F = 6πηrv, the viscous drag on a small sphere of radius r moving at speed v through a fluid of viscosity η.

Give three conditions for Stokes' law to apply.

A small sphere, moving at low speed, with laminar flow.

What is the unit of viscosity?

Pa s (equivalent to N s m⁻²).

What is laminar flow?

Smooth flow in which layers of fluid slide past each other without mixing or eddies.

What happens to the drag if the flow becomes turbulent?

It is larger than 6πηrv, so Stokes' law no longer applies.

What forces act on a ball falling at terminal velocity?

Weight down; upthrust and viscous drag up. W = U + F, so the resultant force is zero.

Why does a falling ball reach a terminal velocity?

Drag increases with speed until weight = upthrust + drag, so acceleration stops.

How does the viscosity of a liquid change with temperature?

It decreases as the temperature rises.

Why do balls fall faster in a hotter oil?

The oil is less viscous, so a higher speed is needed before drag + upthrust = weight.

In the falling-ball method, why are timing marks placed well below the surface?

So that the ball has reached its terminal velocity and moves at constant speed between the marks.

How is the radius of a ball bearing measured in the core practical?

Measure the diameter with a micrometer at several places, take the mean and halve it.

Give an expression for viscosity from terminal velocity.

η = 2r²(ρs − ρf)g / (9v), from W − U = 6πηrv.

Viscous drag and Stokes' lawEdexcel A-Level Physics: Flashcards

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State Stokes' law.: F = 6πηrv, the viscous drag on a small sphere of radius r moving at speed v through a fluid of viscosity η.
Give three conditions for Stokes' law to apply.: A small sphere, moving at low speed, with laminar flow.
What is the unit of viscosity?: Pa s (equivalent to N s m⁻²).
What is laminar flow?: Smooth flow in which layers of fluid slide past each other without mixing or eddies.
What happens to the drag if the flow becomes turbulent?: It is larger than 6πηrv, so Stokes' law no longer applies.
What forces act on a ball falling at terminal velocity?: Weight down; upthrust and viscous drag up. W = U + F, so the resultant force is zero.
Why does a falling ball reach a terminal velocity?: Drag increases with speed until weight = upthrust + drag, so acceleration stops.
How does the viscosity of a liquid change with temperature?: It decreases as the temperature rises.
Why do balls fall faster in a hotter oil?: The oil is less viscous, so a higher speed is needed before drag + upthrust = weight.
In the falling-ball method, why are timing marks placed well below the surface?: So that the ball has reached its terminal velocity and moves at constant speed between the marks.
How is the radius of a ball bearing measured in the core practical?: Measure the diameter with a micrometer at several places, take the mean and halve it.
Give an expression for viscosity from terminal velocity.: η = 2r²(ρ_s − ρ_f)g / (9v), from W − U = 6πηrv.

Exam questions on Viscous drag and Stokes' law

A steel ball bearing of radius 1.5 mm moves slowly through glycerol of viscosity 1.4 Pa s. The flow around the ball is laminar.
The ball is released from rest in a deep tank of glycerol. Explain why it eventually falls at a constant speed.2 marks
A student drops identical steel balls through a tall column of oil and measures the terminal velocity. At 20 °C the terminal velocity is 0.048 m s⁻¹ and at 50 °C it is 0.31 m s⁻¹. Assume that the density of the oil is the same at both temperatures and that Stokes' law applies.
Explain why the balls reach a higher terminal velocity in the oil at 50 °C.2 marks
A steel ball of radius 2.0 mm and density 7800 kg m⁻³ falls at its terminal velocity of 0.085 m s⁻¹ through an oil of density 920 kg m⁻³. The flow is laminar. Take g = 9.81 N kg⁻¹. The volume of a sphere is 4πr³/3.
Calculate the weight of the ball minus the upthrust on the ball.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).