Thanks for all of the interest and contributions being made, so I'll try to respond as best that I can.
To Katmar. When we send diesel fuel down the mine, it goes in batches. The pipeline is not allowed to contain a column of fuel by code, so the hydraulics are similar to a rainwater leader - ie., open on the top and bottom so that its a straight through flow. The pipe is therefore running only part full in the cross section. The time it takes for the diesel fuel to run down the pipe in batches is not important.
To Miningman. Your comments would apply to running the pipe full, but that will pressurize the line by whatever head builds up. That is what I'm trying to avoid by treating the line as a drainpipe or rainwater leader. The SG is very high but it's not backfill. I'm not at liberty to reveal exactly what I'm doing yet, as the project is very confidential. I'll reveal more as time goes on.
To bimr. Thanks for that reference regarding the diesel flow. For the benefit of all, I'm copying what you said elsewhere regarding the work done by Dawson and Kalinske - as follows:-
[If you desire to limit the terminal velocity, then you need to limit the flow of fluid into the pipe since the terminal velocity is related to fluid flow.
In a report done by Dawson and Kalinske - "Report of Hydraulics and Pneumatics of Plumbing Drainage Systems' they developed the formulae. The terminal velocity is related to fluid flow and diameter according to the equation:
Vt = 3.0 (q/d)^(2/5) and
Lt = 0.05(Vt)^2
Where Vt is terminal water velocity (fps), and Lt is the developed length to develop terminal velocity (ft). From these formulae it was determined for various standard pipe sizes terminal velocity is about 10-15 fps, and that this velocity is achieved within 10-15 feet of fall.
What this means is that the velocity of falling fluid is about the same regardless if it is falling 2-3 stories, or 100 stories.]
The terminal velocity of 10 - 15 fps is more than where the IAMPO flowrates settle in.
To all. I've pursued the rainwater analogy idea and found what seems to be a reasonable approximation to the issue with the pipe in the mineshaft (see attachment). The pipe does not run full as the fluid is in 'free fall' within the pipe, but neither can it reach the 'free fall' terminal velocity of an unconstrained fall. (Note that much of the fluid will be running down the walls of the pipe as well as away from the walls). According to the source, which is IAMPO, an 8" diameter vertical pipe can carry 913 USgpm. By extrapolation, 1,250 USgpm requires between an 8" and 10" diameter pipeline, running at 7/24th full. In the above Dawson and Kalinski formula the units are inches of pipe diameter and USgpm for fluid flow. I've tried the Dawson and Kalinski formula, but have not yet reconciled the two sources. Maybe there is a problem between the Dawson and Kalinski work (University of Iowa Studies - Bulletin 10 - Report on Hydraulics and Pneumatics of Plumbing Drainage Systems - 1937) and what I'm trying to do. Their lab test pipe was 30 feet long - mine is 3,300 feet long, so the hydraulic results can vary considerably.
Is it possible that the Coriolis effect can make a difference in fluid flowrate by sending the fluid to the pipe wall on a long vertical pipe run?
So I'm still struggling to find the 'correct' and minimum size of pipe to do the job.
Thanks for your continuing comments and valued input.
ECD40