The Physics Behind the Thumb Trick

Have you ever filled a bucket with water from the  garden hose? It’s kind of a slow process. Or at   least it feels slow while you’re standing there  waiting. If you played with a garden hose at all,   you know the trick of putting your thumb over  the end to get a stronger jet. Obviously,   the water is flowing faster with  your thumb on than off. So if you   do that - put your thumb over the end  of the hose - to fill your bucket,   do you think it’s going to fill faster,  slower, or take the same amount of time? Seems like kind of an elementary question,  but I found this in the online notes for a   college physics class. The only issue with the  professor’s answer to the question is that it   was wrong. Pipes seem simple, but there are a lot  of misconceptions about pipes and how they work.    The field we sometimes call Closed Conduit  Hydraulics is a place where intuitions don’t   always serve you well. And “closed conduits”  matter. Lots of essential parts of our lives   depend on fluids moving through pipes. So I put  together a few demonstrations in my garage to   try and correct some misconceptions. Let’s take a  look at what really happens inside a garden hose,   or really any pipe system to gain some intuition.   I’m Grady and this is Practical Engineering. The question I posed about filling up a bucket  was from a lesson on continuity. The basic idea   is that water isn’t very compressible. So in any  closed system, there has to be the same amount   coming in as there is going out. In mathematical  terms, that looks like this. Velocity multiplied   by a pipe’s cross-sectional area is the volumetric  flow rate. So v-in, a-in is equal to v-out, a-out. The professor’s answer was that the time  to fill up the bucket will be the same,   regardless of whether your thumb is over  the end or not. The velocity out is higher,   but the area is smaller. The volumetric  flow rate should be the same in both   cases. It sounds reasonable. Let’s  test it out and see if that’s true. I’m going to speed this up so you don’t  have to suffer through the full duration.    I used a big bucket to show the difference  better. It’s not night and day or anything,   but this makes it pretty clear that  putting your thumb over the end of the   hose actually slows down the flow rate.   This is probably not earth-shattering   news for you, but the reason for the  difference is a little complicated. Just to be clear, this demonstration doesn’t  violate the principle of continuity. In   engineering and physics, when we use conservation  rules to solve problems or answer questions, we   have to be explicit about the boundaries. Usually,  that means applying a control volume, a defined   region of space where we can easily describe  inputs and outputs of flow, energy, momentum, and   so on. In my demonstration, I can define a control  volume here, and it’s easy to show that the flow   rate through the hose is the same as that coming  out of the end. Same thing with my thumb over it:   the velocity in the hose is lower than the  velocity leaving, but the area of the hose   is larger than the nozzle I’ve formed with my  thumb, so it equals out. But you can’t apply the   principle of continuity across different control  volumes. In other words, these are completely   different situations. And if I change this  demo up a little bit, it will be more obvious. Now I have a mechanical thumb to constrict  the end of the hose. In other words… a valve.   Functionally, this does the exact  same thing. When I turn the valve,   it creates a varying obstruction across  the pipe from wide open to fully closed.    Let’s measure the flow rate for a full range of  valve positions and see what happens. This is a   chart of the data, and you can see there’s a  pretty clear relationship. More restriction;   less flow. This is the answer that the  professor missed by assuming the flow rate   IN was the same in both cases. Again, probably  not earth-shattering news to anyone that when   you close a valve the flow rate goes down.   But you might not have ever considered, “Why? ” To answer that question, we have to look at a  different conservation equation: energy. Basic  physics separates energy into two forms: potential  energy that is stored in some way, and kinetic   energy: the energy of motion. Fluid in a pipe has  both. Potential energy takes the form of pressure   or elevation, kinetic energy in the form of  velocity. The trick is that you can convert   between types of energy, and of course, the  total amount of energy in a closed system doesn’t   change. And knowing this allows you to answer all  kinds of questions. Let me show you an example. This is a basic hydraulic system. A tank on  the left and a pipe that constricts down,   then expands back out. You know I love  graphs, and there is a graph that makes

solving closed conduit hydraulics problems a lot  simpler. It’s called the hydraulic grade line,   and it basically describes the potential  energy in a fluid along its path. In the tank,   there’s hardly any velocity, so all the energy  in the fluid is potential energy. The hydraulic   grade line is equal to the free surface. But  once water enters the pipe, it picks up speed,   so the hydraulic grade line drops down. The  difference is the potential energy converted   to kinetic. At any snapshot in time, we know that  the volumetric flow through a pipe is constant.    You really can’t have more water coming in  than going out, just like we discussed with   continuity. So the hydraulic grade line is  constant as long as the velocity is constant. The fluid has to accelerate as it goes into  the narrower pipe. That converts more of the   potential energy to kinetic energy, so  the hydraulic grade line drops again.    Same thing on the other side. The flow slows  down as it expands into the larger pipe,   so you get a conversion of kinetic energy  back into pressure. If this seems complicated,   just remember that the hydraulic grade line  is basically the answer to the question:   “If I tapped a vertical riser into this part of my  pipe system, how high would the fluid go up it? ” I think this is intuitive for most  people. It’s Bernoulli’s principle   in action. But it’s missing something that makes  it impossible to apply to our garden hose demo.    Let’s hook up some pressure  gauges, and you’ll see what I mean. I put a pressure gauge at the beginning of the  hose and one at the end. When I turn on the water,   we see a pressure just under 70 psi or about 450  kilopascals at the upstream end. At the downstream   end where the water’s coming out, it’s basically  zero. That doesn’t jive with what we’ve learned so   far about the conservation of energy. Let’s sketch  out the hydraulic grade line to figure it out. Here’s our hose. It’s close enough to level  that we can neglect differences in elevation,   so all the potential energy is in pressure.   On the upstream end, it was 70 psi, and on   the downstream end, essentially zero. That makes  sense because the end of the pipe is exposed to   the atmosphere. You can’t really have any pressure  if you don’t have a pipe. That means our hydraulic   grade line looks like this. We know in a pipe with  a constant cross-section that the flow velocity   isn’t changing, and yet, we’re still losing  potential energy along the way. Where’s it going? Well, we need to talk about losses. Of course  we know energy can’t be created or destroyed,   only converted from one form to another. We talked  about pressure, elevation, and velocity already.    But there’s also heat through friction in the  system. No pipe is perfect. You’re always going   to lose some energy along the way. Unlike  pressure or velocity, frictional losses are   unrecoverable. Once they’re lost, they’re lost.   The garden hose example shows it perfectly. Let’s assume the inlet pressure is always  constant. It’s not really, since there are   more pipes upstream of this point in my house’s  plumbing. But assuming a constant inlet pressure,   this hydraulic grade line is always going to look  the same. You can make the pipe smoother, rougher,   longer, or shorter, wider, or narrower. As long  as the shape doesn’t change along its length,   you’re always going to have the inlet pressure  on the left, zero pressure on the right, and a   straight line connecting the two. In other words,  you’re always going to lose 100% of the potential   energy in the water to friction from one side  to the other. How’s that possible? It’s because   the flow in the pipe will speed up or slow down  until it’s true. Frictional losses are roughly   a function of the fluid’s velocity squared, so  higher speed means more losses. Again, assuming   you can maintain a constant pressure on one side  of the system, in effect, what controls how much   flow you can get out of the other end of the  pipe is how much friction happens along the way. And, by the way, that’s kind of a tough  question to answer. The friction is a   function of pipe roughness and turbulence.   Turbulence is a function of the flow rate,   so you have to know the flow rate to calculate  the friction to calculate the flow rate. So these   computations usually require some iteration or  at least some simplifying assumptions. I said   that generally friction scales as a function of  flow squared. I can show that in my demo with the   pressure gauges. If this valve is closed, we get  the full static pressure. There’s no movement,   so there’s no frictional losses anywhere in the  hose. I have the same amount of energy at the   end of the hose as I do at the beginning. When I  open the valve, the difference in pressure grows   because the flow speeds up. And if we plot the  difference in pressure as a function of flow rate,   it looks something like this. Friction  goes up a lot faster than velocity. But friction in a pipe isn’t the only source of  energy losses. Any transition in geometry is going

to have losses, too. And now, we’re back to the  thumb. We sometimes call pipe friction the “major”   losses in a system and those at transitions  “minor losses. ” Researchers have measured   all kinds of situations, making it possible  to estimate how a pipe system will behave,   no matter how complicated it is. And  the results are pretty interesting. For example, at a sharp-edged inlet into  a pipe, the minor loss coefficient can be   around 0. 5. A higher number means more energy  lost. If you round the inlet, you can get that   coefficient down to 0. 03. Huge difference. Same  thing with expansions or contractions. If you   have a sudden change, especially when  the difference between sizes is larger,   you get high loss coefficients. If you make the  transition gradual, the coefficient goes down,   since there’s less turbulence and gentler  acceleration as the fluid changes speed.    And every type of transition has an associated  loss coefficient that can vary a lot depending   on how smooth and consistent that transition is.   In fact, valves take advantage of minor losses   to give you some control over flow, and we already  said that a valve is basically a mechanical thumb. I have one more demonstration to show you. I’m  going to fill this tank two more times. In one   case, I put a cap over the hose with a hole  drilled into it. In the other, I 3D printed   this nozzle that has a smooth taper from the  hose diameter down to the exact same diameter   I drilled in the end cap. With an understanding of  minor losses, it should be an easy guess which one   can flow more water. And here’s the proof. Both  hoses are discharging through the same-sized hole,   but the one with a smoother transition lets a lot more water through. And if you compare the 3D printed   nozzle with the fully open hose, it’s not  quite the same flow rate, but it’s close,   and it’s a lot closer than the sharp  contraction created by the cap with the hole. The point I’m trying to show with this is that a  nozzle or any other type of obstruction you put   in a pipe system doesn’t increase or decrease the  flow from one side or the other. It just creates a   loss in energy that slows down the whole system.   Transitions and pipe roughness create friction,   and the flow rate naturally adjusts  itself until the available energy between   two points is equal to that friction.   And this is not necessarily intuitive. For example, we often compare water in pipes to  electricity in wires: pressure is like voltage,   flow rate is like current, and a narrow or rough  pipe is like a resistor. That analogy works   pretty well for building intuition, but it breaks  down once you care about the details. In a wire,   resistance is usually close to constant  for a given material and temperature,   so current tends to scale more neatly with  voltage. In a pipe, the “resistance” isn’t a   fixed number. Friction losses grow faster  than the flow and can change as the flow   becomes more turbulent. But of course, you can  build that intuition. Think about firefighters. The operator’s job is to run the pump. They choose  a throttle setting based on the pressure needed   at the nozzle. How do they make that choice?   Well, that depends on the diameter of the hose,   the length of the hose, the elevation of the  nozzle if you’re pumping up a hill or a ladder,   and the characteristics of the nozzle itself.   It’s important to get this right. Too little   pressure at the nozzle, and you don’t get enough  flow to quench the flames. Too much pressure and   you can damage equipment or throw the nozzle  operator around with excessive reaction forces.    Firefighters learn the basics of hydraulics  in training, but there are no desks with   graph paper set up at a fireground to work  through a bunch of engineering equations.    Operators need good hydraulic instincts  about how different configurations of hoses,   apparatuses, and nozzles will  affect the required pump settings. Even the plumbing in your house follows these  same simple hydraulic principles. If you have   narrow pipes, or lots of bends, turns, and  transitions, you’ll definitely notice if   someone flushes the toilet while you’re taking a  shower. The shared lines see higher total flow,   meaning more friction, meaning less pressure. I  mentioned earlier that we couldn’t really assume   a constant inlet pressure at my hose bib. That’s  because there are a lot of pipes and transitions   from that point upstream. And it’s true from my  house through my service line through the water   mains all the way to the water towers and  high service pumps at the treatment plant.    The pressure and flow rate I can get out are  almost entirely a function of how much friction   the water encounters along the way, which is a  function of both the flow rate and the geometry   of the pipes. You may even notice that your water  pressure drops in the mornings or evenings when   everyone in your neighborhood is using more. It’s  the same issue: more flow through the water mains

creates more friction, converting kinetic energy  into heat so you get less at the end of the line. The garden hose is a backyard version of the same  problem engineers and operators deal with every   day: how much flow can you get through a real  system, and what does it cost you in pressure?    In a perfect world, you’d convert pressure  to speed and back again with no penalty,   but real pipes always take a cut. Sometimes  that cut is spread out over a long run of   pipe. Sometimes it’s concentrated in  a single valve, elbow, or your thumb.    Either way, the flow rate adjusts until  the available pressure is fully “spent”   on those losses. Once you see it as an energy  budget, the weird stuff starts making sense. I’ve been making  videos like this one for more than 10 years now,  which is crazy to say. And over all that time,   the central thesis of Practical Engineering has  always been what’s in the name: not just the   theory, but how engineering is actually applied to  our everyday lives. To accomplish that goal, I use   these physical, real-world demonstrations, built  in my garage, not only to illustrate the concepts,   but to prove that the theory actually works. Some  of these models are actually pretty complicated,   and for the past year or so, I’ve been getting  some help from today’s sponsor, Send-Cut-Send. I could buy raw materials like steel  and acrylic and cut stuff out myself,   and I’ve done so much of that, but just  look at this. An entire idea from my head   shipped to my door. The quality’s better, the  cuts are way more precise than I would make,   and I don’t have a day's worth of  measuring, cutting, and cleaning up to do. They have a huge catalog of materials  they can cut, bend, countersink, and tap,   so the limit is practically what you can  dream up and put into CAD. Parts are made   in the USA and usually out the door in a few  days, which makes rapid prototyping a dream.    They just started offering CNC machining,  so I’m going to have to try that out soon.    I can’t recommend Send Cut Send enough. If you  have projects that use sheet goods, the link   below is going to give you a discount on your  first order. I really appreciate their support,   and I hope you give them a try. Thank you  for watching, and let me know what you think.