- #1
rico22
- 51
- 0
Homework Statement
Oil is released from a submerged source at a constant flow of rate of Q=(0.1 m3)/s. Density of oil (p=870 kg/m3) is less than that of water and since oil is only sparingly soluble in water a slick will form on the water surface. Once its formed it will have a tendency to spread as more oil is added but also have a tendency to shrink as the oil both evaporates to the air and dissolves in the water. Eventually it would reach a constant size when these two tendencies became balanced.
A mass balance on the slick provides the following relationship: dM/dt = rate of oil slick from the source - rate of dissolution - rate of evaporation
where each term is in kg/s and where M is the mass of the slick. For this particular oil the rate of dissolution per square meter is 0.0000011 kg/m2s and the rate of evaporation per square meter is 0.004 kg/m2s.
The mass M of the slick is related to its size by:
M=pAW
where p is the density of the oil (given above), A is the surface area of the slick in m2, and W is the thickness of the slick in m. The thickness of a shrinking spill will decrease with time. In this case however, you will be looking at the time period between when it starts to grow and when it reaches a constant size. Assuming a constant slick thickness is probably reasonable for this situation and W= 0.001 m is a realistic thickness to use.
What surface area ( in m2) will the slick ultimately have?
Assume that the constant release of 0.1 m3/s of oil begins at t=0 and that A=0 at t=0. About how long will it take for the slick to reach a constant size?
Homework Equations
The Attempt at a Solution
First I converted my flow of rate into kg/s by multiplying it by its density. But the rate of dissolution and rate of evaporation give are per square meter so I guess my question would be if I multiply it by the Area of the slick once it becomes balanced would I be able to then get the rate of dissolution and evaporation in kg/s?
So I could set up my equation like this:
rate of oil to slick from the source = (rate of dissolution + rate of evaporation) A
all in kg/s except the area of course. And if I divide then the rate of oil slick from the source by the rate of dissolution and the rate of evaporation... would this give me, then the balanced area?
Or am I seeing this all wrong?