Flow and Pressure in Pipes Explained

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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