Question

The velocity of a blood corpuscle in a vessel depends on how far the corpuscle is from the center of the vessel. Let R be the constant radius of the vessel; Vm, the constant maximum velocity of the corpuscle; r, the distance from the center to a particular blood corpuscle (variable); and Vr, the velocity of that corpuscle. The velocity Vr is related to the distance r by the equation Vr=Vm (1-r^2 /R^2). Find r when Vr=1/4Vm.

Answer 1

Vr = Vm * ( 1 - r ^ 2 / R ^ 2 )

Vr = ( 1 / 4 ) Vm

( 1 - r ^ 2 / R ^ 2 ) = 1 / 4 Multiply both sides by 4

4 * ( 1 - r ^ 2 / R ^ 2 )= 1

4 - 4 * r ^ 2 / R ^ 2 = 1 Subtract 4 to both sides

4 - 4 * r ^ 2 / R ^ 2 - 4 = 1 - 4

- 4 * r ^ 2 / R ^ 2 = - 3 Multiply both sides by - 1

4 * r ^ 2 / R ^ 2 = 3 Multiply both sides by R ^ 2

4 * r ^ 2 = 3 * R ^ 2 Divide both sides by 4

r ^ 2 = 3 R ^ 2 / 4

r = sqrt ( 3 R ^ 2 / 4 )

r = sqrt ( 3 ) * R / 2