A tanker truck carrying liquid herbicide overturned and caused a spill over a field. The liquid herbicide remained on the soil for 30 min before evaporating into the air. The mass diffusivity of the liquid herbicide in the soil is 2 × 10?8 m2/s. If a concentration of 0.1 percent by weight will destroy most life, determine the depth of the soil at which plant and insect life is likely to be affected by the spill.
What will be an ideal response?
A tanker truck carrying liquid herbicide overturned and caused a spill over a field. The depth of the soil at which plant and insect life is likely to be affected by the spill is to be determined.
Assumptions The herbicide-soaked soil can be modeled as a semi-infinite medium.
Properties The relevant properties are given in the problem statement.
Analysis This problem is analogous to the one-dimensional transient heat conduction problem in a semi-infinite medium with specified surface temperature discussed in chapter 4, and thus can be solved accordingly. The solution can be expressed as
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