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 â€" 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 â€" 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. Ideally, I would like to set up a model (e.g., equation) that represents the variables that I can change to optimize a solution to my problem.

Any suggestions would be appreciated.

Thanks.

I think you need to know some pressures. You can calculate the pressure at the outlet of the pipe that is submerged 50Ft down. And, you know the pump discharge pressure. Knowing the gpm you know the inlet velocity. you should be able to calculate the time. You can get the Reynolds number and get the friction factor from that. I am not sure, since the pipe is sealed, and assuming that the pump doesn't let any thing by, that gravity will assist - if nothing can get into the line there won't be any free fall - that would create a vaccuum. If you put a vent in the top of the vertical pipe you run the risk of discharging out the vent as opposed to the bottom of the line. This, of course, is if I am understanding your problem correctly.