- [Instructor] In this screencast,
I'm going to show you how to calculate
an equivalent length for minor head loss.
This length is the length
of straight pipe that would cause the same amount
of head loss as the total minor head loss.
So, let's consider a galvanized iron pipe.
It has a diameter that's equal to 0.075 meters,
and it has a 90 degree threaded elbow.
And what we want to know is,
what is the equivalent length.
And how would this change,
instead of having a 90 degree threaded elbow,
we have a flanged elbow.
What is the corresponding equivalent length for this?
And for this problem,
we're going to assume that the flow is wholly turbulent.
So we'll start with the equation for equivalent length.
So the equivalent length is equal to K sub L,
which is the lost coefficient times the diameter
of the pipe divided by the friction factor.
And this K sub L is the lost coefficient
and it depends on the geometry.
So we'll start with K sub L.
These values are tabulated in any fluid mechanics book.
And here, when we look them up, we find that it is equal
to 1.5 for the threaded elbow and 0.3 for the flanged elbow.
One thing to keep in mind,
these lost coefficients are not material dependent.
So we could have a copper pipe instead of an iron pipe
and we'd have the same two loss coefficients.
So how do we find the friction factor?
So the friction factor,
we're gonna have to get from the Moody chart.
And in order to use the Moody chart,
we're gonna need to know the Reynolds number
and the roughness factor divided by the diameter.
The first thing is this Reynolds number.
Because our flow is wholly turbulent,
we don't need a Reynolds number.
We can just use the line in the Moody chart
for wholly turbulent.
Here, we're gonna have to look up the roughness factor.
And that's where the material does matter.
So we have a galvanized iron pipe.
So we go and we look up the roughness factor for that.
And that's going to be equal to 0.15.
And this is where you have to be careful.
The roughness factor is given in millimeters, not meters,
but everything else is in meters.
So make sure that you use the correct order of magnitude.
So now, let's calculate our epsilon roughness factor
divided by D.
So this is equal to 0.15 times 10 to the minus three meters.
And our diameter, go back to our problem,
is given right here.
And so we divide that by 0.075 meters.
And so we find that this ratio
of roughness factor to diameter is equal to 0.002.
So with this number and the fact that it's wholly turbulent,
let's go to the Moody chart
and figure out what our friction factor is.
So again, we know that our epsilon over D roughness factor
over diameter was calculated to be 0.002,
though that's right there.
And we're looking for where it intersects
the wholly turbulent flow line,
which is right there.
And if we do a straight line across
to the friction factor over here,
we find that the friction factor is equal to 0.023.
So let's go back and put that into our equation.
We'll start with the threaded elbow,
so that equivalent length is equal to our loss coefficient,
which is 1.5 times our diameter,
which is 0.075 meters
divided by the friction factor of 0.023.
And our equivalent length for a threaded elbow
is equal to 4.9 meters.
We do the same thing for the flanged elbow.
The only thing that changes is our loss coefficient.
So our diameter stays the same as does the friction factor.
And when we calculate that equivalent length,
that's gonna be equal to 0.98 meters.
As expected, this is considerably lower
than the threaded elbow, but certainly significant.
So this problem had only one fitting,
but equivalent length can be calculated for many fittings
by calculating that equivalent length for each one
and summing them up to get the total length.