let us discuss about the pressure distribution
in a closed accelerated container.
in previous section we already discussed.
that in an open container when it is accelerated.
the free surface of liquid get incline, with
the horizontal depending on the acceleration
of container.
say if we are having a completely closed container
which is enclosing, a fluid. and say container
is accelerating with an acceleration ay. here
we can say all the layers of fluid will incline.
to the horizontal with the same acceleration
. with the same angle theta which is given
as, tan inverse of ay by g which we have earlier
calculated , or this is the angle which all
the layers, will make with the horizontal,
with in the fluid.
now in such a situation there is no part of
fluid which is exposed to atmosphere, so if
we wish to find out the least pressure point
it can be taken at.
the, top right corner.
of the container in this situation we can
say . this is the least pressure point.
in the fluid body which is enclosed in the
container because.
from this point only pressure will start increasing
as g-effective is acting in this direction.
because of, the resultant effect of, pseudo
acceleration and the gravity g. and this angle
is same as theta.
now in such a situation say if we wish to
find out pressure at point ay, which is at
a depth h below the top surface . of the container
and at a distance l from the front surface
of the container.
then here we can calculate it, in either of
three ways which we have discussed in the
previous section.
but the best way out is , successive increment
in pressure, like , we can consider the least
pressure point pressure will be zero.
so if we wish to find out pressure at this
point which is at a depth h below.
this point, so we can say pressure at this
point will be zero plus, h-ro-g. and if we
are having pressure at this point at this
point pressure can be written as, this plus,
l-ro-ay. as pseudo acceleration is acting
in this direction.
so along the horizontal line pressure difference
will only be due to this pseudo acceleration.
and this is the pressure at point ay. so using
such equation we can directly write down the
pressure at ay which can be written as h-ro-g
plus , l-ro-ay. so just be careful whenever
you wish to find, the pressure at a point
it can be obtained , by writing the equation
of successive increase in pressure from one
point to another then another to final destination
where pressure is required.
same equation can be written by moving along
this path first is say if here we consider
pressure to be zero . pressure at this point
can be written as zero plus l ro ay. as along
the length of L pressure is only varying due
to ay. and now if we know the pressure at
this point pressure at point ay can be written
as. this is the pressure zero plus, l-ro-ay.
plus, due to a vertical depth h pressure will
only vary due to gravity, so it’ll be h-ro-g.
you can see the same result we are getting
no matter whichever path we are following.
