Viscous drag and Stokes' law Edexcel International A Level Physics revision
Not started
Learn it
In plain words
Drop a ball bearing into a jar of syrup and it sinks slowly at a steady speed. Three forces are at work: its weight pulling down, the liquid buoying it up, and the liquid's stickiness dragging on it. At a steady speed they balance, and that lets you measure how sticky the liquid is.
4 things to know
- Stokes' law gives the viscous drag on a small sphere moving slowly through a fluid: F = 6πηrv, where η is the viscosity of the fluid, r the radius of the sphere and v its speed.
- It applies only to small spheres at low speeds, where the flow is laminar (smooth, with no turbulence).
- At terminal velocity the forces on a falling sphere balance: weight = upthrust + viscous drag.
- Viscosity depends on temperature. Most liquids get less viscous as they warm up.
Worked example
A sphere of radius 1.0 mm falls at a terminal velocity of 0.050 m/s through oil of viscosity 0.30 Pa s. Find the viscous drag on it.
- F = 6πηrv.
- = 6π × 0.30 × 1.0 × 10⁻³ × 0.050.
- = 2.8 × 10⁻⁴ N.
Tips and tricks
- Quote the conditions for Stokes' law: a small sphere, a low speed, laminar flow.
- In the falling-ball experiment, time the ball only after it has reached terminal velocity, and well away from the walls of the tube.
It lands in your notebook with its questions as flashcards.
Viscous drag and Stokes' law: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
In Stokes' law, F = 6πηrv, what is η?
It measures how much the fluid resists flowing.
A sphere falls at terminal velocity through oil. Which equation is correct?
The two upward forces balance the weight.
What happens to the viscosity of a liquid when it is warmed?
Warm oil flows more easily than cold oil.
What kind of flow does Stokes' law need?
The fluid must flow smoothly round the sphere.
A sphere moves through a liquid twice as fast as before, with the flow still laminar. What happens to the viscous drag?
In Stokes' law the drag is proportional to the speed.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 8 marks. Write your answers on paper, then check them.
Viscous drag and Stokes' law
Edexcel International A Level Physics WPH · 8 marks · papermunch.org
Name ______________________________ Date ______________
Write down the equation linking the forces on a sphere falling at terminal velocity through a liquid.[2]
Show answerHide answer
Weight = upthrust + viscous drag.
A steel ball of weight 4.1 × 10⁻⁴ N falls at terminal velocity through glycerol. The upthrust on it is 0.7 × 10⁻⁴ N. Find the viscous drag.[3]
Show answerHide answer
3.4 × 10⁻⁴ N. The drag and the upthrust together balance the weight.
State two conditions for Stokes' law to apply, and explain why the temperature must be kept constant in a falling-ball experiment.[3]
Show answerHide answer
The object must be a small sphere moving slowly, so that the flow is laminar. Viscosity changes a great deal with temperature, so the drag would change.
Answers: Viscous drag and Stokes' law
- 1. Weight = upthrust + viscous drag.
- 2. 3.4 × 10⁻⁴ N. The drag and the upthrust together balance the weight.
- 3. The object must be a small sphere moving slowly, so that the flow is laminar. Viscosity changes a great deal with temperature, so the drag would change.