In this lesson, we will discuss the Moody
chart.
The Moody chart’s primary purpose is to
provide a graphical representation of the
Colebrook equation.
Before inexpensive computers became widely
available, it provided a means of quickly
estimating the Darcy friction factor f.
The Moody chart shows the value of the friction
factor as a function of Reynolds number for
various values of the relative roughness.
Notice that the x and y axes both use a log
scale.
If the Reynolds number of a flow is below
approximately 2000, the friction factor is
only a function of the Reynolds number and
can be calculated directly from the formula,
64 over the Reynolds number.
This formula is represented graphically by
a line on the left side of the Moody chart.
If the Reynolds number is between approximately
2000 and 4000, the flow is in the transitional
regime.
There is no accurate method of determining
the friction factor for this range of Reynolds
numbers.
Most of the Moody chart is dedicated to the
turbulent flow regime, in which the Reynolds
number is greater than 4000.
Recall from the Colebrook equation that the
friction factor for turbulent flows is a function
of both the Reynolds number and relative roughness.
The only way to plot a function of two variables
on a two-dimensional graph is to hold one
variable constant while varying the other.
In the case of the Moody chart, the Reynolds
number is varied while holding the relative
roughness constant.
For example, suppose the pipe you are examining
has relative roughness is 0.002.
You would use the curve shown in orange to
determine the value of the friction factor
at different Reynolds numbers.
Now suppose the Reynolds number of the flow
is 10000.
Draw a vertical line from 10000 on the x-axis
until it reaches the orange line.
Now draw a horizontal line from the intersection
point to the y-axis and read the friction
factor.
For this example, the friction factor is approximately
0.032.
Moody charts only show curves for a limited
number of relative roughness values.
In this particular chart, curves for 18 relative
roughness values are presented.
When you encounter a pipe flow problem in
which the relative roughness is not shown
on the Moody chart, a rough interpolation
between two curves usually will suffice.
For example, if the relative roughness of
a pipe is 0.0015, you can estimate a curve
between the 0.001 and 0.002 curves.
Although this method introduces some additional
error into the value of the friction factor,
the error is relatively minor compared to
other potential sources of error such as uncertainty
in the actual value of the roughness.
It is important to remember that frictional
losses occur in all pipes, even if they are
hydraulically smooth and have very small relative
roughness values.
Pipes made of glass and plastic are examples
of pipes that are hydraulically smooth.
For these type of pipes, the friction factor
is found using the lowest curve on the Moody
chart.
At relatively high Reynolds number values,
notice that all of the curves become horizontal,
which means the friction factor is a very
weak function of the Reynolds number.
We call this flow regime “wholly turbulent.”
Physically it represents a flow where the
size of the viscous sublayer has been reduced
to the size of the roughness.
