In hydraulic transport of solids by pipeline, when the fluid velocity exceeds a critical value, the solid particles will rise and be carried by the fluid along the pipe. A model pipeline system is to be used to study this critical velocity. From experience, the critical velocity (vc) is known to be a function of the pipe diameter (D), particle diameter (d), the fluid density (), the fluid viscosity (), the density of the solid particles (s), and the gravitational acceleration (g). a. Use the method of dimensional analysis to determine the pertinent dimensionless groups for the process. b. The model used is 1/5th in scale as compared to the prototype, and fluid density scale ratio is kept at 1.0. Can all similarity requirements be met with this model? What should the viscosity ratio be? c. If a test from the model gives a critical velocity of 3.8 m/s, what would the predicted critical velocity in the prototype be (assuming all similarity requirements are satisfied)?