In this screencast we are going to talk about
what is known as a moody chart, which relates
a frictional factor losses considered in pipe
flow in other systems, to that of the Re number
and relative roughness.
This is the moody chart and you can see its
a log based scale.
With 2 y-axis and an x-axis.
On the x-axis we have the Re number on the
right y-axis we have the relative roughness,
and the relative roughness is indicated with
each of the black lines that you see.
So for instances if we had calculated relative
roughness 0.001.
We would follow along this line to whatever
or Re number was.
Then we would go to the left and determine
what our frictional factor would be.
Now this is different depending on the type
of flow.
We have laminar flow we are working only in
this region over here, and we know that the
relationship for frictional factor and laminar
flow is just 64/Re, which indicates that it
is a linear relationship, and that is exactly
what you see here on your left.
Now when we work with turbulent flow systems
we start moving to this right.
Using all the lines indicated as such.
There are two lines specifically that we need
to mention.
One, that being a smooth pipe.
So whenever we say that we assume a smooth
pipe flow.
We would use this bottom line, and this dotted
line is when we have holey turbulent flow,
and the relative roughness is the how we are
going to calculate our friction factor.
Lets go through an example on how to read
this plot.
So here in the first example we are told we
have a Re number of 2x10^5 for water through
1000 ft piping that has an inner diameter
of 3 inches.
We are asked to figure out what the major
losses are.
So when we think of major losses we will write
hL as our head loss.
We are going to say that is equal to the frictional
factor times the length of pipe over the diameter
times our velocity over 2g.
This is something you typically see in a fluid
mechanics dynamics problem.
What we are most interested in is this frictional
factor, since probably given the velocity
or something that we can back calculate from
the Re number.
Knowing that we could look up the information
for water.
We are told the length and the diameter.
So we can calculate the losses.
Lets just focus on the frictional factor.
We need 2 pieces of information to use the
moody chart, and calculate the frictional
factor.
One is the relative roughness.
Now we would have to look up the roughness
of whatever piping system we are using.
As you can see on the left we have a chart
were we pulled this information.
Lets assume somewhere in the middles.
So we are going ahead and say 0.01 ft.
This is over our diameter, which is 3 inches.
So 3 inches over 12 in/ft is going to give
us 0.25 ft.
This gives us a relative roughness of 0.04.
The other piece of information we would need
is the Re number, which we are given as 2x10^5.
Lets look at our Moody chart.
Given that we are at 0.04, we are pretty high
in the moody chart.
We are somewhere a long this line, and our
Re number of 2x10^5 will follow up this line,
and along our relative roughness line, and
we will read what our frictional factor is
along the left side of this chart.
You can see we are somewhere in between 0.06
and 0.07.
A little on the higher side.
So we would estimate that our frictional factor
is 0.066.
We would use that below in our calculation
for our losses, and determine some other condition
in our system based on this information.
So if we can take a look at this system.
It is important to realized that with this
kind of roughness the Re number really does
not have an effect in a certain range.
Probably from right about here to as high
as 10^8.
So the roughness plays a significant role
in effecting the frictional factor, but the
Re number not so much, and you can see that
at lower friction factors the Re number does
play a higher role, but there are still regions
were the lines are straight, and increasing
the Re number will not increase the frictional
factor.
Now that is not the case for laminar flow,
and we can see that in an example.
We have a Re number of 1000 fir glycerol through
50 ft of cast iron.
Given an inner diameter of 4 inches.
We are asked to calculate the losses associated
with this.
So again we calculate the relative roughness.
In this case our roughness for cast iron is
0.00085 over 0.33 since we are working with
feet.
This comes out to 0.0025.
Our Re number again is given to use in our
problem, which is 1000.
So we can go up to our moody chart.
For 1000 we are going to be somewhere right
along this line.
You can see that our roughness actually does
not place a factor in this, and that all that
matters.
Since we are in laminar flow, is that we calculate
it by reading it off the chart or to be a
little bit more accurate we can say that the
frictional factor is equal to 64 divided by
the Re number.
So we read 0.066.
We can calculate it by 64 divided by 1000.
This gives us a frictional factor of about
0.064.
So pretty close to how we read it.
So hopefully this gives you a good idea on
how to read a moody chart.
