When Deepwater Horizon, the oil rig operated by British Petroleum, sank in the C

Question

When Deepwater Horizon, the oil rig operated by
British Petroleum, sank in the Caribbean on April 22,
2010, the pipe it was attached to broke near the ocean
floor at a depth of 1500 m. The pipe extended 1300 m
below the ocean floor into the subterranean cavity
where the oil was located. The pipe had a diameter of
30.0 cm and officials estimate that oil flowed from the
pipe at a rate of 10,000 m3 per day. If the density of seawater is 1030 kg/m3
and the density of oil is 900 kg/m3, by what percentage would the pressure in the
cavity have needed to decrease to allow the flow of the
oil to stop

Explanation / Answer

Using the the bernoulli equation you can ignore the first and last pressure, because you are just looking for a ratio. And you can set the second velocity term to zero. This leaves you with: Rhogh1+(1/2)Rho(V1^2) = Rhogh2. Again because you are looking for a ratio of pressure you do not need to use the pressures In the equation, once solved you will get a number that is equal to the percentage that the pressure has to decrease. Plugging in the numbers: (don't forget to put velocity in m/s) (900)(9.8)(-1500)+(1/2)(900)(.11574^2)=(900)(9.8)(-2800) -1322993=-24696000. The ratio of these numbers is. .535 This means pressure has to decrease by 53.5% to account for no flow.

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