Hydraulics exercise - Buoyant force

[Matt.Sz]

Hi
I'm first year Civil Engineering student, taking a resit in Fluid Mechanics. Our lecturer left us a bunch of revising exercises. I have a problem with one, can anyone help? This lecturer is currently away and doesn't reply to emails.
Here's the exercise:

A steel pipeline designed to convey oil of relative density 0.8 has an internal diameter of 90cm and an external diameter of 95cm. It is lying on the sea bed, completely immersed and it is anchored at intervals of 8m along its length. Sea water density is 1020kg/m^3 while the density of steel is 7900 kg/m^3. Calculate the largest (the worst case) upward force on each anchor.The given answer is 11.70kN, but I get 28.45kN every time socould someone explain it step by step? Thank you

[swansont]

Could you show your work, step-by-step?

[Matt.Sz]

I start by calculating the weight of the displaced water by the pipe, as the buoyant force equals the weight of displaced water.
Area of the end of pipe: A= pi x 0.95^2/4 = 3.15x0.26 = 0.71 m^2
Volume: V=area x lenght= 8m x 0.71m^2 = 5.69 m^3
Mass of displaced water: M=rho x volume = 1020kg/m^3 x 5.69m^3 = 5799.5 kg
Weight of the displaced water: W=m x g = 5799.5kg x 9.81 N/kg = 56893.1 N
And this is in total so one anchor is half of it so 28446.3 N

I assume I forgot about something as there's loads of unused data left, but my lecturer used to give us a bad answer once in a while as well so don't know haha

[swansont]

One anchor per 8m, so you don't divide by 2. If you have 800m, there will be 100 anchors
Pi is 3.14 (small error; about 20 kg)

You have the buoyancy force. Is there nothing pulling down on the pipe, other than the anchor?

 

[Matt.Sz]

If I substract the weight of the pipe with oil in it (35071.1kg that is 344041.5N) then the result is negative. And it's logical as it's fully submerged and it's supposed to remain on the sea bed?

I mean the buyoant force is the only force acting upwards and the question is about this force...

[Endy0816]

What happens if we assume the oil supply has been disrupted, leaving air?

Edited August 22, 2017 by Endy0816

[Matt.Sz]

It took me so long to realise that "the worst case" means an empty pipe, thank you all! Got the right result finally

[Endy0816]

lol, your professor definitely didn't make it obvious, even throwing in a red herring  by providing oil density. A good question there, glad we could help you find the right result.

[studiot]

Endy definitely deserves a  +1 for spotting this.

Matt you can clcik on the heart at the bottom right of the post to upvote someone's post.

 

As a matter of interest how would air get into the pipe if the oil stopped?
The pipeline will contain air when it is first laid and perhap gas if it is used for gas transmission at some point.
You may wish to know that it is common to pump water through subsea pipelines in the absence of oil or gas.

Also water is pumped into the geosubstrate to help remove the maximum quantity of oil/gas.

 

You have to fill the pipes and pores up with something.

Edited August 22, 2017 by studiot

[Endy0816]

Not trained in this area specifically, but maybe a pipe or valve left open to the atmosphere on our imaginary oil rig and a pump left running on the shore.

Be really hypothetical but somehow we manage to pull off crazy hypotheticals regularly.

Weight of the pipe was the other big peice Swansont had covered. There's actually a buoyancy calculation for vessels that is similar, upward buoyancy force minus downward weight.

I always like it when we are able to help people out. Sometimes teaching via questions feels like pulling teeth, but then there's times like this where it works wonders.

[Area54]

15 hours ago, Endy0816 said:

lol, your professor definitely didn't make it obvious, even throwing in a red herring  by providing oil density. A good question there, glad we could help you find the right result.

In the real world we often do not know exactly what data will be necessary to solve a problem. It makes problems more realistic if the examiner includes non-essential information. And it teaches an important lesson, preparing the student for that "real world".

[swansont]

36 minutes ago, Area54 said:

In the real world we often do not know exactly what data will be necessary to solve a problem. It makes problems more realistic if the examiner includes non-essential information. And it teaches an important lesson, preparing the student for that "real world".

That's one of the reasons you practice: to see what information you need.

Adding extraneous information is a tactic used in writing questions. I've done it. Students without a firm grasp of the material will often try and work the extra information into their solution. It's one more lever for seeing who knows the material and who doesn't.  

11 hours ago, Endy0816 said:

Not trained in this area specifically, but maybe a pipe or valve left open to the atmosphere on our imaginary oil rig and a pump left running on the shore.

From a practical standpoint, it doesn't matter. It's the worst-case scenario in terms of buoyancy. It's also a bit of a lesson that you can't always envision all of the possible disasters that might befall your project. Just because you can't think of how you might end up with air in the pipe doesn't mean it won't happen. One of the more dangerous things you can do is say "that will never happen" for something that isn't physically impossible.