We have already studied one dimensional
two dimensional and three dimensional
flow which gives us small understanding
of kinematics of fluid flow that is flow
of a fluid to study this in detail we'll
consider a steady flow and an unsteady
flow
steady flow and unsteady flow now what
do you mean by steady flow steady flow
is the flow of liquid in which or a flow
of fluid in which it's fluid parameters
are not dependent upon time means
something is not dependent upon time in
mathematical expression we can write
that is velocity acceleration viscosity
all the three fluid parameters are not a
function of time not a function of time
means they are not dependent upon time
if they are not dependent upon time
this means the change with respect to
time of all the fluid parameters will be
zero so this can be written as DV by DT
is equal to zero change in acceleration
versus time is equal to zero with
respect to time is equal to zero and
change in viscosity with respect to time
is equal to zero now we know that the
velocity is a function of X Y Z and e it
is dependent upon four variables three
variables are spatial coordinates or
space coordinates and the fourth
variable is the time coordinate so we
can write down that is dou u by dou T is
equal to 0 dou V by dou T is equal to 0
and dou W by dou T is equal to 0 now why
do we use D over here and over here
because velocity is a function of one or
more variables that is why we use blue
over here while considering the velocity
along X
y direction and Z direction so this
comprises of a steady flow this
comprises of steady flow now what is an
unsteady flow unsteady flow is a flow in
which unsteady flow is a flow in which
we'll consider it is dependent upon time
that is all the fluid properties are
dependent upon time that is velocity
acceleration and viscosity are a
function of time that means your dou V
by dou T is not equal to zero similarly
dou u by dou T is not equal to zero
dou W by dou T is not equal to zero now
during this entire part we can write
this in terms of differentials let's
check out one differential for this
entire unsteady flow so we'll consider
the u component of velocity what is U
component of velocity that is velocity
along X Direction that is change in
velocity along X Direction is not equal
to zero if it is not equal to zero
either this part will be greater than
zero or this part will be less than zero
if it is greater than zero the velocity
along that direction is increasing if it
is less than zero then the velocity
along that direction is decreasing let
us consider if it is increasing so you
will write this differential as dou u by
dou T is equals to it is not equal to
zero
if it is not equal to zero either it is
greater or less will consider this K as
greater than zero a variable has a
positive value so if you
multiply that is do you is equal to K
into duty and if you integrate over an
entire limits or just if we integrate we
will get this as U is equals to K T plus
C that means U is a function of time and
it is dependent upon type hence this
flow is called as what unsteady flow I
hope you have understood what is basic
difference between steady flow and
unsteady flow one is dependent upon time
which is unsteady flow one is
independent upon type which is steady
flow thank you
