Solid particles at 40 % (wt/wt) concentration with density of 3000 kg/m3 are transported in a pipe with diameter 100 mm. The particles have size of 0.25 mm, and the liquid base is water.

(a) Calculate the particle deposition velocity in water using Wasp et al. (1977). (3 marks)

(b) Calculate the pressure drop gradient at the particle deposition velocity (using Heterogenous hydraulic calculation method). Use water properties to calculate pressure drop of liquid phase. (4 marks)

(c) Calculate pressure drop at fluid velocity 10 times larger than particle deposition velocity. We assume that flow regime will be homogenous at fluid velocity 10 times the particle deposition velocity, and in that case, the mixture viscosity can be characterised by power law model with consistency index (K) = 1 Pa.s and power index (n) of 0.5. (8 marks)