Problem #3 Buoyancy, centripetal, and drag forces are important when analyzing p

Question

Problem #3

Buoyancy, centripetal, and drag forces are important when analyzing particles undergoing centrifugation, which is used in the separator in the apheresis problem. Assuming the cells being centrifuged during platelet separation are solid spheres, the following force diagram applies.

Fd = Drag force Fb = Buoyancy force Fg = Gravitational force

Fd

Fb

You were given the equations for the centripetal and drag forces in class. Here, you will derive the centrifugal force equation.

Fg

1a) First we will solve the ideal system with no drag. The net force on the object is then: FNET= Fb- Fg ? FNET= mdma - moa?FNET= (mdm– mo)a

mdm = Mass of the displaced medium mo = Mass of the object

Given this equation, derive the equation for centrifugal force: 4/3pa3??rO2

(HINTS: 1. Centripetal acceleration is given by the equation a = v2/r where v = velocity and r = the radius of the centrifuge. 2. Linear velocity can be written as v = rO where O = rotational velocity.)

b) In fluid mechanics, you will learn that Fd = 6pµaU is the drag force on a solid sphere of radius a moving at velocity U in a medium with viscosity µ. This equation is called Stokes’ Law. Derive the settling velocity of the particle, U, by equating the centripetal and drag forces.

c) Given that the red blood cell is 4.5 micron in diameter and a platelet is 3 micron in diameter, estimate the settling velocity of red blood cells and platelets in plasma. (HINT: Rotational velocity must have units of radians/min, not rotations/min, for the equation to work. Answer will be negative since velocity is pointed down by definition of the force diagram.)

Useful information: µplasma = 1.2 cP (centipoise) ?plasma = 1.024 g/ml r = 10 cm

Explanation / Answer

Sorry, but the equation makes no sense. It is all scrambled up. Please be clear.

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