The contributors to the thread "Variation in Level" certainly know their 'Pees', 'Iees', and "Dees", while in my case its way over (excuse the pun) my head!

Now, if you can, solve the following problem:

A process fluid tank can be filled by two fill lines in 4 and 5 hours, respectively. It can be emptied by two drain lines in 3 and 6 hours, respectively. If the tank is half-filled and all lines are opened simultaneously, will the tank fill up? Or will it empty? In how many hours?

Regards,

Phil Corso, PE {Boca Raton, FL, USA}
[[email protected]] ([email protected])

 

Hello,

Provided the outlet flowrate does not depend on the level, the tank will be empty in 10 hours.

Regards,
Andrey Romanenko

 

Fill rate = 0.45 tanks per hour (1/4 + 1/5).
Empty rate = 0.50 tanks per hour (1/3 + 1/6).

Net = Empty at 0.05 tanks per hour.

Time to empty 1/2 tank = 0.5 (tanks) / 0.05 (tanks per hour) = 10 hours.

 

The half a tank where empty after 10 hours if all channels open.

 

Empty, in 10 hours?

 

The fill lines have flow rates of 0.25 and 0.20 tanks/hr, for a total available of 0.45 tanks/hr. The drains are 0.33 and 0.166 tanks/hr, for a total of 0.50. Therefore the tank will empty with a net outflow of 0.05 tanks/hr. Since it's starting at 0.50 tank, it will be empty in 10 hr.

As far as being impressed with us PIDer's, I for one am at least as impressed with your (seemingly encyclopedic) knowledge of power distribution and transformers. You usually lose me about the second sentence.
--
Steve Myres, PE
Automation Solutions
(480) 813-1145

 

Oh well...

Assume 1 m3 is the tank volume. Then the flow rate in the first filling line is 1/4 m^3/hour, that in the second is 1/5 m^3/hour - decimalising gives 0.25 m^3/hour and 0.2 m^3/hour.

Total fill rate is then 0.45 m^3/hour. For the outflow, the two flows are 1/3 and 1/6 respectively, and the total
outflow rate with both open is 0.333 + 0.1666 = 0.5 m^3/hour.

So the tank will slowly drain at a rate of 0.05 m^3/hour, and from half full will take .5/.05 = 10 hours. I haven't done the calc from half empty.

Do I get the lollipop?

Bruce

 

10 hours to empty.

 

Can I answer it please... it will take 10 hrs to empty.

Ah - nice little exercise for the brain - or maybe I've made a complete idiot of myself...

Andy Clegg

 

I believe that the tank will be empty in 10 hours.

 

It will empty after 10 hrs.

Regards,
Shailesh C Patel

 

Empty in 10 hours.

Robert Scott
Ypsilanti, Michigan

 

<p>It will empty in 10 hours.

<p>Add the fill rates and subtract the empty rates to find the total rate when all lines open:
<pre>
Time Flow Tot flow
Fill1 4 0.25
Fill2 5 0.2 0.45
Empty1 3 0.3333
Empty2 6 0.1666 0.5
Diff
0.05
</pre>

 

You must be an optimistic engineer.

 

Tank filling 201: if the tank contains beer, and is being observed by 'x' thirsty engineers ....

 

Replying to those who submitted answers:

The Good News:
All of you who gave the answer '10 hours' have won the Yellow Ribbon or 3rd prize. There were two stand-outs;

a) Those with the answer '10' used the RxT approach. It is certainly an acceptable solution since the original question was presented to high-school students. (SATs today, Regents in my yute) However, only ANDREY ROMANEKO provided the constraint that made the RxT solution acceptable.... "provided the outlet flowrate does not depend on the level..." For that, Andrey is entitled to the Red Ribbon or 2nd prize.

b) Steve, while I appreciate the "apple" it won't get you an upgrade to from yellow red ribbon.

The Bad News (or Now, The Rest of the Story)
Andrey recognized that level does affect efflux. Hence, a more exacting mathematical solution is required. My challenge... should you accept... is to try for the "Blue Ribbon!"

BTW, this "problem" should not be misconstrued as a putdown nor demeaning, especially you IT engineers and techs.

Of course, the above paragraph was my PC statement. My sympathies have always been with instrument and electrical techs. My 2nd job as an EE was to serve as an electrician's helper in a very hostile environment.... the Chief thought I was put there to replace him. Note, I mentioned 2nd job. So, in anticipation of your next question... my 1st job as an EE involved horse-manure... but that's another story for another time!

Regards,
Phil Corso, PE {Boca Raton, FL, USA}
[[email protected]] ([email protected])

 

Phil: If that's the case, you'll need to give us more tank geometry i.e.: where the inlets are, because unless they're at the top, filling against head will have to come into the solution as well.

 

You can use your own ABC (Analysis Basis Criteria) making the soution as simple or complicated as you want! For example, I set Cv, Cd, and Cc to uinity.

Regards,
Phil Corso, PE {Boca Raton, FL, USA}
[[email protected]] ([email protected])

 

If we are trying to be cute, my solution is that the tank will never go empty under the conditions described. The inflow water will flow though the tank to get to the outlets, therefore there must be water in the tank as long a the inflow continues. The tank therefore will not go empty.

Mark Blunier

 

Respondng to Mark's Aug 30, 2:21pm comments... an astute observation.

You are on the road toward the Blue Ribbon (1st prize!) (Who said ITs don't know no math!)

Regards,
Phil Corso, PE {Boca Raton, FL, USA}
[[email protected]] ([email protected])