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Unformatted text preview: ACM 95/100c Problem Set 1 31st March 2006 Due by 5:00PM on 4/7/2006 Please deposit all problem sets in the slot in 303 Firestone Please remember to include your section number and section instructor Each problem is worth 10 points - each part of a multi-part problem is weighted equally Some of the solutions to some of the problems may be available from old solution sets. Your educational experience will be enhanced if you don't succumb to the temptation to use them but in general you can consult any written source out there for the non collaboration problems and you can collaborate freely on those problems marked collaboration allowed . Problem 1 (Collaboration allowed) As a result of runo from the surrounding land follow- ing a rainstorm, a large lake of depth h receives a sudden in ux of a soluble phosphate compound in its upper layers. The phosphate then di uses down- ward into the rest of the lake. Assuming that the phosphate concentration c is a function of depth z (measured positively downward from the lake surface) and time t only, and that the rate at which phosphate di uses across any hori- zontal cross section is proportional to c/z , show that c satis es an equation of di usion type. Check that the equation is dimensionally consistent. Explain why reasonable additional conditions to be satis ed by c are c z = 0 at z = 0 and z = h ....
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This note was uploaded on 01/08/2011 for the course ACM 95c taught by Professor Nilesa.pierce during the Spring '09 term at Caltech.
- Spring '09