now that we have studied shear in fluid
mechanics we can go back to viscosity
and define it more formally previously
we had said viscosity is the ratio
between stress and strain rating and we
had said this because we were looking at
a brick and we strained the brick and
for this strain we had to apply some
shear and we had said viscosity mu is
defined as the shear stress divided by
the rate at which the brick is being
strained the strain rate yes
so the ratio between tau and dV dy and
now that we have studied here we can
generalize this equation and we can say
we're not looking just as a brick at the
brick but instead at a flow in general
and we take any arbitrary layer of fluid
and in this layer we're looking at the
derivative of velocity with respect to
distance and we can say now that
viscosity is defined as the magnitude of
the shear tensor [in that direction] divided by the rate at
which the velocity is changing according
to direction and so this I think just
settles the topic of viscosity
just a quick notion that viscosity is
generally or more formally called
dynamic viscosity but when people say
viscosity this is what they mean mu the
unit of viscosity is Pascal seconds but
if you're at a party and you feel a bit
lonely and people start talking to you
you can impress them with all your
knowledge about fluid mechanics if you
tell them that actually Pascal seconds
here can be converted to kilograms per
meter per second which is also a Newton
second per meter squared and this will
surely impress them also if you're stuck
on a date and you have nothing to say
to your date then you can start talking
about the different units of viscosity
and there's an alternative unit which is
called Poise which is very annoyingly
defined as 0.1 Pascal second and this
fits in really cool sentences that are
sure to impress your date like "my orange
juice has a viscosity of one point
centipoise" was which is really cool also
makes you win at Scrabble anyway these
are different viscosities for different
fluids and we look at them in a big
diagram that is not too difficult to
work on I hope you have four fluids a
crude oil for which you look at the
values on this curve and you look to the
left water where you look on that curve
here and you look at the values on the
left and then two gases air and CO2
for which you look at those two
curves here and you look at the values
on the right now this is I hope not too
difficult to to read but it's a bit
confusing as to the magnitude because on
the left you have a scale which is
logarithmic well on the right you have a
scale that's linear and you should
really pay attention to what this means
2 times 10 to the power minus 2 this is
10 times higher than 2 times 10 to
the power minus 3 here which itself is
10 times higher than 2 times 10 to the
power minus 4 here and that value here
itself is 10 times higher than this
value here 2 times 10 to the power minus
5 so that it's very easy to read values
on this diagram but it's a bit harder to
see the differences in between the values
and if you represent the exact same data
on this diagram here you represent those
with a linear scale you get this diagram
and this diagram shows you the same four
flow is crude oil water and air and CO2
are both stuck up on top of one
another very very close to the 0 axis down
here in such a way that you cannot read
any useful value there this is how very
much more viscous crude oil is in
comparison to air and CO2 so pay
very good attention to the scales in in
this diagram when we use this
logarithmic scale it is for convenience
because we want to represent several
curves that are very very far apart onto
a single diagram but keep in mind that
air is many hundreds of times less
viscous
than a viscous fluid like crude oil so here you
are this is all you need to know about
viscosity as an engineer.
