In this illustration we are going to
discuss about flow velocity in viscous
fluid here we are given that in the
arrangement shown in figure of viscous
fluid whose density is Rho flows along a
tube out of a white tank a this is the
tank a find the velocity of this liquid
flow if these h1 h2 h3 are given as 10
20 and 35 centimeter all the distances l
are equal now in this situation we can
see if the flow velocity coming out is V
and obviously flow velocity throughout
the tube must be V because the cross
sectional area is constant so if we
consider points a B and C then we can
use poiseuille's equation between points
A and B we can write four points between
A and B the cross sectional area S
multiplied by flow velocity which is the
rate of flow of fluid that is equal to
PI R to power 4 by 8 ETA L multiplied by
the pressure difference which is here we
can see the difference of pressure
between these two points A and B is H 1
Rho G and if we talk about between
points B and C then also you can see
here sv should be equal to PI R to power
4 by 8 et al pressure difference between
two points is h2 minus h1 x ro G and
here as the two left hand side comes in
equation 1 and 2 are same that means
right hand side must also be seen and
here you can see as h1 is 10 and you can
see the value of h2 minus h1 is also 10
so this is in accordance with the fluid
flow which is homogeneous so both of
these equations are coming out to be
correct for sv and if we talk about this
point D then we
right between points C and D here if we
consider up to this level say this
height is H 3 prime which is not as
specified in the problem because this is
the level which is being maintained so
we can directly write over here between
point c and d sv we can write it as PI R
to power 4 by 8 et al and this should be
equal to H 3 prime minus h2 x ro G and
on calculation as this should be equal
to 10 centimeter we can CH 3 prime is
equal to 30 centimeter because ash 2 is
given as 20 centimeter now here we can
see this is an extra distance of five
centimeter which is there and providing
the velocity head or hair pressure is P
atmospheric so this is the extra
pressure head which is producing or
which is causing the fluid to flow
because the pressure difference across C
and D B and C and E and D must be
maintained same for it to flow at
constant velocity though st h three
prime is the pressure head which is
maintaining the flow velocity and this
extra distance which is fice and
dimitra's h3 is given as 35 centimeter
is causing the velocity to generate in
the fluid so we can say the extra
pressure head which is causing
fluid to flow is due to h3 minus h3 play
prime column which is equal to 5
centimeter this implies the flow
velocity will get V is equal to root 2 G
H 3 minus H 3 prime how we are
calculating this you can apply
Bernoulli's theorem if the system is not
there and there is a small hole created
over here then the flow velocity which
is produced by this velocity head will
be simply by Doris Ellis theorem we are
getting this we can write by Tory
Sally's theorem neglecting viscosity in
wide container
here was on this container we can
neglect the velocity as a container is
very wide so flow velocity here is very
low so the velocity with which liquid
will come out from this point is root of
2gh 3 minus h3 prime on calculation we
can get it root of two x g we can take
here as 10 and h3 minus h3 prime here is
0.1 so this coming out to be this is
point zero five so this coming out to be
one meter per second that is a result of
this problem
