In this illustration we'll be studying about,
water filling a tank with a hole.
we are given that a cylindrical tank of base
area ay, has a small hole of area small ay
at the bottom. and at time t equals to zero
a tap starts supplying water into the tank
at a constant rate alpha meter cube per second.
and we are required to find the maximum level
to which water can be filled in the tank.
here, we can draw the situation first where,
we are given with the tank. with a hole. and,
through a tap, when, water, starts, filling
in, as the liquid level rises over here, the
liquid starts, draining out. and at any instant
we can say if it is at a height y. and, the
whole size is small we can say the flow velocity
or reflex velocity we are already studied
by torricelli's theorem.
then it is given as 2 gee, y. and the water
filling rate is given to us is alpha meter
cube per second.
now in this situation here we can write that
if. water is filled.
to a level y in tank.
the, ejection velocity. of water.
from hole is, this we can write as we have
written it is root 2 gee y. and, if we talk
about the ejection.
volume rate.
of water, in ejection volume rate we can write
as velocity multiplied by the cross sectional
area of the hole.
which is ay multiplied by root 2 gee y. and
here we can say, the water level.
in tank. will become.
constant.
when.
water supply rate.
is equal to water ejection rate.
so in this situation here we can say this
supply rate we are already given as alpha.
and the ejection rate we have written as,
ay root of 2 gee y. so on simplifying this
is giving us the value of y which is alpha
square by, 2 gee ay square.
that is the level at which the ejection rate
and supply rate becomes equal.
so this would be the result of, the maximum
level to which water will rise and then it'll
become constant.
