Gravity flow of oil in pipe.

Try this one?


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When the pipe is full you can use Darcy-Weisbach, but it seems that you want to be able to estimate flows for part-full pipes as well. There are plenty of online references and calculators for open channel or part-full pipes - such as the one linked by LittleInch.

As you have mentioned, open channel formulas don't use the viscosity. Note that in Darcy-Weisbach the viscosity is only used in the determination of the friction factor and the pressure drop in turbulent flow is only weakly influenced by the Reynolds Number (and therefore viscosity). Also, in open channel flow the range for the Reynolds Number is much less than in pumped pipe flow.

So for your oil you should get reasonable estimates using the online open channel calculators. As a check calculate the flow rate for a full pipe using both the Darcy-Weisbach and open channel equations and see how well they agree.

Katmar Software - AioFlo Pipe Hydraulics

"An undefined problem has an infinite number of solutions"

Open channels and drain lines usually have a fall or slope which is far more important than the height of the fluid in the pipe.
but what sort of viscosity are we talking about here?

Thick lubricating oil and viscosty > prob 50cP are like treacle. Very difficult to drain effectively.

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

Thanks for the replies.

In retrospect, I could have provided more detail.

The application is for draining a very small bund - less than 200mm high. The vessels in the bund will overflow it if the oil is not drained away effectively. The oil is has a kinematic viscosity of 33 mm^2/s, density of 0.92g/cm^3, so it flows fairly well.

I tried using the Hagen-Poiseuille Equation, but the results were unreasonably high. A 1000mm long 3" (67mm ID) pipe with 100mm fall could flow almost 15L/s. Based on THIS METHOD, I'm expecting around 5L/s which intuitively 'feels' about right.

The open channel flow calculator provides a more reasonable value of 8.6 L/s (based on a full pipe), but I can't see how to solve it manually. The variables end up in a loop [Re < W < Q < Lambda < Re]. WHen I search open channel flow, I keep getting the Manning equation which doesnt' consider viscosity.

Thanks again.

I think most people just size it "by eye". A 3" drain line is rather small and could easily get blocked by leaves, gunk, dirt etc.

I would have min 4" and possibly 6", especially if its only 1m long....

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

With the additional information you have provided I have "run the numbers" using Darcy-Weisbach and my results are significantly lower than yours. Most of the information you can see in the included graphic but what is not shown is that you need to include the entrance losses of getting the oil into the pipe and also the energy consumed in accelerating the oil from standstill to about 1 m/s.

Note that the pressure drop is shown as zero because you have atmospheric pressure at both ends, but the driving force comes from the -0.1 m elevation change.

As an illustration of the effect of viscosity, if the viscosity is changed to 1 cP (water-like) the flow increases to 3.64 liter/second. A 30 fold change in viscosity changes the flow rate by 6%.

Following LittleInch's advice - a 100 mm ID would give a flow of 7.8 l/s and a 150 mm ID would give 18.5 l/s.

You can use any flow formula, but for those that assume circular pipe, you must substitute Diameter of a circular pipe with the "hydraulic radius" at any given height of flow. You can then account for viscosities different than water at 20°C


--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

_G_

That's a strange handle....

Anyway, back to basics as we don't really know what it is you have here?

I think most of us are assuming this is an open channel flow but is it?
How does this drain work if its a bund?
Why is it full of oil?
To what depth?

Does the pipe start full and end up half empty ( that's a difficult one to calculate)

One metre long is probably not long enough to establish steady state / steady height which most of the formulae assume.

how much are you trying to drain? 10 l, 1000 l, 10,000 l?

Designing something this small is not going to work and is really just a waste of time and effort compared to just looking around you and seeing what size works and what doesn't.

but some answers tot he above might concentrate everyones response...

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

You should probably use a culvert flow calculation such as

You have to register at the site to use the calculator, or do it yourself using the method and formulas shown on that page.

I'll let you do that.
Please let us know what answer you get.

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."