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Forced Gravity Discharge Velocity

Forced Gravity Discharge Velocity

Forced Gravity Discharge Velocity

(OP)
I would like to know the average velocity and friction loss in a gravity discharge line.  I am pumping water (it is actually a chemical feed that is mostly water so let’s just analyze the problem as if it were water) at constant (the pump is positive displacement type with sufficient head to overcome moderate discharge pressures) flow rates (anywhere from 1 to 5 gpm) to a vertical line that runs straight down (vertically) 200 feet into a water reservoir.  The vertical pipe is PVC and 1 inch nominal inside diameter (during design it may range for 0.5 inch to 1.0 inch with the exact ID dependent on wall thickness/schedule).  The pipe is immersed (i.e., submerged) in the water reservoir 50 feet down (so PVC pipe is actually 250 vertical feet long).  There is a backpressure valve at the top of the vertical pipe that will keep the feed line full for immediate discharge to the top of the vertical pipe when the pump is turned on.  It is very important in this process application to know how long it will take for the feed to travel the vertical 200 feet distance as immediate (or as near as practical) feed to the reservoir is desired when the process logic turns on the feed.  

Question No. 1 – Assuming that the vertical line is sealed (i.e., no air can enter or escape at the surface) at the top, how long will it take (i.e., velocity) for the initial flow to reach the reservoir elevation? Head loss?

Question No. 2 – If I add a vent at the top (e.g., open air vent with no significant inlet restriction or vacuum-breaker vent that releases at 1 psi differential) will this help, hurt, or make no difference to the answer in Question No. 1 above? Head loss?

I sort of see this problem as bracketed between ‘plug flow’ of a full line (minutes) and ‘free fall’ in a large empty line (seconds); however, the process can accept seconds (but not minutes) as the travel time from top (elevation 0 feet) to bottom (elevation -200 feet).  Due to space limitations I can not go to a much bigger line and due to large turndown flow rates (5:1) I imagine that my head loss could be a problem (don’t know for sure).   Also, I may be missing some element of this dynamic process of which I should be aware.  

Any suggestions would be appreciated.  

Thanks.  

RE: Forced Gravity Discharge Velocity

It looks to me as though your Question 1 and Question 2 boil down to the same situation. I would imagine that during construction and operation the air would be almost totally removed from the vertical line.  Both situations would give you "plug flow" and a residence time of minutes.

The obvious way to reduce the residence time is to make the pipe diameter smaller, but this is not feasible because of your large turndown required. A 10mm ID pipe would bring your residence time down to 15 seconds or so at 5 gpm (at the cost of very high pressure drop) but as soon as your flow dropped to 1 gpm your residence time would increase to over a minute.

The only way I can see for you to approach the "free fall" situation would be to install a much larger pipe, say 3", but you said that might not be possible. It would have to be pressurised with air or some suitable gas to ensure that there was no liquid in the pipe. The pressure at your back pressure valve would be 200 ft water or 87 psi and this may not be possible. This way the water would fall down through the air without having to displace the water ahead of it, but it would still not achieve true free fall because the water would actually run down the wall of the pipe. I cannot see a way to achieve anything better than this.

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

RE: Forced Gravity Discharge Velocity

Dumb question, but why do you even have a pump?  YOu have 150' of elevation head.  Is your pump a metering pump to control dosage?  If so, you could still do the job without the pump by using controls.

As I see it from your description, when the valve at the top of the pipe opens, I assume it opens at about the same time the pump starts.  As long as the pipe stays full, the rate in the pipe equals the pump discharge rate.  That knoweldge will let you calculate your transit time.  

If the pipe is full and stays full then there is no chance for plug flow to start because there is no vapor pocket in the line.  Plug flow assumes presence of a gas/vapor  pocket.  Thus your pipe is full (closed cross-section) and the velocity and hence transit time is determined by the pumpng rate, not gravity free-fall.  If you get an air leak then all bets are off.  Who knows what the real transit time is.  Two-phase flow prediction in any line is only good to ±25% accuracy.

Can you inject a tracer into the pipe to measure your transit time?  Fluoroscine dye, or a radioactive tracer?  If you are in potable water service there may be some other tracer you can use.

Hope I understood your situation correctly?
Thanks!
Pete

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