Fluid Velocity - Gravity Fed - Pipeline

[IGSAM]

Hello,
I want to calculate how long will a line take to drain, knowing the volume, slope & the fluid’s properties.
My problem is that I do not know which formula to use to calculate this:
• Fluid is in a pipeline so I cannot use Manning’s formula
• Fluid is slurry so I cannot use Hazen-Williams equation
What would you suggest to use?
The application is a line that will need to be drain in an event pond if there is complication with the pumps. Fluid is a slurry (mix of water and solid particles).

Thanks!

 

[LittleInch]

What you will also need to work out is how the volume is replaced. Unless you have a vacuum breaker at your high point then you're into open pipe flow with all sorts of things going on (glugging, vapour locks, half pipe flow....)

What size, volume, slope are we looking at here?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[bimr]

Don't know of any method to make such a calculation. Suggest you make the calculation for water and then estimate the time from there.

 

[IGSAM]

Hi Little Inch,

The total lenght of the line is quite long; it is a tailing line (5km to be extended in the futur). The drain is situated at 182m of the pumps discharge and will drain only a part of the line (the rest will drain in the tailings.
Total Volume to drain : 122.7 cubic meter
Size of line : HDPE 800mm DR11 (inside DIA is 655mm)
Average slope is 1%

There is vaccuum breaker at the high points. And a vent point right after the outlet of the pumps.

Hi bimr,
I thought of doing that to give me an initial estimate, but the content is made out of 42% solid particles. So I except the time this slurry will take to drain to be much higher than the water and I have no idea how (or if it can be done) to do a relative proportion of the velocity of the line vs viscosity.

 

[zdas04]

If the slurry is reactive (i.e., the solids and the liquids react to form a non-Newtonian fluid) then you are truly out of luck, none of the attempts to categorize the friction term of a non-Newtonian fluid have resulted in correlations that work at all. Many slurries are reactive, but most are not.

For a non-reactive slurry you can get good results by calculating a mixture density and using that in calculating Reynolds Numbers and dP in Darcy-Weisbach (don't use any correlation that "skips" using friction factors since your 42% solids will put the density way out of the range of something like Hazen-Williams). If you have a lab test for slurry viscosity use that, if not then you have to guess the impact of the solids on water viscosity and I would guess something like 3 times the water viscosity, but that is not even an educated guess.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[LittleInch]

I'd mussed it was slurry.

However you normally work out your fluid flow for this stuff should work.

If you have a vacuum valve providing air into the top and an even slope, you essentially have a known pressure drop per unit length based on height. Then run a few case to get the same flow versus pressure drop per unit length.

At 1% slope though you might start to run into other problems such as separation and settling as it's doubtful you'll get a sufficient velocity to keep it all in suspension. It might even just stop and not flow at all. Slurry is strange stuff and most of the time you need to do some practical testing to get the required physical properties.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[fel3]

IGSAM…

Mannings CAN be used for pipelines, both pressure flow and open channel flow. It's not just for channel flow. I use Mannings all the time for open channel flow in sanitary sewers and storm drains and sometimes for low head flow in large diameter storm drains and irrigation pipelines. Even Hazen-Williams can be applied to open channel flow, but I don't know anyone who does.

However, Mannings may or may not be appropriate for a slurry. If the slurry has similar fluid characteristics to water (e.g. density, viscosity, etc.), then you should be OK with Mannings. If the fluid is significantly different, then you may need to fall back on Darcy and use the Colebrook-White Equation (or one the many explicit approximations to CW) for the friction factor. Colebrook-White includes the Reynolds Number and that's where your fluid's specific characteristics will reside.

==========
"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill