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All pipes carrying fluids experience losses 
of pressure caused by friction and turbulence

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of the flow. It affects seemingly simple 
things like the plumbing in your house

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all the way up to the design of massive, way 
more complex, long-distance pipelines. I’ve

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talked about many of the challenges engineers 
face in designing piped systems, including

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water hammer, air entrainment, and thrust forces. 
But, I’ve never talked about the factors affecting

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how much fluid actually flows through a pipe 
and the pressures at which that occurs. So,

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today we’re going to have a little fun, test 
out some different configurations of piping,

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and see how well the engineering equations 
can predict the pressure and flow.

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Even if you’re not going to use the equations, 
hopefully, you’ll gain some intuition from seeing

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how they work in a real situation. I’m Grady and 
this is Practical Engineering. In today’s episode,

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we’re talking about closed conduit 
hydraulics and pressure drop in pipes.

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This video is sponsored by HelloFresh, 
America’s number 1 meal kit. More on that later.

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I love engineering analogies, and in this case, 
there are a lot of similarities between electrical

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circuits and fluids in pipes. Just like all 
conventional conductors have some resistance

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to the flow of current, all pipes impart some 
resistance to the flow of the fluid inside,

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usually in the form of friction and turbulence. 
In fact, this is a lovely analogy because

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the resistance of a conductor is both a function 
of the cross-sectional area and length of the

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conductor—the bigger and shorter the wire, the 
lower the resistance. The same is true for pipes,

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but the reasons are a little different. The fluid 
velocity in a pipe is a function of the flow rate

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and the pipe’s area. Given a flowrate, a 
larger pipe will have a lower velocity,

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and a small pipe will have a higher velocity. 
This concept is critical to understanding the

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hydraulics of pipeline design because friction and 
turbulence are mostly a result of flow velocity.

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I built this demonstration that should help 
us see this in practice. This is a manifold

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to test out different configurations of pipes and 
see their effect on the flow and pressure of the

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fluid inside. It’s connected to my regular 
tap on the left. The water passes through

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a flow meter and valve, past some pressure 
gauges, through the sample pipe in question,

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and finally through a showerhead. I 
picked a showerhead since, for many of us,

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it’s the most tangible and immediate connection 
we have to pressure problems in plumbing. It’s

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probably one of the most important factors in the 
difference between a good shower, and a bad one.

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Don’t worry, all this water will be given 
to my plants which need it right now anyway.

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I used these clear pipes because they 
look cool, but there won’t be much to see

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inside. All the information we need will show 
up on the gauges (as long as I bleed all the

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air from the lines each time). The first one 
measures the flow rate in gallons per minute,

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the second one measures the pressure 
in the pipe in pounds per square inch,

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and the third gauge measures the difference 
in pressure before and after the sample

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(also called the head loss) in inches of water. In 
other words, this gauge measures how much pressure

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is lost through friction and turbulence in the 
sample - this is the one to keep your eye on. In

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simple terms, it’s saying how far do you have to 
open the valve to achieve a certain rate of flow.

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I know the metric folks are giggling at these 
units. For this video, I’m going to break my

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rule about providing both systems of measurement 
because these values are just examples anyway.

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They are just nice round numbers that are easy 
to compare with no real application outside the

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demo. Substitute your own preferred units if you 
want, because it won’t affect the conclusions.

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There are a few methods engineers use to estimate 
the energy losses in pipes carrying water,

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but one of the simplest is the Hazen-Williams 
equation. It can be rearranged in a few ways,

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but this way is nice because it has the variables 
we can measure. It says that the head loss (in

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other words the drop in pressure from one end of a 
pipe to the other) is a function of the flow rate,

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and the diameter, length, and roughness of 
the pipe. Now - that’s a lot of variables,

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so let’s try an example to show how this works. 
First, we’ll investigate the effect the length

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of the pipe has on head loss. I’m starting 
with a short piece of pipe in the manifold,

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and I’m testing everything at three flow rates: 
0.3, 0.6, and 0.9 gallons per minute (or gpm).

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At 0.3 gpm, we see pressure drop across the pipe 
is practically negligible, just under half an

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inch. At 0.6 gpm, the head loss is about an inch. 
And, at 0.9 gpm, the head loss is just over 3

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inches. Now I’m changing out the sample for a much 
longer pipe of the same diameter. In this case,

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it’s 20 times longer than the previous example. 
Length has an exponent of 1 in the Hazen-Williams

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equation, so we know if we double the length, 
we should get double the head loss. And if we

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multiply the length times 20, we should see the 
pressure drop increase by a factor of 20 as well.

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And sure enough, at a flow rate of 0.3 gpm, we 
see a pressure drop across the pipe of 7.5 inches,

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just about 20 times what it was with the short 
pipe. That’s the max we can do here - opening

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the valve any further just overwhelms the 
differential pressure gauge. There is so much

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friction and turbulence in this long pipe that I 
would need a different gauge just to measure it.

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Length is just one factor that influences the 
hydraulics of a pipe. This demo can also show

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how the pipe diameter affects the pressure 
loss. If I switch in this pipe with the same

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length as the original sample but which has 
a smaller diameter, we can see the additional

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pressure drop that occurs. The smaller pipe 
has ⅔ the diameter of the original sample,

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and diameter has an exponent of 4.9 in our 
equation. That’s because, as I mentioned before,

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changing the diameter changes the fluid velocity, 
and friction is all about velocity. We expect the

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pressure drop to be 1 over (⅔)^4.9 or about 7 
times higher than the original pipe. At 0.3 gpm,

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the pressure drop is 3 inches. That’s 
about 6 times the original. At 0.6 gpm,

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the pressure drop is 7.5 inches, about 
7 times the original. And at 0.9 gpm,

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we’re off the scale. All of that is to say, we’re 
getting close to the correct answers, but there’s

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something else going on here. To explore this 
even further, let’s take it to the extreme.

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We’ll swap out a pipe with a diameter 5 times 
larger than the original sample. In this case,

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we’d expect the head loss to be 1 over 5^4.3, 
basically a tiny fraction of that measured with

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the original sample. Let’s see if this is the 
case. At 0.3 gpm, the pressure drop is basically

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negligible just like last time. At 0.6 and 0.9 
gpm, the pressure drop is essentially the same as

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the original. Obviously, there’s more to the head 
loss than just the properties of the pipe itself,

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and maybe you caught this already. There is 
something conspicuous about the Hazen-Williams

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equation. It estimates the friction in a pipe, 
but it doesn’t include the friction and turbulence

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that occurs at sudden changes in direction or 
expansion and contraction of the flow. These

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are called minor losses, because for long pipes 
they usually are minor. But in some situations

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like the plumbing in buildings or my little 
demonstration here, they can add up quickly.

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Every time a fluid makes a sudden turn (like 
around an elbow) or expands or contracts (like

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through these quick-release fittings), it 
experiences extra turbulence, which creates

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an additional loss of pressure. Think of it like 
you are walking through a hallway with a turn. You

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anticipate the turn, so you adjust your path 
accordingly. Water doesn’t, so it has to crash

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into the side - and then change directions. 
And, there is actually a formula for these minor

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losses. It says that they are a function of the 
fluid’s velocity squared and this k factor that

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has been measured in laboratory testing for any 
number of bends, expansions, and contractions.

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As just another example of this, here’s a sample 
pipe with four 90-degree bends. If you were just

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calculating pressure loss from pipe flow, you 
would expect it to be insignificant. Short,

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smooth pipe of an appropriate diameter. The 
reality is that, at each of the flow rates tested

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in the original straight pipe sample, this one has 
about double the head loss, maxing out at nearly

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6 inches of pressure drop at 0.9 gpm. Engineers 
have to include “minor” losses to the calculated

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frictional losses within the pipe to estimate the 
total head loss. In my demo here, except for the

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case of the 20’ pipe, most of the pressure drop 
between the two measurement points is caused by

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minor losses through the different fittings in the 
manifold. It’s why, in this example, the pressure

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drop is essentially the same as the original. Even 
though the pipe is much larger in diameter, the

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expansion and contraction required to transition 
to this large pipe make up for the difference.

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One clarification to this demo I want to make: 
I’ve been adjusting this valve each time to keep

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the flow rate consistent between each example 
so that we make fair comparisons. But that’s not

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how we take showers or use our taps. Maybe 
you do it differently, but I just turn the

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valve as far as it will go. The resulting flow 
rate is a function of the pressure in the tap

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and the configuration of piping along 
the way. More pressure or less friction

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and turbulence in the pipes and fittings 
will give you more flow (and vice versa).

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So let’s tie all this new knowledge 
together with an example pipeline.

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Rather than just knowing the total 
pressure drop from one end to another,

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engineers like to draw the pressure continuously 
along a pipe. This is called the hydraulic grade

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line, and, conveniently, it represents the 
height the water would reach if you were to tap

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a vertical tube into the main pipe. With a 
hydraulic grade line, it’s really easy to see

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how pressure is lost through pipe friction. 
Changing the flow rate or diameter of the pipe

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changes the slope of the hydraulic grade line. 
It’s also easy to see how fittings create minor

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losses in the pipe. This type of diagram 
is advantageous in many ways. For example,

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you can overlay the pressure rating of the pipe 
and see if you’re going above it. You can also

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see where you might need booster pump stations 
on long pipelines. Finally, you can visualize how

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changes to a design like pipe size, flow rate, 
or length affect the hydraulics along the way.

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Friction in pipes? Not necessarily the 
most fascinating hydraulic phenomenon. But,

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most of engineering is making compromises, usually 
between cost and performance. That’s why it’s so

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useful to understand how changing a design can 
tip the scales. Formulas like the Hazen-Williams

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and the minor loss equations are just as useful 
to engineers designing pipelines that carry

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huge volumes of fluid all the way down to 
homeowners fixing the plumbing in their houses.

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It’s intuitive that reducing the length of a pipe 
or increasing its diameter or reducing the number

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of bends and fittings ensures that more of the 
fluid’s pressure makes it to the end of the line.

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But engineers can’t rely just on intuition. 
These equations help us understand how much

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of an improvement can be expected without having 
to go out to the garage and test it out like I

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did. Pipe systems are important to us, 
so it’s critical that we can design them

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to carry the right amount of flow without too 
much drop in pressure from one end to the other.

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It’s time for everyone’s favorite segment of

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me trying to cook while my wife 
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Goofing around in the kitchen is one 
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