Department of PhysicsThe Open University of Sri

Lanka

Content

Learning Outcomes

Defining viscosity

Newton’s formula

Variation of viscosity with temperature

Poiseuille's formula

Learning OutcomesAfter completing this session you should be able to

explain what is viscosity

explain the differences between fluid flow, steady (laminar flow) and turbulent flow

explain Newton’s formula

explain the variation of viscosity with temperature

Defining viscosity

Viscosity is a measure of a fluid's resistance to flow.

Low viscosityFlow easily

High viscosityDoes not flow easily

Milk Ketchup

Steady flow

When a fluid moves slowly, its flow is orderly. If every fluid passing through a given point follows the same line of the flow it is named as Laminar flow or Steady flow.

Slow

Slow

Fast

Turbulent flow

The motion of a fluid in which the elements move irregularly and in a much more complex manner is said to be a turbulent flow.

Water flowing from a tap is also another good example for both Steady flow and Turbulent flow

Turbulent flow

Steady flow

Newton’s formula for Coefficient of Viscosity ()

Newton’s law of viscosity states that “Shear stress (Tangential pressure) is directly proportional to Velocity gradient”

Velocity, U

fluidGradient

Shear stress (T)

Boundary plate (2D, moving)

Y

U

Boundary plate (2D, stationary)

Units and dimensions of viscosity-

11212

skgmsNm

sm

N

d

VA

F

1112

2

TMLTL

MLT

Units

Dimensions

Variation of viscosity with temperature in a gas

The viscosity in a gas will increase with temperature

Variation of viscosity with temperature in liquids

Temperature 0C

Liquids show a reduction in viscosity with increasing temperature

Vis

cosi

ty

Poiseuille's formula

2R P1 P 2

21 PPP

dtdVQ

L

Parabolic velocity profile

Volume flow rate Q=dV/dt

Volume flow rate of liquid = QL

PRQ

4

L

PRQ

8

4 viscosity =

Radius of the tube = R

L

PPressure gradient =

Author : D. L. N. Jayathilaka

Web Content Developer : B. Krishni Perera

Produced by The Open University of Sri Lanka

2014