in this example, we are given in a horizontal
pipe line, the flowing oil pressure falls
by 8 newton per meter square, between 2 points,
seperated by 1 km. we are required to find
the change in ki-netic energy per kg of oil
at these points.
we are also given the density of oil to be,
800 kg per meter cube. and here we can directly
write, by using, bernawlli’s theorem, we
have, we can write, as the pipeline is horizontal
we can write, p 1 plus, half ro v 1 square,
is equal to p 2 plus, half ro v 2 square.
as the height level is same, we can ignore
the gravitational potential energy on both
sides of equality. and in this situation the
change in ki-netic energy per unit volume
can be written as, half ro, v 2 square minus
v 1 square, this is equal to p 1 minus p 2,
and we are given that, the pressure difference
is 8 newton per meter square between the 2
points.
so we calculate the change in ki-netic energy
per kilogram, this can be written as half
of, v 2 square minus v 1 square.
so we need to divide it by the density that
is p 1 minus p 2 by ro. so it’ll be 8 by
8 hundred, that can be given as, zero point
zero 1 joule per kg. that’ll be the answer
to this problem.
