Viscosity

Summary

• Viscosity (also known as dynamic viscosity, absolute viscosity, or simple viscosity) is…
  • represented by the Greek letter η (eta)
  • defined informally as the quantity that describes a fluid's resistance to flow
  • defined mathematically as the ratio of the shearing stress (F/A) to the velocity gradient (∆v_x/∆y or dv_x/dy) in a fluid

    η =	F/A
    	∆vx/∆y

    or

    η =	F/A
    	dvx/dy

  • often expressed using Newton's equation for fluids (which is similar to Newton's second law of motion).

    F	= η	∆vx
    A		∆y

    or

    F	= η	dvx
    A		dy

  • Units
    • The SI unit of viscosity is the pascal second [Pa s].
    • The Gaussian unit of viscosity is the poise [P = dyne s/cm²].
    • Ten poise equal one pascal second [10 P = 1 Pa s].
• Kinematic viscosity is…
  • represented by the Greek letter ν (nu).
  • defined informally as a measure of the resistive flow of a fluid under the influence of gravity
  • defined mathematically as the ratio of the viscosity of a fluid to its density

    ν =	η
    	ρ

  • Units
    • The SI unit of kinematic viscosity is the square meter per second [m²/s].
    • The Gaussian unit of kinematic viscosity is the stokes [St = cm²/s].
    • Ten thousand stokes equal one square meter per second [10,000 stokes = 1 m²/s].
• Factors affecting viscosity
  • Viscosity varies with material. (Viscosity is a property of materials.)
  • The viscosity of simple liquids…
    • decreases with increasing temperature
    • increases under very high pressures
  • The viscosity of gases…
    • increases with increasing temperature
    • is independent of pressure and density