We use pipes to carry all kinds of fluids. Pretty much anyone can tell you how they work. You put a liquid or a gas in one side and it comes out the other. But, designing pipe systems is not always as simple as it seems. Pipes don’t float in the air on their own; they have to be held in some way. We often bury pipes to protect them and keep them out of the way, but the ground isn’t always that good at holding pipes together. Hey I’m Grady and this is Practical Engineering. Today, we’re talking about thrust forces in pipe systems.

Designing systems of piping might seem intuitive. I think most people have a general understanding about how pipes work because most of us have them in our home delivering fresh water to the taps and carrying our waste away. But, the bigger a pipe gets and the more pressure it contains, the more complicated it becomes. Engineers design systems of pipes that can be enormous - sometimes big enough to drive a car through - and that can hold many times the pressure of your typical household plumbing. Those larger diameters and higher pressures create greater forces, and those forces need to be accounted for in design. There are two types of forces in pipelines that engineers need to consider: hydrostatic and hydrodynamic.

Hydrostatic forces are the ones that don’t require any fluid to be moving. They result just from the pressure within a pipe. A fluid’s pressure is its force applied over an area. Pressure works in every direction at the same time. So, within a section of pressurized pipe, you have forces acting on the walls of the pipe. This force is resisted by the hoop of pipe material. But, you also have forces acting along the axis of the pipe. This force is equal to the pressure times the area of the pipe, and it’s resisted by the fluid in the adjacent section of pipe. I can demonstrate this with clear tubing in my video. Even though the tube slides into this straight coupler fairly easily, I can pressurize it without too much issue. If you ignore the small leaks from the imprecision of my demo, you’d hardly know anything was happening at all if you weren’t paying attention to the pressure gauge. That’s because, in this example, all the hydrostatic forces are balanced. But, there’s not always an adjacent section of pipe to resist this longitudinal force. Eventually, you get to the end of the pipe where you need a cap, or you get to a place where you need to make a bend, a tee, or a wye. These are places where you end up with an imbalance in hydrostatic forces within the pipe. Let’s try pressurizing this demo for a couple of cases where the hydrostatic forces aren’t balanced to see what happens.

With a tee, you have two thrust forces that do balance each other out, and one that doesn’t. Can you guess what happens when I pressurize the tubing? The force from the top tube has nothing to resist it, so it easily separates the fitting from the tube. With an elbow, there are unbalanced forces in both directions. It doesn’t take much pressure for the fitting to pop right off. Now, this is a pretty cool demo if I do say so myself, but maybe it’s a little simplistic and perhaps even a bit self evident. Plus, it only shows the hydrostatic forces that occur within pipes. Actually, there’s a pretty cool demonstration of both hydrostatic and hydrodynamic forces: a water rocket. I’m okay explaining this concept to kindergartners, but I’ve asked for some help from the team behind the water rocket altitude world record and awesome YouTube channel, Air Command Rockets, to show how these two types of force work in an entirely different setting than pipelines.

Thanks Grady. Let’s have a look at how water rockets produce thrust. Now, it doesn’t matter if you’re a conventional rocket or water rocket, your life is governed by the thrust equation, which is derived from Newton’s second law. And here it is in its simplified form. Over here you’ve got the thrust, or the force, that the rocket produces to propel it upwards. And that’s made out of two terms. This one is the momentum thrust, and that’s just the mass flow rate, in other words the rate at which the water or air flows through the nozzle, times the velocity at which it exits. And, over here is the pressure thrust, and that relates to the exit pressure versus the ambient pressure. So, while the rocket is sitting on the pad pressurized, this term is zero because there’s no flow out of the nozzle. So, we end up with the pressure inside versus the outside times the nozzle’s cross sectional area. That’s the actual force of the rocket trying to get off the pad. So, when you release the rocket, the momentum thrust comes back into play. The compressed air is pushing the water out through the nozzle. And, the water comes out at probably about one tenth of the speed of sound for regular types of rockets, which is quite low. But, the mass flow rate is high because the water is so heavy. Now, when the water runs out and the compressed air starts coming out, the mass flow rate really drops because air is so much lighter than water. But, the exit velocity gets very high because the air comes out at the speed of sound. So as it turns out during the air phase only, you get about two thirds the amount of thrust as you get with the water phase. And this is in fact why water rockets use water for improved performance. Now all of this is an oversimplification, and in real life it’s a little bit more complicated than that, simply because you have a finite volume inside of the rocket, and as soon as you release it, the pressure stops dropping and so does the force that it generates. So you end up with a decayed thrust curve like here. Now, let’s have a look at a couple of examples of the water rocket. This one is a low pressure one. This one would be a typical one that you’d launch and it produces about 100 N peak thrust. And, this one over here is a higher pressure one (if you really crank up the pressure) and this one generates about 2,500 N peak thrust, so that’s a lot more. And, here’s what happens when you crank up the pressure too much. Okay back to you Grady before we blow something else up.

Just like in rockets, engineers call these forces in pipelines “thrusts.” But unlike those aerospace guys and gals, civil engineers don’t want the things they design to go flying through the air. We want our pipelines to stay put, which means in this case thrust is a bad thing and must be resisted. I know what you’re probably thinking after seeing all these demonstrations. “Just glue the joints.” And I promise we’re getting there, but the reality is that a lot of the pressure piping we use underground, particularly in municipal settings - such as water mains for drinking water and force mains for sewers - use push-on fittings. These joints use gaskets and tight tolerances to achieve a watertight seal, but they don’t provide longitudinal restraint. The pipes can still slide fairly freely in and out of the joint. We use these types of push-on fittings because they are inexpensive, reliable, and most-importantly, they are easy to install speeding up the construction time which benefits everyone, from the contractor to the owner to even the citizens waiting on a road to open back up after a main break. In plumbing we use glue or threaded connections for pipes, but those options are a lot less feasible for certain types of large diameter pipes. But, because push-on fittings don’t offer any longitudinal restraint, we have to provide that restraint somewhere else. In most cases, that comes from burying the pipe. Encasing the line in compacted soil holds it in place to prevent the pieces from slipping apart.

But, it’s not that simple. These pipelines can be under enormous pressure, sometimes two or three times the pressure at the tap in your house, and in some industrial settings many times higher. Also - and this is straight from geotechnical engineering 101 - soil isn’t that strong. Anyone who’s ever tried to walk through the mud knows this. So, we rarely trust soil on its own to hold our pipelines together underground. Relying on soil for restraint is essentially asking the soil to be as strong as the pipe material. If it doesn’t hold the pipe still against hydrostatic and hydrodynamic forces, you can get separation of joints and leakage from the pipes. Fixing this can be a huge endeavor, leading to loss of service and creating significant expenses. For water mains, it takes a maintenance crew closing traffic, excavating the line, repairing the damaged section, backfilling, and restoring the pavement. And, although public works crews are awesome at this job, most people would agree that it would be better to avoid the need in the first place if possible.

So, what do we do? The classic solution to this problem is thrust blocks: masses of concrete that distribute thrust forces over a larger area against the soil. If you could make the subsurface invisible so you could see all the water mains below your city, it’s a fairly sure bet that at each and every bend, tee, wye, or reduction there is an adjacent block of concrete transferring thrust forces to the soil through the larger bearing area of the block so that the strength of the soil isn’t exceeded. In fact, one very important job of a pipeline engineer is sizing the thrust blocks based on the type of fitting, test pressure of the pipe, and soil conditions at the site. But, thrust blocks aren’t a panacea for thrust forces in pipes. They’re big and bulky, they get in the way of other subsurface utilities, they make it difficult to excavate and repair lines when needed, and because they’re made of concrete, they often take several days to cure before you can pressurize and test the line before backfilling. So, the other way we deal with thrusts in pipelines is to take a cue from the plumbers and provide longitudinal restraint at the joints themselves.

If you restrain the joints for some distance on either side of a location that creates a thrust force, like a bend in the pipe, you essentially convert that entire section of pipe into its own thrust block. This allows you to distribute the thrust force over the length of the restrained section. A wide variety of pipe fittings that can provide longitudinal restraint are becoming more popular. They’re still usually more expensive than using concrete reaction blocks, but they have a lot of other benefits as described. Of course, in certain situations, it makes more sense to fully restrain a subsurface pipe. Most petroleum pipelines are fully welded at every joint, and you can fuse polyethylene pipe at the joints as well. It’s the engineer’s job to decide what type of restraint is needed based on all the considerations involved. Next time you see a crew working on a pipeline, try to sneak a peek into the trench and see which type of restraint system they’re using, or ask one of the workers if they’re installing thrust blocks or restrained fittings (or both) to make sure the pipe stays put. Thank you, and let me know what you think!