A thin layer of particles rests on the bottom of a horizontal tube as shown in Fig. P7.60. When an incompressible fluid flows through the tube, it is observed that at some critical velocity the particles will rise and be transported along the tube. A model is to be used to determine this critical velocity. Assume the critical velocity, \(V_{c}\), to be a function of the pipe diameter, \(D\), particle diameter, \(d\), the fluid density, \(ho\), and viscosity, \(\mu\), the density of the particles, \(ho_{p}\), and the acceleration of gravity, \(g\).

(a) Determine the similarity requirements for the model, and the relationship between the critical velocity for model and prototype.

(b) For a length scale of \(\frac{1}{2}\) and a fluid density scale of 1.0, what will be the critical velocity scale (assuming all similarity requirements are satisfied)?

Figure P7.60

Transcribed Image Text:

V