Mechanics of Fluids

28 Fundamental concepts
rate of shear is (1/G)∂τ/∂t so the total rate of shear in the material is
(τ/µ) + (1/G)∂τ/∂t.
The fluids with which engineers most often have to deal are Newtonian,
that is, their viscosity is not dependent on either the rate of shear or its
duration, and the term mechanics of fluids is generally regarded as referring
only to Newtonian fluids. The study of non-Newtonian liquids is termed
rheology.
1.6.6 Inviscid fluid
An important field of theoretical fluid mechanics involves the investigation
of the motion of a hypothetical fluid having zero viscosity. Such a fluid is
sometimes referred to as an ideal fluid. Although commonly adopted in the
past, the use of this term is now discouraged as imprecise. A more meaningful
term for a fluid of zero viscosity is inviscid fluid.
1.7 SURFACE TENSION
Surface tension arises from the forces between the molecules of a liquid and
the forces (generally of a different magnitude) between the liquid molecules
and those of any adjacent substance. The symbol for surface tension is γ and
it has the dimensions [MT −2 ].
Water in contact with air has a surface tension of about 0.073 N · m −1 at
usual ambient temperatures; most organic liquids have values between 0.020
and 0.030 N · m −1 and mercury about 0.48 N · m −1 , the liquid in each case
being in contact with air. For all liquids the surface tension decreases as
the temperature rises. The surface tension of water may be considerably
reduced by the addition of small quantities of organic solutes such as soap
and detergents. Salts such as sodium chloride in solution raise the surface
tension of water. That tension which exists in the surface separating two
immiscible liquids is usually known as interfacial tension.
As a consequence of surface tension effects a drop of liquid, free from all
other forces, takes on a spherical form.
The molecules of a liquid are bound to one another by forces of molecular
attraction, and it is these forces that give rise to cohesion, that is, the tendency
of the liquid to remain as one assemblage of particles rather than to behave
as a gas and fill the entire space within which it is confined. Forces between
the molecules of a fluid and the molecules of a solid boundary surface give
rise to adhesion between the fluid and the boundary.
If the forces of adhesion between the molecules of a particular liquid and
a particular solid are greater than the forces of cohesion among the liquid
molecules themselves, the liquid molecules tend to crowd towards the solid
surface, and the area of contact between liquid and solid tends to increase.
Given the opportunity, the liquid then spreads over the solid surface and
‘wets’ it. Water will wet clean glass, but mercury will not. Water, however,
will not wet wax or a greasy surface.