Prob31(1) - Turbulent Flow Transport Problem 3.1 Scales of...

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Turbulent Flow & Transport Problem 3.1: Scales of turbulent motion . An ordinary hand-held electric kitchen mixer is to be used for mixing 1.5 liters of liquid. The mixer has counter-rotating strirrers with blades formed from 6 mm wide metal strips (look at your kitchen mixer for an example), and is to be operated at its maximum power rating of 175 watts. Suppose the liquid to be mixed is basically water ( μ =0.001 kg/ms, ρ =1000 kg/m 3 ). Based on the information given, and making reasonable order of magnitude estimates of whatever else you need, provide order of magnitude estimates of (a) the length, velocity and time scales associated with the smallest scales of turbulent motion in the liquid, (b) the length, velocity and time scales associated with the largest eddies of the turbulent motion, and (c) the turbulent diffusion coefficient associated with the mixing process. Compare this with the molecular diffusion coefficient for something like a dissolved salt or sugar in water. (d) Estimate, to order of magnitude , the mixing timescale
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