Question 1

What does viscosity mean in a fluid?

Accepted Answer

Viscosity is the property of a fluid by which it resists relative motion between its different layers. For tangential motion between layers, the viscous force increases with contact area and with the velocity gradient across the layers.

Question 2

What is Stokes' law for a sphere?

Accepted Answer

For a small sphere moving slowly through a viscous fluid, the drag magnitude is F = 6pi eta r v. The drag acts opposite to the sphere's velocity relative to the fluid and is linear in both radius and speed only within the required slow-motion condition.

Question 3

Why does a falling sphere reach terminal velocity?

Accepted Answer

At release, the sphere has zero velocity, so viscous drag is zero, although upthrust is already acting. As its speed increases, upward drag increases until drag plus upthrust equals weight; the net force and acceleration then become exactly zero.

Question 4

How does terminal velocity depend on radius and viscosity?

Accepted Answer

For a falling sphere, v_t = 2r²(rho_s - rho_f)g/(9eta). Thus terminal speed is proportional to the square of radius and density contrast, and inversely proportional to fluid viscosity. Doubling radius gives four times the speed, while doubling viscosity gives half the speed.

Question 5

What happens if the sphere is less dense than or equally dense as the fluid?

Accepted Answer

If rho_s is less than rho_f, the sphere rises because upthrust exceeds weight, and drag points downward opposite its upward motion. If the densities are equal, weight and upthrust balance from the start, so a sphere released from rest has no acceleration or terminal motion.

Viscosity, Stokes' Law & Terminal Velocity — The Falling Sphere's Drag Race

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