Gravity flow in a mine shaft 1

[ChristopherFehr]

I am trying to calculate the flow rate by gravity in a 1" sch 80 pipe in the shaft of one of our mines. The pipe is 4300 ft long with a 4300 ft elevation diference, effectively all of the pipe is vertical. Currently we are allowing one tank on surface to feed the tanks under ground at about 75 l/min by gravity alone. I would like to determine the expected change in internal pressure and flow if we add a pump to the surface supply. The fluid is diesel and the delivery driver tells me that he has done it before and he is unable to increase the flow rate even though the pump on his truck can supply up to 50 psi.

Thanks

 

[Zapster]

I suspect that you have additional restrictions in the line besides straight pipe friction for the 4300 foot segment. Save yourself some time with the calculations, by looking at it this way. 50 psi is equivalent to 97 feet of #2 diesel based on a SG of 0.84. So you currently have 4300 feet of static head at the top of the line, so adding an additional 97 will give you 4397 feet of head. What increase in flow would you expect with a 2 percent increase in static head?

 

[rconner]

Not claiming to be an expert in this but suspect at nearly 10 feet/sec flow velocity in this very small size but very long length fuel pipe that the head loss for even a vertical pipeline with substantial head available at least at the bottom might be horrendous (I'm not surprised that 50 psi more driving pressure at the top is reported insignificant).
You may need to give a little more data (e.g. temperature, type diesel etc.) to get a more accurate response from the more learned folks on the forum.

 

[sailoday28]

While this may seem minor, don't forget to take into account the increase in air pressure at the lower elevation. 4300 ft vertical should yield an increase in elevation air pressure of about 2 psi, unless the mine shaft is somehow kept at atmospheric pressure.

 

[unclesyd]

There is an almost identical thread posted previously with a lot of discussion.
I didn't participate and have been unable to find it, maybe someone who participate will be able to find it.

 

[katmar]

The theoretical maximum flow under gravity would be around 110 litre/minute, so I agree with Zapster that there are probably other restrictions (valves, bends etc) that you have not mentioned. Under free flooded gravity flow there would be a zero pressure gradient down the pipe i.e. the head due to the height difference is totally balanced and offset by the friction losses. However, if you got a blockage, or closed a valve, near the bottom you would get a very high pressure - around 1550 psi.

Because all of the potential 1550 psi is being consumed by friction losses it means that the potential additional 50 psi that you could get from the truck offloading pump is trivial. And the 2 psi of additional air pressure at the bottom of the mine is even more trivial. Your uncertainty in pipe diameter and roughness will far exceed this.

I suspect that the earlier thread to which UncleSyd referred is thread378-81608

regards
Harvey



Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[sailoday28]

katmar (Chemical)How is 1550psi arrived at? If it is a hammer effect, did you include friction prior to valve closure?
Regards

 

[ChristopherFehr]

Thanks Guys,

Between this thread and the archived one above I've resolved most of my concerns.

Chris

 

[katmar]

sailoday28, No, I did not take hammer into account. You are right to point this out. If a valve was shut suddenly with a 4300 foot long slug of diesel hurtling down at 10 ft/sec the instantaneous pressure would be huge.

I got 1550 psi by saying 4300 ft diesel = 3600 ft water = 1550 psi approx. I.e. this is the static height only.

Harvey

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[CanuckMiner]

Eeek! A properly designed fuel delivery system in a mine would not have a valve at the bottom of the delivery pipe that could be closed. Any control valves (e.g. diversion valves) would need to fail open.

Cheers,
CanuckMiner

 

[ChristopherFehr]

Don't worry Canuckminer, no valves in the system. It's been in operation as is for around 20 years, the only change we are considering is going from a gravity fed surface tank to pumping from the delivery truck.

Chris