Problem 1 A solid steel sphere of SG = 7.85 and diameter of 0.02 m is falling at its terminal velocity through water. Water has a density of 1000 kg/ms and a viscosity of 1.002x10-3 Pa.s. What is its velocity of the sphere? Express your answer in units of ft/s. Problem 2 a) A hollow sphere with a diameter of 5.0 mm and a mass of 0.05 g is released in a column of liquid and attains a terminal velocity of 5.0 mm/s. Given the density of the liquid is 900 kg/m3, determine the viscosity of the liquid assuming that the walls of the container holding the liquid are infinitely far away from the sphere. b) Repeat your calculation of viscosity for a column that has a diameter of 25 mm. In doing this, first derive an expression for the viscosity as a function of @ then use this expression to solve for the viscosity. The figure below may be useful. * 1 + 2 10 0, /De Problem 3 You wish to capture particles with a 3 um radius suspended in a fluid that has a linear density gradient with a density of 1.12 g/cm3 at the bottom and 1.00 g/cm3 at the top. You layer a thin particle suspension on the top of the 6 cm column of fluid with a viscosity of 1.0 cp and allow particles to settle. a) How long must you wait for particles with a density of 1.07 g/cm3 to sediment to within 0.1 cm of their isopycnic level (i.e., within 0.1 cm of the position where the density of the particles and the density of the fluid are equal)? b) Instead of settling due to gravity, you choose to use a centrifuge running at 800 rpm. If the top of the fluid is 5 cm from the center of rotation, how long must you run the centrifuge for the particles to move to within 0.1 cm of their isopycnic level