ENB221 Lecture Fluid Mechanics
Deforms under the action of a shear Deforms (flows) under the action of a shear force.
force Flows under the action of their own weight
Takes the shape of any solid body it is in contact with
A fluid is a substance which deforms continuously under Conversely: if a fluid is at rest, there can be no shearing
the action of shearing forces, however small they may forces acting upon it, therefore, all forces must be
be. perpendicular to the places upon which they act.
Difficult to compress, leads to the commonly Easy to compress so changes of volume with
used assumption of an incompressible fluid pressure are large and cannot be neglected
A given mass of liquid occupies a fixed volume, A given mass of gas will expand continuously
irrespective of size and shape of container unless restrained
Takes the shape of a container and forms a free Will always completely fill a vessel, will not form
surface a free surface.
Shear stress in a moving fluid
Shear stresses develop in a moving fluid if the fluid particles move relative to each other with different velocities
When a fluid is in contact with a solid boundary the fluid in contact with the boundary adheres to it; it has the same
velocity as the boundary (which is 0 if the boundary is not moving)
In a fluid the rate of shear strain is direcly porportional to
shear stress. Rate of shear strain (or shear strain per unit
Rate of shear strain is propotional to shear stress.
In derivative form it becomes:
This is Newtons Law of Dynamic Viscosity and μ is the coefficient of Dynamics Viscosity (a proportionality constant)
Newtonian and Non-Newtonian Fluids
Newtonian fluids obey Newton’s law of viscosity, that is, a fluid’s shear stress is linearly related to its velocity
gradient. This is the most common type of fluid (water, alchohol). Non-newtonian fluids do not obey Newton’s law,
other laws describe their behaviour (toothpaste, axle grease).
1 Week 2 Tuesday, 27 August 2013 ENB221 Lecture Fluid Mechanics
Density is defined as: the quantity of matter contained Density is defined as: the quantity of matter contained
in a unit of volume. There are a number of different ways in a unit of volume. There are a number of different ways
to express the density of a material to express the density of a material
Mass Density is defined as: The mass of a substance per Specific Weight is defined as: The weight of a substance
unit volume (ρ). per unit volume (γ)
Relative Density is defined as: The density of a substance Specific Volume is defined as: The reciprocal of mass
with respect to that of water (SG) d