Viscosity or liquid friction
Solid surfaces in contact exert a frictional force on each other when they are moved. In a similar
way, the relative motion of layers of liquid is restricted by friction.
The rate at which your blood flows through your body, the rate at which oil flows along poipe
lines and the rate at which dust particles fall through the air are all affected by the viscosity of
the fluid (gas or liquid).
The frictional forces within a fluid give rise to a property known as the viscosity of the liquid. The
greater the viscosity the less easy it is for the fluid to flow and the stickier it feels. The viscosity
of a liquid also affects how easily solids can move through it - try and imagine the difference
between swimming in water and in treacle!
Consider the flow of liquid down a pipe as shown in the following diagram.
Liquid flow Liquid flow
The liquid will be moving from left to right due to the pressure difference between the ends of
the tube. However because the friction between the fluid and the walls of the tube is greater
than between two adjacent layers of liquid the liquid in the centre of the pipe will be travelling
faster than that at the edges.
Imagine that the liquid is moving in layers, rather like the cards in a pack, and assume that no
one layer crosses another layer. The frictional forces within the liquid act between one layer and
another. Such motion is called laminar flow. The velocity of particles at a given distance from
the centre of motion is constant. However if the layers do intermix we will get turbulent flow.
A streamIine is a curve whose tangent always lies along the direction of motion of the fluid at
that point. The streamlines never cross and in laminar flow they do not alter with time. (Figure
2(a)) but this is not the case with turbulent flow (Figure 2(b)). Clearly it is important for a vehicle
moving through a fluid that the flow of the fluid around it is laminar so that the drag on it may be
reduced to a minimum.
Laminar or streamlined flow Turbulent flow
Figure 2(a) Figure 2(b)
Construct a series of solid shapes with cross-sections as shown in Figure 3. Place them one at a
time into a tank and allow water to flow round them. A few crystals of potassium manganate(vii)
(potassium permanganate) should be introduced into the stream to show the direction of flow.
Investigate the nature of the flow of water round these obstacles noting the streamlines. The effect
of the speed of water flow should be studied by varying the pressure head of the water flowing into
Moving a tube through a fluid
Alternatively we could consider a stationary fluid and a moving tube. It is then clear that as the
tube moves through the fluid it will drag some fluid along with it, while the fluid at the centre of
the tube will lag behind. There is therefore a larger relative velocity between the tube and the
central fluid than there is between the tube and the fluid in contact with it. This change in
velocity with distance is called a velocity gradient.
The velocity gradient is defined as the
change in velocity with distance across the
tube. (Figure 4).
Velocity gradient = dv/dr
For laminar flow:
The frictional force is directly proportional to the product of velocity gradient and the
cross-sectional area of the tube.
Fluids that behave in this way are known as Newtonian fluids.
You can write the relationship as a formula:
F = A x velocity gradient
where is a property called the coefficient of viscosity for the fluid.
This defined as:
Viscosity () = tangential stress/velocity gradient
and is therefore very similar to the shear modulus for a solid. The units of the coefficient of
viscosity are N s m-2, kg m-1s-1 or Pas, and it has dimensions ML-1T-1.
The values of some coefficients of viscosity are given in the table below. Since viscosity varies
with temperature they are all given for 20 0C.
Fluid Viscosity (Pas) Fluid Viscosity (Pas)
Air 1.8 x 10-5 Water 1.0 x10-3
Glycerol 8.3 x 10-1 Golden syrup 100
Castor oil 2.42 Mercury 1.5 x10-3
(The viscosity of blood depends on the concentration of the red blood corpuscles and therefore
can be used to detect red blood corpuscle deficiency.)
The viscosity of a fluid changes markedly with temperature and some illustrations of the
variation of viscosity with temperature are shown below:
Pitch 5x 1010 Pas at 273 K Water 0.0018 Pas at 273 K
1 x 101 Pas at 373 K 0.0010 Pas at 293 K
An oil 5.3 Pas at 273 K 0.0007 Pas at 310 K
0.99 Pas at 293 K
0.23 Pas at 3l3 K
You have probably noticed that tarmac roads become sticky in summer, the change in the
viscosity of the tar from 273 K to 373 K being enormous!