Page 26 - Aerodynamics for Engineering Students

Basic concepts and definitions 9

through thick oil needs much more effort. This is because the viscosity of oil is high
compared with that of air.

Dynamic viscosity

The dynamic (more properly called the coefficient of dynamic, or absolute, viscosity)
viscosity is a direct measure of the viscosity of a fluid. Consider two parallel flat
plates placed a distance h apart, the space between them being filled with fluid. One
plate is held fixed and the other is moved in its own plane at a speed V (see Fig. 1.3).
The fluid immediately adjacent to each plate will move with that plate, i.e. there is no
slip. Thus the fluid in contact with the lower plate will be at rest, while that in contact
with the upper plate will be moving with speed V. Between the plates the speed
of the fluid will vary linearly as shown in Fig. 1.3, in the absence of other influences.
As a direct result of viscosity a force F has to be applied to each plate to maintain
the motion, the fluid tending to retard the moving plate and to drag the fmed plate
to the right. If the area of fluid in contact with each plate is A, the shear stress is F/A.
The rate of shear strain caused by the upper plate sliding over the lower is V/h.
These quantities are connected by Newton's equation, which serves to define the
dynamic viscosity p. This equation is

F
A
- = P(;)
Hence
[ML-'T-2] = [p][LT-'L-'] = /p][T-']

Thus
[p] = [ML-lT-']
and the units of p are therefore kgm-ls-l; in the SI system the name Poiseuille (Pl)
has been given to this combination of fundamental units. At 0°C (273K) the
dynamic viscosity for dry air is 1.714 x kgm-' s-l.
The relationship of Eqn (1.5) with p constant does not apply for all fluids. For an
important class of fluids, which includes blood, some oils and some paints, p is not
constant but is a function of V/h, Le. the rate at which the fluid is shearing.

Kinematic viscosity
The kinematic viscosity (or, more properly, coefficient of kinematic viscosity) is
a convenient form in which the viscosity of a fluid may be expressed. It is formed

-
I
Fig. 1.3