In the preview screencast.
We went through the following problem using
a guess and check irritative method.
So the first thing we did is we took our energy
equation shown here, and then we wrote all
of our known and converted it to the appropriate
units.
Then simplified our energy equation.
So at that point, once we plugged every thing
in we got our energy balance down to a very
simplified form that just had the friction
factor f, and our diameter D. So this was
a guess and check irritative method.
What I want to show you here now is how we
can do this analytically in a computer solver
based program.
The moody diagram is based on empirical evidence
lots of experiments.
It is someone specifically Colebrook came
a long and said there is probably a relationship
here, and came up with empirical equation
that matched the non-laminar range of the
moody diagram.
So this relationship is here.
Which is a function of the Re number, The
relative roughness, and the friction factor
f.
So again using this kind of equation you solve
for one of the variables given the other 2.
So this is what we are going to do.
We are going to rearrange this equation and
set it equal to 0.
So that it looks like the following.
If we simplify this if it is only a function
of the diameter D, and the friction factor
f, using values we already had before.
We can get rid of epsilon, we can also get
rid of the Re number here.
So know we have a relationship between f and
D based on the Colebrook equation here.
We can take this in conjunction with our energy
equation, which is also a function of f and
D. As you recall the energy equation looked
like the following.
So what do we do at this point?
Well lets rewrite the energy equation to solve
for f.
So know we have a relationship for f.
We have a relationship between D and f.
That must be equal to 0.
We are missing one last thing, set D our diameter.
So this follows the same train of thought
we had last time.
Choose a D, this gives us f.
Using that f and that D does that solve this
equation.
This is were excel comes in handy.
We only need 3 cells.
We will have a cell for the diameter, cell
for the friction factor, and lastly our Colebrook
equation.
So here lets just put in a diameter.
Here we have to type in our expression for
our friction factor.
Lastly we enter our Colebrook equation.
So we have our 3 cells that we need.
We know the colebrook equation has to be equal
to 0.
So we go to data, what if analysis, and goal
seek.
It may different depending on the excel you
are using.
We want to set this to 0, and we want to do
that by changing the diameter.
So you could also us solver to do this.
Goalseek is pretty quick.
You get a value of 0.409.
If you recall in the last screencast based
on guessing and checking we said 0.41 was
pretty close.
So when we convert this in terms of inches
we get 4.912 inches for our diameter.
So it may not worth custom making a pipe to
meet those specification.
It is a good starting point to do some analysis
to see if we can use a 5 in pipe.
So hopefully this gives you an idea on how
to set up the irritative approach in excel
and quickly solve this without doing a guess
and check method.
