Please explain and provide step by step solution for full points Problem 2: Term
ID: 1767525 • Letter: P
Question
Please explain and provide step by step solution for full points
Problem 2: Terminal velocity of sedimentation After suspending cells or beads in a microscope chamber filled with an aqueous solution, we have to wait for them to settle down to the chamber bottom. We would like to get some idea how long this takes. We consider a spherical particle of radius R made from a material with density rho. Recall that the Reynolds number is much smaller than 1 for this situation. Derive the expression for the terminal velocity v with which the particle sinks in water. Hint: Before reading on, test yourself and try to think about how to approach this problem! "Terminal velocity" implies constant velocity. At low Reynolds number, inertial forces can be neglected. Therefore, the particle immediately starts moving at the terminal velocity. According to Newton's first law, motion at a constant velocity means that the net force acting on the particle is zero. What are the forces acting on the particle? Gravity causes the particle to sink. It is opposed by buoyancy. Thus, according to Archimedes' principle, we need to use the apparent immersed weight (particle weight minus weight of displaced fluid) when calculating the downward force. This force is balanced by the drag force (given by Stokes' law) that acts in the opposite direction. Translate the above information into the force balance and solve it for v. Simplify the solution so that the final expression only contains four quantities (one of which is the difference between the densities of the bead material and of water).Is the terminal velocity proportional to the radius, the cross-sectional area, or the volume of the bead? How long does it take a borosilicate (glass) bead with a radius of 2 mum to sink over a distance Of 1 mm in water at room temperature? How long does the same take if the bead is made from polystyrene? (Look up the densities of these common materials. The viscosity of water is 1 :enterprise.)Explanation / Answer
Please explain and provide step by step solution for full points Problem 2: Term