A thin layer of particles rests on the bottom of a horizontaltube as shown in Fig

Chapter 7, Problem 7.60

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A thin layer of particles rests on the bottom of a horizontaltube as shown in Fig. P7.60. When an incompressible fluid flowsthrough the tube, it is observed that at some critical velocity theparticles will rise and be transported along the tube. A model isto be used to determine this critical velocity. Assume the criticalvelocity, Vc, to be a function of the pipe diameter, D, particlediameter, d, the fluid density, , and viscosity, , the density of theparticles, p, and the acceleration of gravity, g. (a) Determine thesimilarity requirements for the model, and the relationship betweenthe critical velocity for model and prototype (the prediction equation).(b) For a length scale of 12 and a fluid density scale of 1.0,what will be the critical velocity scale (assuming all similarityrequirements are satisfied)?

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