oil gusher question math and engineering

[Botany]

If the pipe that is burst is 22" with the 1" walls that would
give the pipe a diameter of 21" and a radius of 10.5"

so the area of the opening would be:

area = pi x r squared = area = 3.14 x (10.5 x 10.5)

area = 3.14 x 110.25 = 346.19 (aprox) square inches

*********************

now the force of the flow in 100,000 psi ..... i read that figure on the internets

how do you figure the total force of oil and natural gas flow out of
the broken pipe?

[BadgerKid]

1. Pressure = force / area.

[randr]

2. Other conciderations

The pipe we are being shown is the end of the bottom section that obviously broke when the whole thing came down. The other end somehow makes its way back to the well head at which point is is obviously bent, kinked, and probably leaking as well. There is a reason BP is holding investigators away and my guess is that they are only showing the small leak.

[Botany]

5. The keeping of nobel prize winner Sec. Chu and company out of the loop

is a big "tell." Last I heard was that there were three leaks too.

As a person w/ a background in ecology "they" really have screwed the pooch.

A really complex engineering / geo-physics problem with the stakes being the
life of the planet.

[izquierdista]

3. More facts needed

You need to know how effective that force is at pushing mass out of the pipe. That requires knowing the viscosity or the Reynolds number of the fluid in the pipe. A safe assumption would be that the oil/gas mixture is above its critical point, so there is only one phase flow coming out of the pipe. Viscosity would also be dependent on temperature, but assuming that it rises adiabatically from the reservoir below, a rough guess of 300-400F would be reasonable.

[Botany]

7. I wonder if the flow would be turbulent or laminar

BP must be holding back some info & data.

[NJmaverick]

8. Most likely turbulent

[NJmaverick]

4. This is what you need to consider when talking about this problem

Bernoulli's equation

http://www.princeton.edu/~asmits/Bicycle_web/Bernoulli.html

[Botany]

6. thanx

not enough info to do the math ...... BP has the data though.

[PVnRT]

9. Pressure x Area = Force, but the real concern is how much is coming out

Given your numbers, the force at the exit point of the leak (assuming the pipe is fully broken open) would be 34.6 million pounds, 17,300 tons. Of far more concern is how much of that oil is getting out and making its way towards the gulf coast. Unfortunately, there's no good way to estimate that easily:

From Crane's flow of fluids paper (pretty much an engineering standard), you have

Pressure drop = 3.62*(K*density*flow rate sqaured) / (diameter^4)

The pressure drop is 100000 psi (since that is probably gauge pressure, the absolute pressure is 102,400 psi, and that minus 2400 psi at one mile under the ocean is 100,000 psi). K for exiting a pipe is 1.0, density is around 60.7 lb/cubic foot (for Mexican crude, the best number I can find), and we already know the diameter. Rearranging the equation results in a flow rate of 65.33 cubic feet per second, or 29,300 gpm. That's 42 million gallons per day using a rough estimate, 1000000 barrels per day. So, you can't really use the Bernoulli theorem (or any one of its derivations) to find this flow rate. It's usually estimated based on what the spill looks like, and that's an imperfect science at best.

In this case, the flow out of the pipe is most likely limited by whatever the sonic velocity of oil at those conditions are, which I'm not going to bother with now, as well as any other fittings or other items that might be restricting flow in the line.

[Botany]

10. A restoration ecologist friend of mine told me that ....

.... they drilled to 25,000 feet under the sea floor and not he 18,000 feet they said they
were going to drill to ..... not only 1 mile of sea water but 1.5 miles more of rock, earth, and oil
overburden pressure on the "stuff" coming out of the pipe.

The complexity of this problem is mind numbing.

thanx for your input of info ..... I kind of get it.

[PVnRT]

13. That tells me there is a lot of head loss prior to the exit point

I wonder if the 100,000 psi is where the oil is sitting or at the exit of the pipe. That could change the calculation dramatically.

[damntexdem]

11. Well, technically, if the pipe is 22" and the walls 1", then the inside diameter is 20" ...

So the radius is 10", and the area 314 sq. in. So a bit less -- but the point remains.

[Botany]

12. Oh ..... me dumb so it 1" on both sides of the pipe?

:dunce:

thank you for the correction.

DU has some very smart people