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when fluid flows past an object or an
object moves through a stationary fluid
the fluid exerts a force on the object
we can split the force into two
components
one acting in the same direction as the
fluid flow
which is called drag and one acting
perpendicular to the flow direction
which is called lift if the fluid is a
gas
like air we call these aerodynamic
forces
and if it's water or any other liquid we
call them
hydrodynamic forces this video is going
to focus on the drag force
and i'll cover lift in a separate video
most of the time
drag forces are undesirable they can
have a huge effect on the fuel
consumption and performance of vehicles
for example
and so engineers go to great lengths to
minimize them
we'll explore some interesting ways of
reducing drag
later on in the video including how the
airline industry could save millions of
dollars a year
in fuel costs by using a drag reducing
innovation
based on artificial shark skin but to
optimize the design of
objects affected by drag forces we first
need to understand
where these forces come from so let's
start by covering the basics
drag forces are caused by two different
types of stress
which act on the surface of an object
first we have the wall shear stresses
these stresses act tangential to the
object's surface
and are caused by frictional forces that
arise because of a fluid's viscosity
then we have the pressure stresses they
act perpendicular
to the object's surface and are caused
by how pressure is distributed
around the object the drag force is the
resultant
of these two stresses in the direction
of the flow
so if we know exactly how the stresses
are distributed over the surface of our
object
we can integrate them to obtain the
resultant drag force
the component of drag caused by the
shear stresses
is called friction drag and the
component caused by the pressure
stresses
is called pressure drag or form
drag pressure drag is most significant
for blunt bodies
like this sphere it is essentially
caused by a difference in pressure
between the front
and rear of an object pressure drag
increases significantly if flow
separation occurs
which is when the fluid boundary layer
detaches from the body
creating a wake of recirculating flow
this creates an area of low pressure
behind the body
called the separation region and results
in a large drag force
if you're trying to reduce drag forces
you'll want to minimize flow separation
at all costs flow separation can also
cause
vortex shedding which can generate
unwanted vibrations
and instability
to understand why flow separation occurs
let's look at flow on the upper surface
of the sphere
as the fluid passes over the surface of
the sphere it is initially
accelerating and so pressure is
decreasing
in the direction of the flow this is
called a
favorable pressure gradient beyond a
certain point
the flow then begins to decelerate
and so pressure in the flow direction is
increasing
this increase in pressure is called the
adverse
pressure gradient and it has a
significant effect
on the flow close to the wall if the
pressure increase is large enough
the flow will reverse direction and
since it can't travel backwards because
of the oncoming fluid
it detaches from the surface resulting
in flow separation
flow separation occurs at around 80
degrees for a smooth sphere
in laminar flow if the boundary layer
is turbulent instead of laminar it's
better able to remain
attached to the surface and flow
separation is delayed until around 120
degrees
which reduces the pressure drag
significantly
this is because turbulence introduces a
lot of mixing between the different
layers of flow
and this momentum transfer means the
flow can sustain a larger adverse
pressure gradient
without separating this is why golf
balls have dimples
instead of being perfectly smooth the
dimples
generate turbulence which delays flow
separation
reduces drag and allows the ball to
travel further
this idea of using turbulence to delay
flow separation
and reduce pressure drag is also why
some airplane wings have small
vortex generators protruding from them
bodies that travel through fluids like
plane wings
or submarines are usually designed to be
streamlined in a teardrop shape
to minimize the effect of flow
separation
for very streamlined bodies like this
airfoil at a shallow angle of attack
pressure drag is small because flow
separation
is significantly delayed or doesn't
occur at all
for bodies like these it's the wall
shear stresses which contribute most
to the total drag force the drag
component caused by these stresses
is called friction drag friction drag
increases with the viscosity of the
fluid
and is most significant for bodies which
have a large surface area
aligned with the direction of flow
we saw earlier that turbulence delays
flow separation
which reduces the pressure drag but for
friction drag it has the opposite effect
laminar and turbulent boundary layers
have very different velocity profiles
the velocity gradient at a wall is
steeper in turbulent boundary layers
than in laminar ones and so turbulence
produces
larger shear stresses so to reduce
friction drag you want to delay the
transition to the turbulent regime
and maintain laminar flow for the
largest possible distance
around the object it has been estimated
that obtaining laminar flow
over the wings and fin of commercial
aircraft could reduce the total drag
force
by around 10 to 15 percent but this is
very difficult to achieve techniques
like
hybrid laminar flow control have had
some success
it involves using suction to pull air
through small holes
into the wing which delays the onset of
turbulence
research has also focused on minimizing
the friction drag
associated with a turbulent boundary
layer
when trying to minimize drag engineers
very often look to nature for
inspiration
sharks are a particular interest because
of the unique
microstructure of their skin shark
scales contain
microscopic ridges which are aligned
with the direction of flow
these ridges modify the turbulent
boundary layer
in the near wall area and this has the
effect of reducing friction drag
research indicates that coating a
commercial airliner with artificial
shark skin
of similar microstructure could reduce
its total drag force
by two percent which would result in
massive fuel savings for the industry
this approach has yet to be widely
implemented on commercial aircraft
partly due to challenges associated with
manufacturing
but this could change as the technology
improves
we've seen that the magnitude of
pressure and friction drag
depends on the geometry of a body
relative to the direction of flow
the most obvious example of this is a
flat plate
if we position the plate at 90 degrees
to the flow
it is a blunt body flow separates easily
creating a separation region
and so the pressure drag is large but
the friction drag is
almost zero since shear stresses aren't
aligned with the drag direction
if we rotate the plate by 90 degrees
we now have a very streamlined body the
pressure drag
is small since there's no separation
region behind the body
but the friction drag is now much more
significant
this logic also applies to airfoils
where the angle of attack has a large
influence on the drag force
at high angles of attack separation
occurs which significantly increases the
drag force
streamlining a body to reduce drag it's
important to remember
that friction drag will increase as the
pressure drag
reduces and so these two aspects need to
be carefully balanced
the shape that has the smallest total
drag force won't necessarily be the one
that is most streamlined
i mentioned earlier that we can
integrate the pressure stresses
and the wall shear stresses to obtain
the total drag force
the problem is that in the vast majority
of cases
it's pretty much impossible to know the
detailed distribution of these stresses
and so we usually represent the total
drag force
using the drag equation instead
the cd term is the drag coefficient
it captures all of the hard to measure
parameters
like the effect of the geometry of the
object or the effect of the flow regime
and can be determined either
experimentally using a wind tunnel for
example
or by running numerical simulations
the other terms in the equation are the
fluid density rho
the free stream velocity v which is
usually assumed to be steady and uniform
and a which is a reference area that
will depend on how the drag coefficient
was determined
for airfoils and other streamlined
bodies a
is usually the plan form area and for
blunt bodies
it's usually the projected frontal area
the drag coefficient can vary quite
substantially with reynolds number
let's look at how it varies for a few
different two-dimensional shapes
for a flat plate oriented at 90 degrees
to the flow
the drag coefficient doesn't vary
significantly with reynolds number
because flow separation will always
occur at the edge of the plate
and so although it is a blunt body it
isn't affected by whether flow is
laminar or turbulent
for blunt shapes like this disc we see a
large decrease in the drag coefficient
at the transition between laminar and
turbulent flow
because flow separation is delayed when
the boundary becomes turbulent
reducing the drag force and for
streamlined bodies
the drag coefficient reduces gradually
as reynolds number
increases since viscous forces are less
significant at higher reynolds numbers
but the drag coefficient begins to
increase
after the transition to turbulent flow
because as we saw earlier
a turbulent boundary layer produces
larger shear stresses
for a sphere the drag coefficient graph
looks like this
one interesting thing about this graph
is that it's a straight line for
reynolds number
less than 1 and the line is defined as
24
divided by reynolds number at these very
low reynolds numbers
flow separation doesn't occur even for
very blunt bodies
like the sphere and so all of the drag
comes from friction drag plugging this
equation for cd
into the drag force equation gives us an
interesting expression
this is called stoke's law and it is an
exact solution for the drag force
acting on a sphere for reynolds numbers
less than one
it's one of few cases where we have an
analytical solution for calculating the
drag force
and it has some very useful applications
we can use it to easily calculate the
terminal velocity of a sphere
falling in a fluid so long as reynold's
number is low enough
as a sphere falls through a fluid its
velocity will increase
and so will its drag force terminal
velocity
is reached when the weight of the sphere
perfectly balances the drag force
so that the sphere stops accelerating
the drag force is defined by stoke's law
and the weight of the sphere is easy to
calculate based on its volume
and density we just need to remember to
subtract the density of the fluid as
well
to account for the buoyancy force and so
based on stoke's law we can obtain this
equation for the terminal velocity of
the sphere
we can apply this equation to create a
viscometer
which is used to measure the viscosity
of a fluid
to do this a sphere is dropped into a
tube of liquid
which is long enough that the sphere
will reach terminal velocity
the terminal velocity can be measured by
timing how long it takes the sphere to
pass between two points
marked on the tube and so the viscosity
of the fluid can be calculated using the
equation we just derived
we know that pressure stresses and shear
stresses are the two fundamental causes
of drag
but in some cases specific components of
the drag force are named because of
how they're caused even though they're
just different forms of pressure or
friction drag
in aviation for example three important
sources of drag
are induced drag wave drag
and interference drag if you'd like to
learn more about these sources of drag
i've covered them in the extended
version of this video
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at induced drag
wave drag and interference drag to make
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and that's it for this review of
aerodynamic drag
thanks for watching