Problem 5.2

A 1-kg mass of dye is dumped into a 10 m² channel at a location designated as
x = 0. Downstream, at x = L = 100 m, the concentration of the dye is measured. The test is
repeated for three different flow rates, u = 0.001, 0.1, 1 m/s. For simplicity, the diffusion
coefficient is D = 1 m²/s for each condition.

a) For each case estimate the advection and diffusion time-scales, and the Peclet Number.
b) The curves below represent the three cases. Label each curve with the appropriate Peclet
number.
c) For which curves will the peak concentration observed at L occur at the advection time
scale? Calculate the peak concentration for these cases.
d) The injection of mass required 10 seconds. Considering the other relevant time scales,
can this injection be considered instantaneous?

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