Harvey:
This is a very interesting thread and one that I feel is not only important in its understanding of fluid flow, but also one that deserves more detail and attention as you’ve ably addressed. As I inferred, this query is full of holes that need plugging: no flow rate is stated, no total vertical height is given, and neither is mention made of gravity flow. I think we now all concede that all we have as a driving force is gravity flow; i.e., no pump is being used. Somehow I suspect this is an academic problem, but I totally agree with your description of the basic flow characteristics – except that I don’t quite understand whether you are describing a definitive, derived height of a slug of diesel or if you mean that the entire vertical pipe would be diesel-full
You state that “the diesel fuel would be flowing fast enough down the pipe so that the friction would exactly match the static head providing the driving force” but doesn’t this infer that the entire height is diesel-full? If, as you state, the total height could be “several thousand feet” then we’ve got a hefty design scope that must be designed and made operational:
1) 2,000 vertical feet of diesel fluid yields a hydrostatic head of approximately 700 psig, I believe;
2) If the hydrostatic head pressure at the bottom of the pipe is 700 psig, then an expansion has to be controlled into the target tank using a control valve; this means that flash vapors could be produced and this would have to be taken care of (another subject for a later time).
3) Needless to say, if the pipe is kept diesel full, it must be mechanically designed to withstand the pressure and operate as such.
4) If the total pipe is indeed diesel-full, doesn’t this raise the concern of maintaining such a pressured condition in an underground mine? I believe this concern was mentioned previously.
I agree that a self-venting, 1-1/2” vertical pipe is limited to approximately 5 gpm; but that’s the pipe size that is given. With an assumed specific gravity of 0.8 the 6 kg/sec of diesel is equal to approximately 120 gpm. This seems like a very high flow rate for 1-1/2” pipe and more in line with a 2” pipe size. Could you furnish the equation or method of arriving at the flow of 6 kg/sec?
For operational control of keeping the vertical pipe devoid of diesel when the gravity transfer is not being done, it would seem that self-venting flow is the only way to go. A conceptual design would include a flow control on the outlet of the top source tank prior to its introduction into the vertical gravity fill line. This would allow for shut-off at the source outlet, leaving the vertical line dry after the transfer. I know it was stated that the target tank is smaller than the source; but the query once again fails to state if the method of fill is to transfer 100% of the source tank 100% of the time. I’m assuming that would not necessarily be the case. But then again, I could be guessing wrong.
Regards,
Art Montemayor
Spring, TX