Viscosity of Fluids & Stokes’ Law
Investigate internal fluid friction, Newton’s viscosity law F = η A (dv/dx), dynamic viscosity coefficient η, streamline and turbulent flow, Poiseuille’s pipe flow formula Q = (π P r⁴)/(8 η L), Stokes’ drag F_d = 6πηrv, and terminal velocity v_t.
Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.
Learning Objectives
- Define the coefficient of dynamic viscosity η and derive its SI unit (Pa·s or N·s·m⁻²).
- State Stokes’ Law for a spherical body, explain its validity conditions, and derive the terminal velocity equation.
- Apply Poiseuille’s equation to determine volume flow rate through cylindrical tubes under laminar conditions.
Core Theory & Concepts
Viscosity is internal fluid friction that resists relative motion between adjacent fluid layers. When a solid sphere moves slowly through a viscous fluid, viscous shear layers impart a drag force formulated by Sir George Gabriel Stokes as F_d = 6πηrv.
Stokes’ Drag Law
For a sphere of radius r moving at laminar speed v through a fluid of viscosity η: F_d = 6πηrv.
Terminal Velocity Equation
When downward weight equals buoyant upthrust plus viscous drag, acceleration ceases and terminal velocity is attained.
Common Misconceptions
Terminal velocity is directly proportional to sphere radius r.
Syllabus Topic Outline
- 1Viscous shear resistance between adjacent laminar fluid layers
- 2Newton’s law of viscosity: F = η A (dv/dx) and velocity gradient
- 3Streamline versus turbulent flow and critical velocity
- 4Poiseuille’s formula: Q = (π P r⁴) / (8 η L) and fourth-power radius dependence
- 5Stokes’ Law: F_d = 6πηrv and terminal velocity derivation v_t = 2r²(ρ - σ)g / 9η
- 6Stokes’ viscometer experimental design and wall effect precautions