Coefficient of viscosity by terminal velocity — practice questions

Question 1 · difficulty L1 · recall

Viscosity measures a fluid's resistance to

• A. electric current only
• B. magnetic flux
• C. relative motion between neighbouring layers
• D. nuclear decay

Question 2 · difficulty L1 · understanding

Stokes' law for drag on a small sphere moving slowly through a viscous fluid is

• A. F=πηr²v²
• B. F=6πρrv
• C. F=ηv/(6πr)
• D. F=6πηrv

Question 3 · difficulty L2 · understanding

Terminal velocity is reached when

• A. net force on the falling sphere becomes zero
• B. gravity vanishes
• C. viscosity becomes zero
• D. the sphere stops moving

Question 4 · difficulty L2 · application

For a sphere of radius r in the Stokes regime, terminal velocity varies approximately as

• A. r
• B. r²
• C. 1/r
• D. 1/r²

Question 5 · difficulty L3 · application

If fluid viscosity doubles with all else fixed, terminal velocity

• A. doubles
• B. quadruples
• C. halves
• D. stays unchanged

Question 6 · difficulty L3 · application

A sphere denser than the liquid reaches terminal speed because increasing speed causes

• A. weight to decrease to zero
• B. buoyant force to become infinite
• C. mass to vanish
• D. viscous drag to increase until forces balance

Question 7 · difficulty L4 · analysis

Why should the sphere's terminal speed be measured away from the liquid surface and container bottom?

• A. To reduce entry transients and boundary effects
• B. To make gravity larger
• C. To eliminate buoyancy
• D. To change sphere radius

Question 8 · difficulty L4 · analysis

Two otherwise identical spheres have radii r and 2r in the same fluid. In the ideal Stokes regime, terminal speeds are in ratio

• A. 1:2
• B. 1:4
• C. 2:1
• D. 4:1 with smaller sphere faster

Question 9 · difficulty L5 · analysis

A sphere of density equal to the fluid density is released in the ideal model. Its gravitational settling terminal speed is

• A. infinite
• B. independent of viscosity and nonzero
• C. zero
• D. equal to g

Question 10 · difficulty L5 · analysis

If measured terminal velocity is 4% too high, viscosity calculated from η∝1/vt will be approximately

• A. 4% too high
• B. 8% too high
• C. unchanged
• D. 4% too low