A student injects 5 mL of 20% Rhodamine solution in water (with specific gravity 1.15 g/mL) instantaneously and uniformly over the tube cross-section (𝐴𝐴 = 0.8 cm3) at the point 𝑥𝑥 = 0 and the time 𝑡𝑡 = 0. The tube is filled with stagnant water. Assume the molecular diffusion coefficient if 𝐷𝐷 = 0.13·10-4 cm2/s.
• What is the concentration at 𝑥𝑥 = 0 at the time 𝑡𝑡 = 0?
• What is the standard deviation of the concentration distribution 𝑡𝑡 = 1 second after injection?
• Plot the maximum concentration in the tube, 𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚(𝑡𝑡), as a function of time over the interval 𝑡𝑡 = [0, 24 h].
• How long does it take until the concentration over the region 𝑥𝑥 = [-1, +1] meters can be treated as uniform? (A uniform distribution is one where the minimum concentration within a region is no less than 95% of the maximum concentration within that same region.)
BIOE2397 Homework #6
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