Tank drain flow rate and drain time calculations

[calguyv7]

I have a very simple problem, but I am trying to gain confidence in the calculations for drain down time and flow rate for a free-flow tank drain situation.

I have used free calculators at

http://www.freecalc.com

and

http://www.e-funda.com,

and I calculated the results by hand from my fluid mechanics notes. the hand calculation formula i used is

t = (area of tank)/([sqrt(2g)*area of pipe]*[integral_from h1_to_h2_of {h^-.5}])

simplified t = [A_t/(A_o*sqrt(2g))]*2*sqrt(h)

a 20000 gallon tank with 14 foot water height is draining out the bottom to a tank located just below it

I calculated for schedule 80 PVC pipe sizes 4, 6 and 8 inches.

I get drain down times of 2031, 902, and 510 seconds for average flow rates of 590, 1330 and 2350 gpm. That seems rather high to me, can anyone confirm I am even using the right formula / online calculators? this seems really simple but i just don't believe my answers...

 

[vpl]

1) Is this homework?
2) Are you getting the same answers with the online calculators and your hand calcs?
3) Are they in the same ballpark?
4) Since you say your hand calcs are from your notes, did you check your textbook, to make sure you copied the formula correctly?
5) Since you give your times in seconds with a flow rate in minutes, did you do your conversions correctly?




Patricia Lougheed

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[cvg]

recommend Brater and King, Chapter 4 gives the general equation for discharge through orifice under falling head. The actual equationjused may take different forms depending on the shape and orientation of your tank.

 

[calguyv7]

vpl - certainly not homework although i did these in school once upon a time. this is for industrial plumbing at work.

i did double check all my unit conversions (gallons to cubic feet, etc). yes the hand calculations

cvg - thanks for the photocopy, this does verify the formula I used. i see you are a civil engineer, do you have experience with industrial plumbing and flow rates? does around 600-2300 gpm sound accurate for a large tank free flowing through a 4-8 inch pipe with 14 feet of head?

 

[Bribyk]

For comparison, yesterday I was draining one of our systems with a constant 1 or 2 ft of head through a 2" X 1' vertical steel pipe and the flowrate was 25-50 US gallons per minute. Through a 4" pipe this would be about 625 to 2500 gpm with only 2' of head. You might be a little low with your estimate.

 

[786392]

Dear calguyv7,
There is that 'behaviour of falling(or Free-Falling)bodies'

under the effect of gravitational pull;sometimes,somewhat forgotten

but does impact vertical flows downwards much more noticeably

as may be felt/noticed on directionally upward vertical flow against the gravitational pull.

Best Regards
Qalander(Chem)

 

[5250081]

I have always been exposed to Newtonian fluids in my piping engineering career. I have just learned that dilatant liquids, i.e. liquids which their viscosities increase with an increase in shear force applied on them do exist, e.g. clay slurries. If one do pump sizing calculations, how does he compensate for these effects of viscosity changes especially the motor selection to counter the effects of this increased resistance to pumping.