Question

Problem 18.87 Drops of an oil that has a mass density of 700 kg/m3 are released from a broken undersea oil pipe that is 1200 m below the ocean surface. Use 1000 kg/m3 for the mass density of ocean water. Part A If the drops have an average diameter of 100 μm, how long do they take to rise to the surface? Hint: The drops quickly reach terminal speed and experience a viscous drag force of magnitude Fdwo=(0.0200Pa⋅s)Rv, where R is the radius of the drops and v is their speed. Express your answer to two significant digits and include the appropriate units. Part B After a chemical dispersant is applied to the oil to reduce the average drop diameter to 2.0 μm how long do the drops take to rise to the surface? Express your answer with the appropriate units.

Answer 1

Part A:  Given that the density of oil drop _o = 700 kg/m³, density of water _w = 1000 kg/m³, the drag force is F_d = (0.02 Pa.s)Rv and radius of oil drop is R = (100/2) m = 50 m. Now the velocity of oil drop can be calculated by balancing the forces on oil drop as shown below,

Thus the time taken to reach to the surface is,

  

Part B: When the radius of oil drop is R = (2.0/2)= 1.0 m then the velocity is,

  

  

Thus the time taken is,