The
viscosity of a
fluid is a measure of its
resistance to gradual deformation by
shear stress or
tensile stress. For liquids, it corresponds to the informal notion of "thickness". For example,
honey has a higher viscosity than
water .
Viscosity is due to
friction between neighboring parcels of the fluid that are moving at different
velocities.
When fluid is forced through a tube, the fluid generally moves faster
near the axis and very little near the walls, therefore some
stress (such as a
pressure
difference between the two ends of the tube) is needed to overcome the
friction between layers and keep the fluid moving. For the same velocity
pattern, the stress is proportional to the fluid's viscosity. A
liquid's viscosity also depends on the size and shape of its particles
and the attractions between the particles
A fluid that has no resistance to shear stress is known as an
ideal fluid or
inviscid fluid. In the real world, zero viscosity is observed only at
very low temperatures, in
superfluids. Otherwise all fluids have positive viscosity. If the viscosity is very high, such as in
pitch,
the fluid will seem to be a solid in the short term. In common usage, a
liquid whose viscosity is less than that of water is known as a
mobile liquid, while a substance with a viscosity substantially greater than water is simply called a
viscous liquid.
types --
Shear viscosity
The shear viscosity of a fluid expresses its resistance to
shearing flows, where adjacent layers move parallel to each other with
different speeds. It can be defined through the idealized situation
known as a Couette flow, where a layer of fluid is trapped between two horizontal plates, one fixed and one moving horizontally at constant speed . (The plates are assumed to be very large, so that one need not consider what happens near their edges.)
The magnitude
of this force is found to be proportional to the speed
and the area
of each plate, and inversely proportional to their separation
. That is,
The proportionality factor
μ in this formula is the viscosity (specifically, the
dynamic viscosity) of the fluid.
The ratio
is called the
rate of shear deformation or
shear velocity, and is the
derivative of the fluid speed in the direction
perpendicular to the plates.
Isaac Newton expressed the viscous forces by the
differential equation
where
and
is the local shear velocity. This formula assumes that the flow is moving along parallel lines and the
axis, perpendicular to the flow, points in the direction of maximum
shear velocity. This equation can be used where the velocity does not
vary linearly with
, such as in fluid flowing through a pipe.
Kinematic viscosity
The
kinematic viscosity is the dynamic viscosity
μ divided by the
density of the fluid
ρ. It is usually denoted by the
Greek letter nu (
ν). It is a convenient concept when analyzing the
Reynolds number, that expresses the ratio of the
inertial forces to the viscous forces:
-
Bulk viscosity
When a compressible fluid
is compressed or expanded evenly, without shear, it may still exhibit a
form of internal friction that resists its flow. These forces are
related to the rate of compression or expansion by a factor σ, called the volume viscosity, bulk viscosity or second viscosity
The bulk viscosity is important only when the fluid is being rapidly compressed or expanded, such as in sound and shock waves. Bulk viscosity explains the loss of energy in those waves, as described by Stokes' law of sound attenuation.