Viscosity, Stokes' Law and Terminal Velocity
Viscosity is internal fluid friction with F = η A dv/dx; a sphere in a viscous fluid experiences F = 6 π η r v and reaches a constant terminal velocity.
What is Viscosity, Stokes' Law and Terminal Velocity?
Viscosity is internal fluid friction with F = η A dv/dx; a sphere in a viscous fluid experiences F = 6 π η r v and reaches a constant terminal velocity.
Key formula / rule: F = η A (dv/dx); SI unit of η is Pa s.
Key points
- Derive terminal velocity from the force balance.
- Analyse how temperature affects the viscosity of liquids and gases.
Common exam trap
Assuming terminal velocity is independent of radius.
Definitions
- Term
Viscosity, Stokes' Law and Terminal Velocity
- Meaning
Viscosity is internal fluid friction with F = η A dv/dx; a sphere in a viscous fluid experiences F = 6 π η r v and reaches a constant terminal velocity.
- Term
Viscosity, Stokes' Law and Terminal Velocity — explanation
- Meaning
Terminal velocity is reached when weight balances upthrust plus drag, and depends on the square of the radius, which is why fine dust settles very slowly.
Learning objectives
Derive terminal velocity from the force balance.
Analyse how temperature affects the viscosity of liquids and gases.
Formulae
- Key point
F = η A (dv/dx); SI unit of η is Pa s.
- Key point
Stokes drag: F = 6 π η r v.
- Key point
vterminal proportional to r2 (ρbody - ρfluid)/η.
Prerequisites
PHY-U3-MPM-T2-S1-C2
Common mistakes
Assuming terminal velocity is independent of radius.
Applying Stokes' law to turbulent, high-Reynolds-number flow.
Keywords
Viscosity
Stokes'
Terminal
Velocity
Practice preview
How does the viscosity of liquids and gases change with an increase in temperature?…
easy
What is the SI unit of the coefficient of viscosity (eta)?…
easy
Which of the following statements about viscosity and Stokes' Law is INCORRECT?…
medium