so let's take a look at the concept of
the boundary layer what it is and what
it's good for the boundary layer is an
idea in fluid mechanics and like any
good idea it starts in somebody's mind
at some point and the idea in this case
is coming in the head of a German fluid
dynamicist called Ludwig Prandtl and
the Ludiwg once upon a time
thinks we're gonna split the problems in
halves so every time we have a fluid
flow like for example the airflow around
a frisbee
we're gonna split the problems in two
areas close to the frisbee the fluid
flow is dominated by the friction the
shear of the wall on the fluid and vice
versa while relatively far away from the
frisbee maybe a few centimeters away
from frisbee the flow is almost
unaffected by shear and viscosity it is an
inviscid flow and so Prandtl said we're
gonna split the problems into halves
let's study very close to the frisbee
a flow where the equations will be
dominated by viscosity and once we're
done with this we're gonna study the
rest of the flow in a way where we can
neglect viscosity and a lot of progress
was made with this and he came up with a
name for it that was called the boundary
layer in German Grenzschicht it sounds
like a good name for indie rock band but
it is actually a concept in fluid mechanics
this is a Ludwig Prandtl by the way in
1904 in front of his lab the very
important idea to remember is that the
boundary layer
it's not a very clearly defined area it
is the concept it is a general idea zone
you could say a cloud is a vague idea if
you try to cut too close
what borders of the cloud is you’ll run into trouble trouble and the boundary layer
is the same usually we say the boundary
layer is the zone between the wall and
the area above, the limit where the flow has
already 99% of the free stream velocity
the velocity far away again it's a very
blurry and sometimes
undefinable boundaries boundary that
varies a lot in time that's not so easy
to measure but this is the mean the main
concept so if you take any object this
is a this is a wing a profile in a wind
tunnel the flow comes from left to right
and you go and measure the velocity very
close to the surface here and you go
down with your probe here probably the
tiny window then it comes down you measure
you measure the velocity in meters per
second until you come very close to the
wall and you plot this as a graph on
this lovely analog graphic XY recorder
4302 then you can see that the
velocity is mostly constant far away
from the wall but as you come close to
zero very close to the wall you always
tend to zero and this zone here where
the velocity is low and decreases from
99% of the mainstream value down to zero
the zone is called in general the
boundary layer so if you make a graph
out of this you say this is the velocity
distribution with space this curve here
and the area where you are still 99
percent away from the maximum velocity
this is the boundary layer the thickness
of the boundary layer varies it varies
according to many parameters and the
main idea is to keep in mind is that the
decreases with increasing speed so the
faster you throw the
frisbee and the shallower the layer will
be above it where there is a lot of
shear and conversely the slower you
fly and the thicker it is viscosity
has the opposite effect
yeah so to represent this very slow flow
has a thick boundary layer a very fast
flow or very low viscosity flow will
have a thin boundary layer and we learn to quantify
this later on but this is the
main concept to remember boundary layer
layer always starts laminar if you throw
a frisbee like this with very smooth
body it will start laminar and then as
you go down towards downstream over the
flow then the
boundary layer will transit and by
transit we mean it is going to become
turbulent so from laminar to turbulent
and this point is called a transition
point and we also attempted to measure
and to predict where the transition will
happen and after it's transited it's
becoming turbulent and being turbulent
it's very messy lots of dissipation lots
of variation in speed it grows faster
and it's also thicker you may have this
is important remember that you may have
a laminar boundary layer inside a
turbulent main flow and you may have a
turbulent boundary layer inside the
laminar main flow so that the flow
inside the boundary layer and the flow
outside are connected but then they may
have different characteristics now let
me give you examples this is an airplane
this new Airbus a319 it's the
run-of-the-mill standard medium-range
airplane you will find into these days this
will fly in very laminar flow so far
away from the from the wings and the
fuselage as the flow is affected by the
airplane all this flow is laminar but if
you come close to the fuselage and you
look at the boundary layer [on top of the]
fuselage the boundary layer regime is
completely very deeply turbulent so
you'll have a very turbulent boundary
layer inside the laminar main flow okay
the opposite is true if you have say
very turbulent flow this is the wake
behind the boat generated by the
propellers if you now would take a canoe
for example and you would pass across
this very turbulent flow the boundary
layer on the walls of the canoe would be
laminar inside a very turbulent main
flow
yeah so those two readings are quite
different and now most importantly why
do we study the boundary layer
well we studied because it makes sense
for the engineering it is it is a lot of
time saved yeah so yes
you should definitely invest time into
studying this very small half millimeter
area
because it dictates a lot of other
things inside the flow the main first
reason why we study it is that we never
solve the full Navier-Stokes equation we're
kind of lazy as engineers still since we
don't have the the general answer
mathematical answer to those equations
we would get away with it so we we
inside the boundary layer we model the
velocity distribution so if you run the
computational fluid dynamics simulation
the CFD simulation the boundary layer
will never be completely resolved and
you will just model it and outside of it
you may neglect viscous effects so we
can split the problems in two halves in in
each half we have a non complete
navier-stokes equation it's very useful
so if you're looking at the flow let's
say around an airfoil I would here flow
coming from left to right you may split
the zone in three one is the main zone
outside of it where you can apply
equations where the viscosity plays a
very small role
it's very non dissipative you have the
boundary layer here which is represented
in orange you will start laminar and
then you will transit and it will become
turbulent and inside those we have
models and special equations that focus
on describing this boundary layer the
friction in there and then you have the
turbulent wake here for which there is
no good general model and force you have
to resort to experiments or relatively
complex dynamic simulations so the idea
is this boundary layer is kind of an
area which allows you to split the
problems in separate problems and reduce
your computational time so this is the
deal we never solve the full
navier-stokes equation yay cool the
second reason why we study the boundary layer is
that we can quantify shear forces so if
you want to calculate how much friction there
is on this frisbee you want to predict this
then you need to figure out what the
boundary layer characteristics on the
top of this frisbee are so a good boundary
layer solution is a quantification of
the wall friction and the last thing we
would like to do is we predict
separation and separation is when the
boundary layer
follows your object and then tends to
separate
leave the path of the object if you want
and this is usually in fluid mechanics pretty
nasty sometimes we look for that but
most of the time we try to prevent this
and understanding the boundary layer
controlling it is the key to making sure
the fluid flow will follow the
trajectory of your object so for example
what you don't want to have on the
airplane is a foil like this though the
wing of your airplane with the flow not
following the trajectory and then it's
separating from there this is here this
would be the separation point what you
would like to have is a flow sticking to
the airplane and controlling and
understanding how the boundary layer
works will allow you to do this so how
to measure your boundary layer a 3 step guide there are three
parameters typically in which with which
we measure the thickness of the boundary
layer the first is the actual thickness
is what I call Delta it's what I
described at the start of the video here
Delta is why the distance away from the
wall at which the velocity is 99% over
the main velocity okay so far so good
this is easily understandable and of
course fluid dynamicists find this too
easy to understand and the invent new
ways to measure thickness another
alternate to this is the Delta star it is a
displacement thickness and in this
placement thickness is the distance by
which the flow is pushed away from the
wall because of the presence of the
boundary layer and it's calculated
using this equation but let's not focus
on this right now let me show you what I
mean by the displacement thickness
imagine you have a wall you have a flat
plate like so and on this flat plate you
have a boundary layer building up we
said Delta the thickness the thickness
of the boundary layer at this point is
the distance away from the wall at which
you have the velocity which is 99
percent of the main velocity this is
Delta and Delta will change with
distance so if you do the same
experiment here you will have this lower
thickness and if you do the same
experiment there you have a higher
thickness of thickness keeps increasing
forever and so if you draw all of those
points here as a line you get this this
limit here this this area is the
thickness of the boundary layer this is
quite misleading diagram because it can
suggest that there is some kind of stuff
some kind of extra coat on top of the
body around which the flu is gonna flow
and this is not the case the boundary
layer is transparent it is traversed by
streamlines and so a fluid particle that
comes in here will be entering the
boundary layer at the border of the
boundary right here and it will it will
go through the boundary layer with ever
decrease in velocity as it goes through
here
and doing so it is also pushed slightly
away from the wall the amount by which
is pushed away from the wall it's called
data star this is the displacement
thickness so if you take this streamline here it was at this point here and
now you are at this point there has been
pushed up by some amount this amount
here is called data
star the displacement thickness and like
the main thickness the
displacement thickness will grow with
time will grow with away with distances
we have calculated the displacement
thickness in the previous chapters back
when we were interested in integral
analysis and analysis of existing flows
and we said we we know the velocity at
the start and we look at the velocity at
the outlet and doing so we had derived
this equation we had written this
equation for Delta star so if you
wondering where this comes from go back
to the previous chapters and now is this
existing flows well gone you to find
this equation to figure it figure out
this question but again don't learn it
by heart it's not it's not the focus of
the chapter the third thickness is the
momentum thickness and it's written
Delta star star or it's also sometimes
written in theta but I prefer Delta star
star because then you get to say Delta
star star or Delta double star all the
time which is so cool
and this the thickness of  the fluid that you will need to
remove away from the main flow so that
you get the same amount of drag as the
boundary layer is exerting it's written
where this equation here which again you
can go back to the previous chapters and
figure out because we've done this in an
exercise and I sold exercise in previous
chapters but the rest let me show you
what I would I mean by this so we have
the thickness here in Delta and you have
two displacement thickness and as our
start over here what is the momentum
thickness Delta a star star well you
could put it this way at this point here
the thickness is Delta the thickness
Delta star is the thickness in the main
flow that possesses the same amount of
mass flow as the mass flow that is missing
inside the boundary layer this is how we
calculate it and the momentum thickness
delta star star is the amount of
thickness inside the flow that possesses
the same amount of momentum as this area
here inside boundary layer so it's
basically quantifying how much momentum
has been removed from the boundary layer
sorry has been removed from the main
flow through the boundary layer and
quantifies this as a thickness away so
as a distance away from the wall yeah so
quite an abstract notion but it turns
out these two parameters even though
they're more difficult to grasp and less
easy to visualize they are much more
useful in qualifying the behavior of the
boundary layer especially the ratio of
those two well is a good predictor of
how well the boundary layer sticks or
not to surfaces so this is the reason
why fluid dynamicists always argue about
which Delta is the best delta delta star or
delta star star and the last thing
we are interested in we want to quantify
when we play with boundary layers is the
shear tau and the shear is easy now
since we spent quite a lot of time
before playing with the shear in the
previous chapters
shear is the derivative with respect to
space with respect to distance away from
the wall of the fluid why is velocity
and this is an expressions in this
function of X so it depends on the
distance of the shear exerted by the
boundary layer and the start of the flow
here is much higher than the shear it's
by the boundary layer further down
decreases with distance away
and as usual in fluid mechanics
we like to non-dimensionalize
things and in particular the shear and
so we coefficientize it so we say tau
well divided by 1/2 of Rho times the
main fluid velocity this is gonna be
called the coefficient the shear
coefficient CFX and it's also a function
of x so as we are we study the boundary
layer and we look into the main
characteristics and the main parameters
of the boundary layer this is what we're
going to try to quantify how much
friction has exerted by the boundary
layer on top of the surface so this is
it this is your first short guided tour
about the boundary layer in fluid mechanics.
