Measurement Of Flow Rate Through Pipe Video Lecture | Fluid Mechanics for Mechanical Engineering

hi guys this is a salmon expert and this
is our today's problem we have a pipe
with gradually tapering section and
diameter decreases from 0.4 to 0.25
meters inside the pipe there is
incompressible liquid with density
thousand kilos per meter cubed and the
pipe runs full of this liquid we know
the speed of flow in the smaller part of
our pipe it is 2 meters per second our
task is to find the flow speeds in the
larger part also the volume flow rates
and the mass flow rate let's begin first
we need to find the speed in the larger
side of this pipe and we can find it
from the continue tool a L times the l
equals a s times the s where al and a s
are the cross sections of the larger and
smaller part and the LVS are the flow
rate in this part the cross section of a
pipe is pi times R squared so we have pi
r l squared times the l equals PI R s
squared times the s we can cancel out PI
and from here we derive the L as V s
times RS squared over R l squared and
this gives us 2 times the radius of the
smaller part of the pipe which is half
of the diameter so we get 0.1 25 squared
over half of the diameter of the larger
part and this is 0.2 squared and this
gives us zero point 78 meters per second
so here's the flow rate in the larger
part of our pipe all right guys so here
we found the flow rate
it's in the larger section of our pipe
now let's find the volume flow rate and
the mass flow rate the volume flow rate
is the rate of flow in the volume V per
unit time T first let's write the
formula for volume V equals V for speed
times T times a now if we move T to the
other side we will get Delta V over
delta T equals V times a so actually
this is our formula for the volume flow
rate now we know that the cross section
is PI R squared and here we can use
either smaller or larger size of our
pipe let's take the larger part so we
get VL times pi times our l squared and
this gives us 0.78 times 3.14 times 0.2
squid and equals zero point zero ninety
eight meters cubed per second now we
move down to our last task the mass flow
rate first let's recall the formula that
relates the mass with the volume M
equals Rho times V and now let's have a
closer look at this formula if we divide
both sides by T we'll get the following
and we will have Delta over here we will
get that our mass flow rate is equal to
Rho times the volume flow rate so this
is very simple now we just need to put
our values into the formula so we have
thousand
times 0.0 98 and we get 98 kilos for a
second so now all our tasks are complete
we found the flow rates in the larger
parts of our pipe the volume flow rates
and the mass flow rate thanks for
watching and I see you soon again
you