Calculating Buoyancy of Oil in Water

[just wonderin]

take a glass of water and place a straw in it. Now put oil in the staw.
the amount of oil above the water is given by the equation.

ex)
density of oil=d1(.5)
density of water d2(1)
height of oil column = H(10")

d1/d2 x H = amount of oil under water line(x) x=5"
H-x= amount above(p)p=5"

now say (p) is one fluid ounce " it is in a vertical column". if you changed the shape of the column above the water line would (p) still have to be the same height to push the oil to a depth of (x)? Or is it the mass of the water above to the water below what counts.

I have tried this with wood and the shape of the above part dosent mater. the bottom part always sinks to the same depth.as long as the ratio top/bottom is the same. is this true for liquids?

 

[just wonderin]

more info: what I want to know is if I change the shape of the conainer of the one ounce above the water line so the original height of 5" is now say two inches but still holds one ounce will the oil still sink to 5"?
Its my understanding the above equation only works for a column.

 

[Bob S]

If you put in two straws, side by side, one with water and one with oil, the pressure at the bottom of the two straws is equal. At the top of the liquid column in each straw (meniscus), the pressure is atmospheric pressure. Calculate the pressure in each straw as a function of the distance below the two meniscii, and show that it is equal at the bottom of both straws.

This also true with other liquids. In 1986, about 1800 people were asphyxiated when Lake Nyos (in Cameroon), with compressed and dissolved natural carbon dioxide in the bottom (from a volcasnic fissure), suddenly erupted (like pulling the cork out of a champagne bottle). When the lake erupted. a cloud of CO2 gas (density heavier than air) enveloped the region and asphyxiated 1800 people.

The dissolved CO2 concentration in the lake water was most at the bottom of the lake, and if it rises (like in a pipe), small bubbles of CO2 begin to form, reducing the density relative to the water in the lake. Inserting a vertical 5.8-inch-diameter pipe to the bottom of the 666 food deep lake created a 148-foot high geyser of carbonated water. Read on... (from http://www.smithsonianmag.com/science-nature/killerlakes.html?c=y&page=1 ).

....Using seed money from the European Union and private sources, a team headed by Halbwachs tested garden-hose-diameter pipes in Nyos in 1990, then progressively larger pipes in 1992 and 1995. The experiment worked: the gas began venting. Halbwachs and coworkers were jubilant. Then the money ran out. The Cameroon government said it could not afford the $2 million to $3 million for permanent degassing installations. International aid agencies—more used to reacting to natural disasters than preventing them—did not grasp the concept. Kling, Kusakabe and others lobbied oil companies, governments and other organizations to pay for venting. Finally, in 1999, the U.S. Office of Foreign Disaster Assistance (OFDA) came up with $433,000 for a permanent pipe to be installed at Nyos.

By January 2001, the researchers had assembled rafts and piping at the site. Attached to a raft in the middle of the lake, a 5.7-inch-diameter pipe reached 666 feet to the deepest water layer. The Cameroon military provided emergency oxygen tanks for all workers in case of a rogue carbon dioxide release. After everyone retreated to distant high ground, Halbwachs pushed a remote-control button to activate a pump that primed the pipe. Within seconds a 148-foot spray shot into the sunlight at 100 miles per hour, and the small crowd let out a cheer.