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00:00

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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.

01:01

And so engineers go to great lengths to minimise
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 optimise 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.

02:05

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 minimise flow separation at all costs.

03:10

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

04:10

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.

05:17

Bodies that travel through fluids, like plane
wings or submarines, are usually designed
to be streamlined in a teardrop shape to minimise
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.

06:17

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 minimising the
friction drag associated with a turbulent
boundary layer.
When trying to minimise drag, engineers very
often look to nature for inspiration.

07:23

Sharks are of 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 2%, 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.

08:24

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.
When streamlining a body to reduce drag, it's
important to remember that the 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

09:25

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 C-D 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 planform area.

10:33

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 Reynold's 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 disk 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

11:38

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 numbers
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 C-D into the drag
force equation gives us an interesting expression.
This is called Stokes' Law, and it is an exact
solution for the drag force acting on a sphere
for Reynolds numbers less than 1.
It's one of few cases where we have an analytical
solution for calculating the drag force, and

12:39

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 Reynolds 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 Stokes' 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 Stokes' 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.

13:41

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, which is available
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14:44

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drag, wave drag and interference drag.
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