The Physics Behind the Thumb Trick

0:01 Have you ever filled a bucket with water from the garden hose?

0:04 It’s kind of a slow process.

0:06 Or at least it feels slow while you’re standing there waiting.

0:09 If you played with a garden hose at all,

0:11 you know the trick of putting your thumb over the end to get a stronger jet.

0:15 Obviously, the water is flowing faster with your thumb on than off.

0:19 So if you do that- put your thumb over the end of the hose- to fill your bucket,

0:23 do you think it’s going to fill faster, slower, or take the same amount of time?

0:28 Seems like kind of an elementary question,

0:30 but I found this in the online notes for a college physics class.

0:34 The only issue with the professor’s answer to the question is that it was wrong.

0:39 Pipes seem simple, but there are a lot

0:42 of misconceptions about pipes and how they work.

0:45 The field we sometimes call Closed Conduit Hydraulics is

0:49 a place where intuitions don’t always serve you well.

0:52 And “closed conduits” matter.

0:54 Lots of essential parts of our lives depend on fluids moving through pipes.

0:59 So I put together a few demonstrations

1:01 in my garage to try and correct some misconceptions.

1:04 Let’s take a look at what really happens inside a garden hose,

1:09 or really any pipe system to gain some intuition.

1:12 I’m Grady and this is Practical Engineering.

1:25 The question I posed about filling up a bucket was from a lesson on continuity.

1:30 The basic idea is that water isn’t very compressible.

1:33 So in any closed system,

1:34 there has to be the same amount coming in as there is going out.

1:39 In mathematical terms, that looks like this.

1:42 Velocity multiplied by a pipe’s cross-sectional

1:44 area is the volumetric flow rate.

1:47 So v-in, a-in is equal to v-out, a-out.

1:50 The professor’s answer was that the time to fill up the bucket will be the same,

1:54 regardless of whether your thumb is over the end or not.

1:58 The velocity out is higher, but the area is smaller.

2:01 The volumetric flow rate should be the same in both cases.

2:05 It sounds reasonable.

2:06 Let’s test it out and see if that’s true.

2:09 I’m going to speed this up so you

2:11 don’t have to suffer through the full duration.

2:13 I used a big bucket to show the difference better.

2:16 It’s not night and day or anything,

2:18 but this makes it pretty clear that putting your thumb over

2:20 the end of the hose actually slows down the flow rate.

2:25 This is probably not earth-shattering news for you,

2:28 but the reason for the difference is a little complicated.

2:32 Just to be clear, this demonstration

2:34 doesn’t violate the principle of continuity.

2:36 In engineering and physics,

2:38 when we use conservation rules to solve problems or answer questions,

2:42 we have to be explicit about the boundaries.

2:46 Usually, that means applying a control volume,

2:48 a defined region of space where we

2:51 can easily describe inputs and outputs of flow, energy, momentum, and so on.

2:56 In my demonstration, I can define a control volume here,

2:59 and it’s easy to show that the flow rate through

3:01 the hose is the same as that coming out of the end.

3:04 Same thing with my thumb over it:

3:06 the velocity in the hose is lower than the velocity leaving,

3:09 but the area of the hose is larger than

3:12 the nozzle I’ve formed with my thumb, so it equals out.

3:16 But you can’t apply the principle

3:18 of continuity across different control volumes.

3:21 In other words, these are completely different situations.

3:24 And if I change this demo up a little bit, it will be more obvious.

3:28 Now I have a mechanical thumb to constrict the end of the hose.

3:33 In other words… a valve.

3:35 Functionally, this does the exact same thing.

3:38 When I turn the valve,

3:39 it creates a varying obstruction across the pipe from wide open to fully closed.

3:45 Let’s measure the flow rate for a full

3:48 range of valve positions and see what happens.

3:50 This is a chart of the data,

3:53 and you can see there’s a pretty clear relationship.

3:56 More restriction; less flow.

3:57 This is the answer that the professor missed by assuming

4:00 the flow rate IN was the same in both cases.

4:04 Again, probably not earth-shattering news to anyone that when

4:07 you close a valve the flow rate goes down.

4:10 But you might not have ever considered, “Why?” To answer that question,

4:15 we have to look at a different conservation equation: energy.

4:20 Basic physics separates energy into two forms:

4:23 potential energy that is stored in some way,

4:27 and kinetic energy: the energy of motion.

4:29 Fluid in a pipe has both.

4:32 Potential energy takes the form of pressure or elevation,

4:36 kinetic energy in the form of velocity.

4:38 The trick is that you can convert between types of energy,

4:42 and of course, the total amount of energy in a closed system doesn’t change.

4:47 And knowing this allows you to answer all kinds of questions.

4:51 Let me show you an example.

4:53 This is a basic hydraulic system.

4:55 A tank on the left and a pipe that constricts down, then expands back out.

4:59 You know I love graphs, and there is a graph that makes

5:03 solving closed conduit hydraulics problems a lot simpler.

5:06 It’s called the hydraulic grade line,

5:09 and it basically describes the potential energy in a fluid along its path.

5:13 In the tank, there’s hardly any velocity,

5:15 so all the energy in the fluid is potential energy.

5:18 The hydraulic grade line is equal to the free surface.

5:22 But once water enters the pipe, it picks up speed,

5:25 so the hydraulic grade line drops down.

5:27 The difference is the potential energy converted to kinetic.

5:31 At any snapshot in time,

5:32 we know that the volumetric flow through a pipe is constant.

5:36 You really can’t have more water coming in than going out,

5:40 just like we discussed with continuity.

5:41 So the hydraulic grade line is constant as long as the velocity is constant.

5:47 The fluid has to accelerate as it goes into the narrower pipe.

5:50 That converts more of the potential energy to kinetic energy,

5:53 so the hydraulic grade line drops again.

5:56 Same thing on the other side.

5:57 The flow slows down as it expands into the larger pipe,

6:00 so you get a conversion of kinetic energy back into pressure.

6:04 If this seems complicated, just remember that the hydraulic grade line

6:07 is basically the answer to the question:

6:09 “If I tapped a vertical riser into this part of my pipe system,

6:13 how high would the fluid go up it?” I think this is intuitive for most people.

6:18 It’s Bernoulli’s principle in action.

6:19 But it’s missing something that makes it

6:22 impossible to apply to our garden hose demo.

6:25 Let’s hook up some pressure gauges, and you’ll see what I mean.

6:28 I put a pressure gauge at the beginning of the hose and one at the end.

6:32 When I turn on the water, we see a pressure just under 70 psi

6:36 or about 450 kilopascals at the upstream end.

6:39 At the downstream end where the water’s coming out, it’s basically zero.

6:44 That doesn’t jive with what we’ve learned

6:46 so far about the conservation of energy.

6:49 Let’s sketch out the hydraulic grade line to figure it out.

6:52 Here’s our hose.

6:53 It’s close enough to level that we can neglect differences in elevation,

6:57 so all the potential energy is in pressure.

7:00 On the upstream end, it was 70 psi, and on the downstream end, essentially zero.

7:04 That makes sense because the end of the pipe is exposed to the atmosphere.

7:09 You can’t really have any pressure if you don’t have a pipe.

7:12 That means our hydraulic grade line looks like this.

7:15 We know in a pipe with a constant

7:18 cross-section that the flow velocity isn’t changing,

7:20 and yet, we’re still losing potential energy along the way.

7:25 Where’s it going?

7:26 Well, we need to talk about losses.

7:29 Of course we know energy can’t be created or destroyed,

7:32 only converted from one form to another.

7:35 We talked about pressure, elevation, and velocity already.

7:38 But there’s also heat through friction in the system.

7:42 No pipe is perfect.

7:44 You’re always going to lose some energy along the way.

7:48 Unlike pressure or velocity, frictional losses are unrecoverable.

7:51 Once they’re lost, they’re lost.

7:53 The garden hose example shows it perfectly.

7:56 Let’s assume the inlet pressure is always constant.

7:59 It’s not really, since there are more pipes

8:02 upstream of this point in my house’s plumbing.

8:05 But assuming a constant inlet pressure,

8:07 this hydraulic grade line is always going to look the same.

8:11 You can make the pipe smoother, rougher, longer, or shorter, wider, or narrower.

8:15 As long as the shape doesn’t change along its length,

8:19 you’re always going to have the inlet pressure on the left,

8:22 zero pressure on the right, and a straight line connecting the two.

8:26 In other words, you’re always going to lose 100% of the potential

8:30 energy in the water to friction from one side to the other.

8:35 How’s that possible?

8:36 It’s because the flow in the pipe will speed up or slow down until it’s true.

8:41 Frictional losses are roughly a function of the fluid’s velocity squared,

8:46 so higher speed means more losses.

8:48 Again, assuming you can maintain a constant pressure

8:51 on one side of the system, in effect,

8:53 what controls how much flow you can get out of the other

8:57 end of the pipe is how much friction happens along the way.

9:00 And, by the way, that’s kind of a tough question to answer.

9:04 The friction is a function of pipe roughness and turbulence.

9:07 Turbulence is a function of the flow rate, so you have to know the flow rate

9:12 to calculate the friction to calculate the flow rate.

9:15 So these computations usually require some

9:17 iteration or at least some simplifying assumptions.

9:21 I said that generally friction scales as a function of flow squared.

9:25 I can show that in my demo with the pressure gauges.

9:28 If this valve is closed, we get the full static pressure.

9:32 There’s no movement, so there’s no frictional losses anywhere in the hose.

9:36 I have the same amount of energy at the end

9:39 of the hose as I do at the beginning.

9:41 When I open the valve,

9:42 the difference in pressure grows because the flow speeds up.

9:45 And if we plot the difference in pressure as a function of flow rate,

9:50 it looks something like this.

9:52 Friction goes up a lot faster than velocity.

9:55 But friction in a pipe isn’t the only source of energy losses.

10:00 Any transition in geometry is going to have losses, too.

10:03 And now, we’re back to the thumb.

10:06 We sometimes call pipe friction the “major” losses in a system

10:10 and those at transitions “minor losses.”

10:13 Researchers have measured all kinds of situations,

10:16 making it possible to estimate how a pipe system will behave,

10:19 no matter how complicated it is.

10:22 And the results are pretty interesting.

10:24 For example, at a sharp-edged inlet into a pipe,

10:28 the minor loss coefficient can be around 0.5.

10:31 A higher number means more energy lost.

10:33 If you round the inlet, you can get that coefficient down to 0.03.

10:39 Huge difference.

10:40 Same thing with expansions or contractions.

10:43 If you have a sudden change,

10:45 especially when the difference between sizes is larger,

10:48 you get high loss coefficients.

10:50 If you make the transition gradual, the coefficient goes down,

10:54 since there’s less turbulence and gentler

10:57 acceleration as the fluid changes speed.

11:00 And every type of transition has an associated loss coefficient that can

11:04 vary a lot depending on how smooth and consistent that transition is.

11:08 In fact, valves take advantage of minor

11:11 losses to give you some control over flow,

11:14 and we already said that a valve is basically a mechanical thumb.

11:18 I have one more demonstration to show you.

11:21 I’m going to fill this tank two more times.

11:24 In one case, I put a cap over the hose with a hole drilled into it.

11:28 In the other, I 3D printed this nozzle that has a smooth taper

11:32 from the hose diameter down to the exact same diameter I drilled in the end cap.

11:37 With an understanding of minor losses,

11:39 it should be an easy guess which one can flow more water.

11:43 And here’s the proof.

11:44 Both hoses are discharging through the same-sized hole,

11:48 but the one with a smoother transition lets a lot more water through.

11:52 And if you compare the 3D printed nozzle with the fully open hose,

11:56 it’s not quite the same flow rate, but it’s close, and it’s a lot closer than

12:01 the sharp contraction created by the cap with the hole.

12:04 The point I’m trying to show with this is

12:06 that a nozzle or any other type of obstruction

12:08 you put in a pipe system doesn’t increase

12:11 or decrease the flow from one side or the other.

12:14 It just creates a loss in energy that slows down the whole system.

12:19 Transitions and pipe roughness create friction,

12:22 and the flow rate naturally adjusts itself until the available

12:26 energy between two points is equal to that friction.

12:30 And this is not necessarily intuitive.

12:33 For example, we often compare water in pipes to electricity in wires:

12:37 pressure is like voltage,

12:39 flow rate is like current, and a narrow or rough pipe is like a resistor.

12:44 That analogy works pretty well for building intuition,

12:47 but it breaks down once you care about the details.

12:50 In a wire, resistance is usually close

12:53 to constant for a given material and temperature,

12:56 so current tends to scale more neatly with voltage.

12:59 In a pipe, the “resistance” isn’t a fixed number.

13:02 Friction losses grow faster than the flow

13:05 and can change as the flow becomes more turbulent.

13:08 But of course, you can build that intuition.

13:11 Think about firefighters.

13:13 The operator’s job is to run the pump.

13:15 They choose a throttle setting based on the pressure needed at the nozzle.

13:20 How do they make that choice?

13:22 Well, that depends on the diameter of the hose, the length of the hose,

13:26 the elevation of the nozzle if you’re pumping up a hill or a ladder,

13:30 and the characteristics of the nozzle itself.

13:33 It’s important to get this right.

13:35 Too little pressure at the nozzle,

13:36 and you don’t get enough flow to quench the flames.

13:39 Too much pressure and you can damage equipment

13:42 or throw the nozzle operator around with excessive reaction forces.

13:46 Firefighters learn the basics of hydraulics in training,

13:49 but there are no desks with graph paper set up

13:52 at a fireground to work through a bunch of engineering equations.

13:56 Operators need good hydraulic instincts

13:58 about how different configurations of hoses,

14:01 apparatuses, and nozzles will affect the required pump settings.

14:06 Even the plumbing in your house follows these same simple hydraulic principles.

14:09 If you have narrow pipes, or lots of bends, turns, and transitions,

14:14 you’ll definitely notice if someone flushes

14:16 the toilet while you’re taking a shower.

14:18 The shared lines see higher total flow,

14:21 meaning more friction, meaning less pressure.

14:23 I mentioned earlier that we couldn’t really assume

14:26 a constant inlet pressure at my hose bib.

14:28 That’s because there are a lot

14:30 of pipes and transitions from that point upstream.

14:33 And it’s true from my house through my service line through the water mains

14:38 all the way to the water towers and high service pumps at the treatment plant.

14:42 The pressure and flow rate I can get out are almost entirely

14:46 a function of how much friction the water encounters along the way,

14:49 which is a function of both the flow rate and the geometry of the pipes.

14:54 You may even notice that your water pressure drops in the mornings

14:57 or evenings when everyone in your neighborhood is using more.

15:01 It’s the same issue: more flow through the water mains creates more friction,

15:05 converting kinetic energy into heat so you get less at the end of the line.

15:10 The garden hose is a backyard version of the same

15:14 problem engineers and operators deal with every day:

15:17 how much flow can you get through a real system,

15:20 and what does it cost you in pressure?

15:22 In a perfect world, you’d convert pressure

15:24 to speed and back again with no penalty, but real pipes always take a cut.

15:29 Sometimes that cut is spread out over a long run of pipe.

15:33 Sometimes it’s concentrated in a single valve, elbow, or your thumb.

15:38 Either way, the flow rate adjusts until

15:41 the available pressure is fully “spent” on those losses.

15:45 Once you see it as an energy budget, the weird stuff starts making sense.

15:51 I’ve been making videos like this one for more than 10 years now,

15:55 which is crazy to say.

15:56 And over all that time,

15:57 the central thesis of Practical Engineering has always been what’s in the name:

16:02 not just the theory,

16:03 but how engineering is actually applied to our everyday lives.

16:07 To accomplish that goal, I use these physical,

16:10 real-world demonstrations, built in my garage,

16:13 not only to illustrate the concepts,

16:15 but to prove that the theory actually works.

16:18 Some of these models are actually pretty complicated,

16:21 and for the past year or so,

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