P = V x Q ÷ 18,300 D4 where P is pressure loss, V is SSU viscosity at temp, Q is GPM flow and D is diameter of pipe.
Secondly the term siphon is use figuratively, as the true definition of siphon is a device that draws fluids downhill using stored potential energy provided by gravity.
Like it or not, there is going to be a pump involved.
You're making it far more complicated than you should. No need for complicated formulas, that is what is leading you astray.
Keymaker is right and his simple straw and ballon shows it. You would need far more complicated math to do it by equation because you would have to express what pressure is on the oil at each spot in the pipe. But far easier to just think about it.
Oil at the bottom of the pipe. Pressure from below is higher than the pressure of the oil from above. The oil will rise. It does not matter if there was an opening, a leak, or not. The pressure in the surrounding water is exactly the same as the pressure inside the pipe except for the pressure upwards from the oil wanting to get out from under the mantle. Viscosity only comes into play if it is physically impossible to move. But it isn't. The oil is quite fluid.
Oil at the middle of the pipe a half mile up. In or outside the pipe the pressures cancel each other out. The oil thus has only an upward pressure.
Oil at the top of the pipe. All pressures in and outside the pipe cancel out except for the upward pressure. No matter if the pipe is a mile long or if the pipe is the length of a soda straw or if the pipe is a mile wide or the diameter of a soda straw, the oil will rise. Oil is lighter than water. There is pressure working on the oil because of the tremendous pressure of the mantle. Haven't you ever seen a Hollywood movie where the well blows? Think of that happening but the well is under water except for the very top. Don't you think the oil would shoot out of the top? In this case it even shoots higher because the water pressure outside of the pipe contains the oils and has no reason to seek a less pressurized environment. The only less pressurized environment is straight up.
No pump necessary. The only time this oil is not coming directly to the surface is when, because of the velocity of escape, the oil creates micro-encapsulated bits of oil surrounded by seawater. This type of plume will eventually reach the surface but it might take weeks because the surface area of the small bit of oil is large compared to the volume of oil creating drag so it will take weeks or months to rise. A frothy milkshake takes a while to settle.
This thread is about as inane as it gets. The only one speaking any sense is keymaker and he is being personally attacked because why? Past wrongs? You people have to get a friggin' grip. But you won't. Some of you cannot help yourselves. So pick away.
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