Calculating Terminal Velocity in a Fluid

[jldavid]

Homework Statement

A 1.5-mm-diameter steel ball bearing (7830 kg/m^3) is dropped into a tank of SAE 30 oil. What is its terminal velocity?

The density of oil is 917kg/m^3, and the viscosity of oil is 0.26kg/(m*s).

Help is much appreciated!

Homework Equations

Force of drag = 1/2 * (density of fluid) * (area of sphere) * v^2 * (coefficient of drag)
Force of drag = 3 * pi * (coefficient of fluid) * (diameter of obj) * v

Coefficient of drag = 24 / (Reynolds number)

Reynolds number = (density of fluid * velocity of fluid * chracteristic length)/(viscosity of fluid)

The Attempt at a Solution

When I combine all the equations, the v's cancel out. Is there a different equation I should be using?

 

[dynamicsolo]

When I combine all the equations, the v's cancel out. Is there a different equation I should be using?

Could you clarify this comment? Why do you "combine all the equations"?

The terminal velocity is attained when the net force on the ball in the fluid is zero. What are the forces on the ball bearing? Incidentally, you have two different drag force laws there: what situations do they correspond to and which is applicable to this problem?