All pipes carrying fluids experience losses
of pressure caused by friction and turbulence
of the flow. It affects seemingly simple
things like the plumbing in your house
all the way up to the design of massive, way
more complex, long-distance pipelines. I’ve
talked about many of the challenges engineers
face in designing piped systems, including
water hammer, air entrainment, and thrust forces.
But, I’ve never talked about the factors affecting
how much fluid actually flows through a pipe
and the pressures at which that occurs. So,
today we’re going to have a little fun, test
out some different configurations of piping,
and see how well the engineering equations
can predict the pressure and flow.
Even if you’re not going to use the equations,
hopefully, you’ll gain some intuition from seeing
how they work in a real situation. I’m Grady and
this is Practical Engineering. In today’s episode,
we’re talking about closed conduit
hydraulics and pressure drop in pipes.
This video is sponsored by HelloFresh,
America’s number 1 meal kit. More on that later.
I love engineering analogies, and in this case,
there are a lot of similarities between electrical
circuits and fluids in pipes. Just like all
conventional conductors have some resistance
to the flow of current, all pipes impart some
resistance to the flow of the fluid inside,
usually in the form of friction and turbulence.
In fact, this is a lovely analogy because
the resistance of a conductor is both a function
of the cross-sectional area and length of the
conductor—the bigger and shorter the wire, the
lower the resistance. The same is true for pipes,
but the reasons are a little different. The fluid
velocity in a pipe is a function of the flow rate
and the pipe’s area. Given a flowrate, a
larger pipe will have a lower velocity,
and a small pipe will have a higher velocity.
This concept is critical to understanding the
hydraulics of pipeline design because friction and
turbulence are mostly a result of flow velocity.
I built this demonstration that should help
us see this in practice. This is a manifold
to test out different configurations of pipes and
see their effect on the flow and pressure of the
fluid inside. It’s connected to my regular
tap on the left. The water passes through
a flow meter and valve, past some pressure
gauges, through the sample pipe in question,
and finally through a showerhead. I
picked a showerhead since, for many of us,
it’s the most tangible and immediate connection
we have to pressure problems in plumbing. It’s
probably one of the most important factors in the
difference between a good shower, and a bad one.
Don’t worry, all this water will be given
to my plants which need it right now anyway.
I used these clear pipes because they
look cool, but there won’t be much to see
inside. All the information we need will show
up on the gauges (as long as I bleed all the
air from the lines each time). The first one
measures the flow rate in gallons per minute,
the second one measures the pressure
in the pipe in pounds per square inch,
and the third gauge measures the difference
in pressure before and after the sample
(also called the head loss) in inches of water. In
other words, this gauge measures how much pressure
is lost through friction and turbulence in the
sample - this is the one to keep your eye on. In
simple terms, it’s saying how far do you have to
open the valve to achieve a certain rate of flow.
I know the metric folks are giggling at these
units. For this video, I’m going to break my
rule about providing both systems of measurement
because these values are just examples anyway.
They are just nice round numbers that are easy
to compare with no real application outside the
demo. Substitute your own preferred units if you
want, because it won’t affect the conclusions.
There are a few methods engineers use to estimate
the energy losses in pipes carrying water,
but one of the simplest is the Hazen-Williams
equation. It can be rearranged in a few ways,
but this way is nice because it has the variables
we can measure. It says that the head loss (in
other words the drop in pressure from one end of a
pipe to the other) is a function of the flow rate,
and the diameter, length, and roughness of
the pipe. Now - that’s a lot of variables,
so let’s try an example to show how this works.
First, we’ll investigate the effect the length
of the pipe has on head loss. I’m starting
with a short piece of pipe in the manifold,
and I’m testing everything at three flow rates:
0.3, 0.6, and 0.9 gallons per minute (or gpm).
At 0.3 gpm, we see pressure drop across the pipe
is practically negligible, just under half an
inch. At 0.6 gpm, the head loss is about an inch.
And, at 0.9 gpm, the head loss is just over 3
inches. Now I’m changing out the sample for a much
longer pipe of the same diameter. In this case,
it’s 20 times longer than the previous example.
Length has an exponent of 1 in the Hazen-Williams
equation, so we know if we double the length,
we should get double the head loss. And if we
multiply the length times 20, we should see the
pressure drop increase by a factor of 20 as well.
And sure enough, at a flow rate of 0.3 gpm, we
see a pressure drop across the pipe of 7.5 inches,
just about 20 times what it was with the short
pipe. That’s the max we can do here - opening
the valve any further just overwhelms the
differential pressure gauge. There is so much
friction and turbulence in this long pipe that I
would need a different gauge just to measure it.
Length is just one factor that influences the
hydraulics of a pipe. This demo can also show
how the pipe diameter affects the pressure
loss. If I switch in this pipe with the same
length as the original sample but which has
a smaller diameter, we can see the additional
pressure drop that occurs. The smaller pipe
has ⅔ the diameter of the original sample,
and diameter has an exponent of 4.9 in our
equation. That’s because, as I mentioned before,
changing the diameter changes the fluid velocity,
and friction is all about velocity. We expect the
pressure drop to be 1 over (⅔)^4.9 or about 7
times higher than the original pipe. At 0.3 gpm,
the pressure drop is 3 inches. That’s
about 6 times the original. At 0.6 gpm,
the pressure drop is 7.5 inches, about
7 times the original. And at 0.9 gpm,
we’re off the scale. All of that is to say, we’re
getting close to the correct answers, but there’s
something else going on here. To explore this
even further, let’s take it to the extreme.
We’ll swap out a pipe with a diameter 5 times
larger than the original sample. In this case,
we’d expect the head loss to be 1 over 5^4.3,
basically a tiny fraction of that measured with
the original sample. Let’s see if this is the
case. At 0.3 gpm, the pressure drop is basically
negligible just like last time. At 0.6 and 0.9
gpm, the pressure drop is essentially the same as
the original. Obviously, there’s more to the head
loss than just the properties of the pipe itself,
and maybe you caught this already. There is
something conspicuous about the Hazen-Williams
equation. It estimates the friction in a pipe,
but it doesn’t include the friction and turbulence
that occurs at sudden changes in direction or
expansion and contraction of the flow. These
are called minor losses, because for long pipes
they usually are minor. But in some situations
like the plumbing in buildings or my little
demonstration here, they can add up quickly.
Every time a fluid makes a sudden turn (like
around an elbow) or expands or contracts (like
through these quick-release fittings), it
experiences extra turbulence, which creates
an additional loss of pressure. Think of it like
you are walking through a hallway with a turn. You
anticipate the turn, so you adjust your path
accordingly. Water doesn’t, so it has to crash
into the side - and then change directions.
And, there is actually a formula for these minor
losses. It says that they are a function of the
fluid’s velocity squared and this k factor that
has been measured in laboratory testing for any
number of bends, expansions, and contractions.
As just another example of this, here’s a sample
pipe with four 90-degree bends. If you were just
calculating pressure loss from pipe flow, you
would expect it to be insignificant. Short,
smooth pipe of an appropriate diameter. The
reality is that, at each of the flow rates tested
in the original straight pipe sample, this one has
about double the head loss, maxing out at nearly
6 inches of pressure drop at 0.9 gpm. Engineers
have to include “minor” losses to the calculated
frictional losses within the pipe to estimate the
total head loss. In my demo here, except for the
case of the 20’ pipe, most of the pressure drop
between the two measurement points is caused by
minor losses through the different fittings in the
manifold. It’s why, in this example, the pressure
drop is essentially the same as the original. Even
though the pipe is much larger in diameter, the
expansion and contraction required to transition
to this large pipe make up for the difference.
One clarification to this demo I want to make:
I’ve been adjusting this valve each time to keep
the flow rate consistent between each example
so that we make fair comparisons. But that’s not
how we take showers or use our taps. Maybe
you do it differently, but I just turn the
valve as far as it will go. The resulting flow
rate is a function of the pressure in the tap
and the configuration of piping along
the way. More pressure or less friction
and turbulence in the pipes and fittings
will give you more flow (and vice versa).
So let’s tie all this new knowledge
together with an example pipeline.
Rather than just knowing the total
pressure drop from one end to another,
engineers like to draw the pressure continuously
along a pipe. This is called the hydraulic grade
line, and, conveniently, it represents the
height the water would reach if you were to tap
a vertical tube into the main pipe. With a
hydraulic grade line, it’s really easy to see
how pressure is lost through pipe friction.
Changing the flow rate or diameter of the pipe
changes the slope of the hydraulic grade line.
It’s also easy to see how fittings create minor
losses in the pipe. This type of diagram
is advantageous in many ways. For example,
you can overlay the pressure rating of the pipe
and see if you’re going above it. You can also
see where you might need booster pump stations
on long pipelines. Finally, you can visualize how
changes to a design like pipe size, flow rate,
or length affect the hydraulics along the way.
Friction in pipes? Not necessarily the
most fascinating hydraulic phenomenon. But,
most of engineering is making compromises, usually
between cost and performance. That’s why it’s so
useful to understand how changing a design can
tip the scales. Formulas like the Hazen-Williams
and the minor loss equations are just as useful
to engineers designing pipelines that carry
huge volumes of fluid all the way down to
homeowners fixing the plumbing in their houses.
It’s intuitive that reducing the length of a pipe
or increasing its diameter or reducing the number
of bends and fittings ensures that more of the
fluid’s pressure makes it to the end of the line.
But engineers can’t rely just on intuition.
These equations help us understand how much
of an improvement can be expected without having
to go out to the garage and test it out like I
did. Pipe systems are important to us,
so it’s critical that we can design them
to carry the right amount of flow without too
much drop in pressure from one end to the other.
It’s time for everyone’s favorite segment of
me trying to cook while my wife
tries to capture that on video.
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