Irodov Problem 1.339

Let the density of steel be and that of olive oil be and let the viscosity of olive oil be. Suppose that at some instant the velocity of the sphere is v.

As the sphere sinks, there are three forces acting on it, i) the force of gravity responsible for sinking it given by ii) the buoyant force offered by the fluid given by and iii) the viscous force offered by the fluid .

The mass of the sphere is given by and so from Newton's first law we have,
























From (2) it is clear that the steady state velocity will be . The velocity v will be off by from the steady state velocity by fraction n when,







From (1) we have,

Irodov Problem 1.338

Let the density of the fluid be and the density of the sphere be and let the viscosity of the fluid be . Let the terminal velocity of the sphere in the fluid be v.

As the sphere falls through the fluid there are three forces acting on it, i) the force of gravity , ii) the buoyant force due to the fluid and iii) the viscous force due to fluid on the sphere is given by . Since the body is moving at terminal velocity and there is no acceleration, all these forces must cancel out. Hence, we have,






The Reynold's number for a sphere moving in fluid is given by,

Irodov Problem 1.337

The Reynold's number for a sphere of radius r1 falling through a fluid of density at a velocity v1, is given by . Since at velocity v1 the flow starts to become turbulent, this is the Reynold's number corresponding to turbulent flow. For the other fluid the flow must become turbulent at the same Reynold's number. So we have,