let us discuss about average pressure on side
walls of vessel. here you can see, a vessel
is there which is filled up to the top, up
to say a height h with a liquid. and the dimensions
of the container are h l and w. if we consider
the liquid is filled up to the top. in this
situation at every point in contact with side
wall. the, due to fluid pressure the force
will be acting in the direction, along outward
normal of the wall. say we wish to find out
the average pressure exerted by the liquid
which is in contact with the side wall. obviously
we know at bottom pressure is more as depth
is more. so, liquid will push the wall in
outward direction with more force, the liquid
which is at the top . the depth is less so
we can say it’ll push the wall , in outward
direction with lesser force. so in this situation
if we wish to find out the total force acting
, on this wall . we consider from the free
surface , at a depth y . we consider an elemental
strip on the side wall which is of width d-y.
now we can simply state the, liquid particle
which are just behind this strip will push
this strip in outward direction with the force
d-f. so if we find out . the pressure. due
to. fluid. here we are talking about gawge
pressure only which is due to fluid only . at
a point. behind the elemental strip is . here
we can simply state the pressure will be , y
ro g as , we are not considering p-atmospheric,
because we are finding out the pressure only
due to the fluid. so the pressure just behind
the strip of width d-y , it will be y ro g
because this point is at a depth y , below
the free surface of the liquid. and if we
find out the force, or more precisely we should
write , outward force . on elemental strip.
which is obviously due to the fluid pressure
is. this can be written as d-f and here d-f
will be y ro g multiplied by the area of this
strip which can be written as w d-y. and if
we find out the total force . on side wall.
of vessel. due to fluid pressure is. this
can be calculated as total force is integration
of this d f. and we’ll integrate this expression
y ro g w d-y , within limits from zero to
h, because the total height up to which the
liquid is filled is h so we’ll integrate
this variable y from zero to h. and here only
y is variable ro g w is constant , so the
result will be ro g w , and it’ll be y square
by two within limits from zero to h, so you
can see the result we are getting is half
ro g w h square. this is the total force acting
on the side wall , which is in contact with
the fluid and area, h w. so we can directly
find out the average pressure. on side wall
. is. average pressure can be directly written
as the total force on side wall divide by
the total area of the wall which is in contact
with the fluid that is , height is h and its
width is w so it can be written as f by h
w. if we substitute the value of f here. it’ll
be half of ro g w h square by , h w, here
w and h gets cancelled out it is, half h ro
g. this quite an important relation to be
kept in mind, this you can simply write the,
half pressure . which fluid. exert on bottom.
this half of the pressure, which fluid exert
on bottom as we know that at bottom , pressure
is h ro g ,and if we find out the average
pressure on the side wall it is simply half
of the pressure, which liquid is exerting,
the fluid is exert ting at the bottom of the
container. so just keep this point always
in your mind as in many application directly
we are going to use this result.
