 1/24 conversion factor.  Since this is part of a larger problem, what number is used to solve the rest of the problem?  Is it possible that this subquestion was supposed to ask for the daily rate and then later on he uses a conversion to get to the hourly rate?  

 

[utilityeng]

What answer is author giving for evaporation?

Are all of the variables above given or are you solving for them?

The portion below is straight from the solution (variables provided are the evap rate and the pond surface area):

Total volume of water lost to evap in 1 hr: 2gpd/ft^2 x (1/24) x 1.4 x 43560 = 122,000 gallons

As for the rest of the problem - you are given the run-off tract surface area, the run-off depth, the existing elevation of the pond's surface, and the weir flow rate. You are tasked with solving the drop/rise in elevation of the pond over the course of one hr.

 

[utilityeng]

It looks like the issue is the 1/24 conversion factor.  Since this is part of a larger problem, what number is used to solve the rest of the problem?  Is it possible that this subquestion was supposed to ask for the daily rate and then later on he uses a conversion to get to the hourly rate?  

I think you're on to something. 122K is the answer you'd get if you did not divide by 24 - so it's the daily evap loss. The answer asks for the elevation drop/rise for one hr though. Not at home right now but I'll check the rest of the solution to see if it's converted to hrs later on in the problem. Will advise. 

 

[Jbone27 PE]

Okay well sounds like a mistake then. As mentioned above the hourly conversion (1/24) is left out of the solution. 

 

[utilityeng]

As an update - this does appear to be an error in the solution - the 122K gallon DAILY evap rate is combined with the HOURLY weir flow rate later in the problem, minus the required hrly conversion factor for the evap rate.

However, I wrongly stated earlier that you won't get the same answer in the end - you do.

If you use the correct hrly evap rate (5,082 gal), you get a rise of 3.43 ft (+230ft starting elevation) while if using 122k gallon daily evap rate, you end up with 3.17 ft. The answer (most nearly) is 233.15 ft. There's nothing else close to either solution so you end up at the same spot.

No harm no foul I guess but a shame to waste all that time trying to figure out what I was doing wrong.  

 

[youngmotivatedengineer]

Although it seems like a hassle,  it could be a blessing in disguise. Now you have a better understanding of this type of problem if it pops up on test. You also know what pitfalls to avoid with conversion factor and using the same units.

 

[ptatohed]

ue,

Some 2 cent advice.... typically when you post a thread asking for help and this many members spend their time assisting, you would thank them.  

It also makes members more likely to help in the future.   

 

[utilityeng]

My apologies - the assistance is greatly appreciated!