Calculate the settling velocity of solid cuboid having the dimension of 1.5 time

Question

Calculate the settling velocity of solid cuboid having the dimension of 1.5 times 2 times 3 mm in water at 293.2 K (20 degree C). The mixture contains equivalent-weight percent. The density of the solid particle is (rho_p)= 1.750 g/cm^3. Pure water has it's highest density at 4.0 C = 1000 kg/m^3. Freezing/Melting temperature = 0.00 C (101,325 Pa) Boiling/Condensing temperature = 100.00 C (101,325 Pa) Latent heat of melting = 334 kJ/kg Latent heat of evaporation = 2,270 kJ/kg Molar mass = 18.01528 g/mol

Explanation / Answer

Here, drag force = 998.21 * v2 * (2 * 3 * 10-6) * 1.05/2

                              =   3.144 * 10-3 * v2

Gravity force = (1.5 * 2 * 3 * 10-9) * 1750 * 9.8

                      =   1.5435 * 10-4 N

buoyancy force = (1.5 * 2 * 3 * 10-9) * 998.21 * 9.8

                            =   8.804 * 10-5 N

=>     1.5435 * 10-4    - 8.804 * 10-5     =   3.144 * 10-3 * v2

=>   v =   0.1452   m/sec                    --------------------->    settling velocity of solid cuboid

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