(Solved): A thin layer of sand particles is found to rest at the bottom of a horizontal tube as indicated in ...

A thin layer of sand particles is found to rest at the bottom of a horizontal tube as indicated in Figure P1. As an incompressible fluid (or also known as liquid) flows through the tube, these sand particles are observed to rise and are transported along the tube at some critical velocity. With the aid of a model to determine the critical velocity along with the following assumptions of Critical velocity, Vc to be function of the pipe diameter, D, sand particle diameter, $d$, the fluid density, $?$, sand particle density, $?$ s, fluid viscosity, $?$ and the acceleration of gravity, $g$. Figure P1 (a) Select the suitable repeating variables for this system to conduct the dimensional analysis. Also, provide the suitable explanation on your selection. (b) Perform the dimensional analysis either in FLT system or MLT system to determine the similarity requirements for the model and the prediction equation for this system. Provide all the steps that involved in performing the dimensional analysis for this system. (c) In this study, all other similarities requirements are assumed to be satisfied. The geometry $\frac{1}{5}$ similarity is satisfied at diameter scale of $\overline{5}$ while the similarity for fluid properties is followed a fluid density scale is 2.0 . Determine the critical velocity scale and the particle density scale.