let’s discuss equation of continuity. we
can simply write about it that, this equation,
defines that, for streamlined flow, for streamline
flow of fluid only this equation of continuity
is defined, which is steady, for a fluid,
the mass, entering per second, at 1 end, is
equal to, the mass leaving, per second at
the other end. so at both the ends, we define,
the conservation of mass, as we have already
discussed that during flow the density of
fluid remains constant. so this equation of
continuity is basically defining, that the
flow rate of a fluid, throughout, the flowing
fluid body remains constant. say if we consider
a pipeline, which is having its cross sectional
area as, a-1 and a-2 at the 2 ends. at 1 end
the flow velocity is v-1 and at the other
end flow velocity is v-2. then at any general
cross section in between which is having area
a, say flow velocity is v. then according
to, equation of continuity, we can simply
define, the flow rate of fluid at end a-1
cross sectional area is equal to the flow
rate at end a-2 cross sectional area. so we
can write, the flow volume rate d v-1 by dt,
must be equal to d v 2 by dt. if these are
the ends 1 and 2, we can define these at 1,
and at point 2. now in this situation we know
that, the volume flow rate is given by the
product of cross sectional area and, the flow
velocity. so this can be written as, a-1 v-1.
and this can be written as, a-2 v-2. so this
is the equation of continuity we use in various
cases, or for any general cross section area
we can write the product of cross sectional
area and the flow velocity remains, constant.
this is the relation we use for equation of
continuity for any cross section, throughout
the fluid body, if the flow is stream lined.
