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(#142) Why Pressure Vessels Fail at Discontinuities · Mechanical Engineering Made Simple

• 0:00
  Welcome back to mechanical engineering made simple.
• 0:02
  It's great to be back. Today we have a mission, and
• 0:05
  that mission is to move way, way beyond the basic container.
• 0:10
  You know when most people think of a pressure vessel or a tank,
• 0:13
  they just think of a big steel can holding some stuff, right?
• 0:17
  Maybe it's gas, maybe it's liquid.
• 0:19
  It just sits there. It sits there, it does its job.
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  End of story. Which is, I mean, that's the
• 0:23
  most boring part of the design, really.
• 0:25
  If you're just designing a perfect cylinder to hold
• 0:27
  pressure, you could do that on the back of a napkin.
• 0:30
  Exactly. We are ignoring the boring parts
• 0:33
  today. We are looking at what happens
• 0:35
  when you decide to punch giant holes in that pressure vessel.
• 0:39
  What happens when you strap a vibrating motor to it, Or you
• 0:43
  fill it with solids that act like arches, or, or you heat it
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  up until the steel is screaming to expand but the concrete
• 0:49
  lining inside says absolutely not?
• 0:51
  It's a messy, chaotic world inside those tanks.
• 0:54
  And to navigate this mess, we are tearing through a stack of
• 0:59
  documents from the Pressure Vessel Design Manual.
• 1:01
  We're talking chapters on large openings, special designs, local
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  loads, the the really gritty stuff.
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  And if we had to put a theme on this deep dive, it would be
• 1:10
  discontinuity and stress. Is he?
• 1:13
  A perfect uninterrupted cylinder is easy to calculate.
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  The math is beautiful and simple because the stress flows evenly.
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  You know, like water in a smooth pipe.
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  But real engineering happens at the interruptions, the nozzles,
• 1:29
  the supports, the interfaces where materials are fighting
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  each other. That's where the stress
• 1:33
  concentrates. That's where things fail.
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  So let's start with the most obvious way to ruin a perfect
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  cylinder you cut a hole in it. This was cheese problem.
• 1:40
  Yeah, right now my intuition says OK, I cut a hole to put a
• 1:43
  pipe in, I just need to patch it up with enough metal to replace
• 1:46
  what I removed. Like area replacement, right?
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  That is the old school way of thinking and it gets you into
• 1:52
  trouble fast. It is much more complicated
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  because you are dealing with two completely different types of
• 1:58
  stress now. You have the membrane stress and
• 2:00
  then you have the bending stress.
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  Break that down for us because membrane just makes me think of
• 2:04
  a balloon. That is actually a perfect
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  analogy. Imagine a balloon.
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  The skin is being stretched evenly in all directions.
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  That's membrane stress. It's uniform.
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  But now imagine you take a rigid plastic straw and glue it to the
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  side of that balloon, and then you pull on the straw.
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  You're creating a leverage point.
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  You aren't just stretching the skin anymore, you're trying to
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  snap it. Exactly.
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  That is bending stress. The nozzle acts like a lever
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  arm. It creates a moment.
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  It's flexing about what we call the hard axis.
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  The manual breaks this analysis down into specific cases for
• 2:37
  large openings. And the math is pretty strict
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  here. Very you have to check that your
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  membrane stress, let's call it Sigma M, is less than your
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  allowable stress. That's step one.
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  OK, so the stretching part has to be safe, right?
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  But then you have to check the combined stress Sigma M Lus
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  Sigma B, the membrane plus the bending and the code says that
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  total has to be less than 1.5 * s.
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  Wait 1.5 times? That seems generous.
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  Usually engineering codes are conservative.
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  Why are they letting us go 50% over the allowable stress?
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  It's because the nature of bending versus stretching.
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  You see, if you overload a membrane in tension, it rips.
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  Catastrophic failure. All right, it just tears.
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  The bending is different. The outer fibers of the metal
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  might yield, they might stretch permanently, but the inner
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  fibers are still holding strong. This is what we call the plastic
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  hinge or plasticity reserve. The code is basically saying we
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  know it's going to bend and we'll allow the surface to yield
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  a little bit locally to redistribute the load, but don't
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  go crazy. That makes sense.
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  It's the difference between snapping a rubber band and
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  bending a paper clip. The paper clip bends but doesn't
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  break immediately. Precisely, yeah.
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  Now, if you exceed those limits, you have to reinforce it.
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  You need a reinforcing pad. But this is where I see
• 3:56
  engineers get it wrong constantly.
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  They just slap on more metal. They think I have high stress.
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  I'll just slap a massive 3 inch thick steel plate on.
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  It more metal is better, right? Wrong.
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  The manual brings up the 2/3 rule and some other limits.
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  It's surprisingly picky. It basically says the pad
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  shouldn't be thinner than 0.75 times the shell thickness, but
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  also, and this is key, not thicker than 1.5 times the shell
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  thickness. Why limit the thickness?
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  Why can't I make it super strong?
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  Compatibility. Think about that balloon again.
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  If you glue a thick rigid steel washer to a soft rubber balloon,
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  what happens at the edge of the washer when you inflate the
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  balloon? Oh, it tears right at the edge
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  because the balloon is stretching and the washer isn't.
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  Exactly. If your reinforcement is too
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  thick compared to the shell, it becomes a rigid hard point.
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  It refuses to flex, so instead of distributing the stress, it
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  concentrates all of it right at the toe of the Weld.
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  So you crack the vessel because you made the patch too strong?
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  You did. You want the reinforcement to
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  breathe with the vessel, not fight against it.
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  So it's the Goldilocks zone of steel plates, not too thin, not
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  too thick. It has to move with the system.
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  Now, Speaking of things moving, let's talk about the wobble.
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  Vibration. Specifically, tall, skinny
• 5:12
  towers. The source material paints this
• 5:15
  terrifying picture of a tower just sitting there in the wind.
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  And it's not that the wind is blowing it over like a tree.
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  It's something sneakier. Vortex shedding.
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  This is a critical concept for anything tall and cylindrical.
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  As wind flows around a cylinder, it doesn't just flow smoothly
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  past, it splits and as it rejoins on the backside it
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  creates these low pressure swirls vortices.
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  Like the wake behind a boat. Similar, but these detach in a
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  rhythm, left, then right, then left.
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  It creates an alternating force sideways to the wind direction.
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  And if that rhythm matches the towers natural sway.
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  You get resonance, the tower starts to oscillate.
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  We call this the critical wind velocity.
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  It's like pushing a kid on a swing.
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  If you time the push perfectly, they go higher and higher.
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  The force is just magnify. Incredibly fast.
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  So how do we stop the wobble? The manual suggests stiffening
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  rings. I pictured these like the ribs
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  in a human skeleton. That's a good analogy.
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  They had stiffness to the shell to break up that vibration mode.
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  Basically they change the natural frequency so the wind
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  can't catch it anymore. But sticking with our theme of
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  discontinuity. There's always a price there.
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  Always. Is the shell wants to flex under
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  the wind load? It wants to ovalize or bend the
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  ring says no. So immediately adjacent to that
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  ring, you get a massive spike in longitudinal bending stress.
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  So you fix the global problem, the swaying, but you create a
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  local. Problem exactly?
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  Stress at the ring attachment. And we have to worry about how
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  much it sways to. The rule of thumb mentioned was
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  limiting deflection to 6 inches per 100 feet of height.
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  Which is actually quite a bit of movement.
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  Imagine standing on top of A10 story building and it's swaying
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  6 inches side to side. No, thank you.
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  But the calculation for that deflection really highlights why
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  height is so dangerous. The formula for deflection
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  involves the weight West and the length L raised to the 4th
• 7:09
  power. OK, stop there.
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  L to the 4th power. I want to make sure everyone
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  catches the implication of that exponent.
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  It is the most sensitive variable in the equation.
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  It means if you double the height of your tower, you go
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  from 50 feet to 100 feet. You don't double the deflection.
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  You don't even quadruple it. 2 to the 4th power is 16.
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  Correct. You increase the deflection by
• 7:28
  16 times, you make the tower twice as tall and we become 16
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  times as wobbly. That is terrifying leverage that
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  explains why making things just a little bit taller is an
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  engineering nightmare. It explodes the requirements for
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  stiffness. You are fighting an exponential
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  curve. OK, so we've got wind pushing
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  from the outside. Now let's look at the war
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  happening inside the walls. I want to talk about refractory
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  linings. The battled materials.
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  This sounds like a recipe for disaster.
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  You have a steel shell which we know loves to expand when it
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  gets hot. And you line the inside with
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  refractory concrete, which is basically ceramic and it hates
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  expanding. And you bond them together and
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  heat them to 1000°. What actually happens
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  mechanically when you turn up the heat?
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  Well, the steel shell heats up and expands outward.
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  The hot face, the inside surface of the concrete directly
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  touching the fire, wants to expand the most, but the outer
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  concrete is cooler. So during operation, the hot
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  concrete is pushing against itself.
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  It's in compression. And concrete loves compression.
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  It's happy there. It thrives in it, but the
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  problem isn't heating up. The problem is shut down.
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  The cooling phase. Exactly.
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  Imagine you cut the heat. The steel shell cools down and
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  contracts. It shrinks like a belt
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  tightening around a waist. At the same time, the inside
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  surface of the concrete cools rapidly and shrinks.
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  Since the rest of the material is holding it back, that
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  interface goes into tension. It's being pulled apart.
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  And concrete hates tension. It has almost 0 tolerance for
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  it. That is when you get cracks.
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  The source material mentions checking the modulus of rupture.
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  The design rule is that the allowable tensile stress is
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  roughly 40% of the modulus of rupture at 1000°.
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  If you see that, the lining snaps.
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  You can actually hear it. Sometimes yeah, loud pops inside
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  the vessel is the liner cracks. That's unnerving, but there was
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  1 concept here that blew my mind.
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  Creep. Usually when I hear creep in
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  engineering it's a bad thing, but here the manual acts like
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  creep is the hero. In this specific context, yes,
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  creep is usually the villain, but in refractory linings it's a
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  saving grace. At high temperatures and high
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  compressive stress, the refractory material essentially
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  relaxes. It slowly flows or deforms over
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  time to relieve that internal stress.
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  So it's basically stress relief yoga for the concrete.
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  In a way, yes. The manual notes something
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  counterintuitive. The creep rate allows the
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  material to survive the thermal cycle.
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  Without creep, the stress would build up like a loaded spring
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  until the material shattered. Creep dissipates that energy.
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  Amazing. The material sacrifices its
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  shapes slightly to save its structural integrity.
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  OK, moving from heat to motion, let's talk about agitators.
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  We are turning this pressure vessel into a giant blender.
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  A very violent blender. I always thought you put a
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  propeller in a tank, you spin it, you mix the fluid, done.
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  Simple. That is the common
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  misconception. If you put a paddle in a smooth
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  round tank and spin it, you don't get mixing, you get
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  swirling. The liquid just spins with the
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  paddle. Yeah, lazy riff.
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  Exactly. The whole liquid mash acts like
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  a solid flywheel. The liquid is moving at almost
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  the same speed as the impeller. If there's no speed difference,
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  there's no sheer. And no sheer means no mixing.
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  You're just taking the ingredients for a ride.
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  So how do we fix it? How do we break the lazy river?
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  Baffles. You Weld vertical metal strips
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  to the side of the vessel walls. There's little fins sticking
• 10:51
  out. They look insignificant, but
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  they are doing the heavy lifting.
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  They act as a brake. They stop the fluid from
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  spinning and force it to turn over, converting that rotational
• 11:02
  energy into vertical pumping and turbulence.
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  That chaos is where the mixing happens.
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  But if you're stopping thousands of gallons of spinning liquid,
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  those baffles must be taking a beating.
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  Massive forces. You are essentially slamming a
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  river into a wall. The manual has a specific
• 11:18
  formula for the force on a baffle depends on the horsepower
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  and the impeller RPM. Let's call it in.
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  I looked at that formula, it was force equals a constant times
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  horsepower divided by RPM. Right.
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  And look at the relationship. Horsepower is on top, RPM is on
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  the bottom. So if I lower the RPM the force
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  goes up that feels backwards. Shouldn't have faster mixer hit
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  harder? Think about torque.
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  If you have a motor with the same horsepower but you gear it
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  down to run slow, it produces massive torque like a tractor in
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  low gear. That torque is getting
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  transferred to the fluid and the fluid transfers it to the
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  baffle. So a slow sludge churning mixer
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  exerts way more force on the tank internals than a high speed
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  propeller. That is a gotcha moment.
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  You could design a tank for a fast mixer, then someone swaps
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  in a slow high torque mixer and suddenly RIP.
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  The baffles are torn right off the wall.
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  Happens more often than you'd think.
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  Speaking of things behaving counterintuitively, this was my
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  biggest aha moment in this depth.
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  Dive bins and silos. Yes, where intuition goes to
• 12:22
  die. Seriously, I looked at this
• 12:24
  section and thought why is this even here?
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  If I fill a tank with wheat or coal, isn't it just like filling
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  it with heavy water? And the manual screams no.
• 12:31
  It is definitely not a liquid. Solids have friction, they have
• 12:34
  internal sheer strength. They arch or bridge.
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  The source references the Lambert and Ketchum theories.
• 12:39
  Can you break that down? How is a silo different from a
• 12:42
  water tank? In a water tank, the pressure on
• 12:45
  on the bottom is simple. It's the total weight of the
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  water, 100 tons of water. The floor holds 100 tons.
• 12:52
  OK, standard physics. But in a silo, the grain wedges
• 12:56
  against the side walls. Friction locks it in place.
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  We call it arching. The material creates internal
• 13:03
  arches that push against the walls.
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  This means the walls end up supporting a huge portion of the
• 13:08
  vertical weight. So the floor doesn't feel the
• 13:11
  full weight. No, the pressure on the bottom
• 13:13
  is significantly less than the total weight of the material.
• 13:17
  The manual shows the pressure curve flattening out after a
• 13:20
  certain depth. The pressure on the floor stops
• 13:22
  increasing entirely. That sounds like a good thing.
• 13:24
  Less load on the foundation. It sounds good for the floor,
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  but it's dangerous for the walls because that load didn't
• 13:30
  disappear, it moved. It went into the walls as a
• 13:33
  vertical compressive load. So it's pulling the walls down.
• 13:36
  Yes, the friction creates a drag force.
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  You can actually crumple the silo like an empty soda can
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  because the friction of the grain is dragging the steel
• 13:45
  walls down towards the ground. That is a wild image, a steel
• 13:49
  tower crumpling vertically because the corn inside is
• 13:52
  grabbing onto it. And then there's the flow, the
• 13:55
  angle of repose. Wheat on steel slides
• 13:59
  differently than coal on concrete.
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  This determines if the stuff actually comes out right, right?
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  If you get the friction coefficients wrong, the material
• 14:06
  won't flow. It forms a rat hole, a tunnel
• 14:08
  straight up the middle, and the rest stays stuck or worse, it
• 14:12
  flows unevenly. And that creates an eccentric
• 14:14
  load. Exactly.
• 14:16
  The center of gravity shifts and the silo can literally tip over.
• 14:19
  It's fascinating that sand and water, which looks similar,
• 14:22
  behave so completely differently in a tank.
• 14:24
  It's all about the sheer strength.
• 14:26
  Liquids have none, Solids have plenty.
• 14:29
  All right, we have time for one last section.
• 14:30
  The coolest shapes, spheres and coils.
• 14:33
  First off, spheres. Why don't we build everything as
• 14:35
  a sphere? Geometric efficiency.
• 14:38
  A fear is the strongest shape for holding pressure.
• 14:42
  It distributes stress perfectly evenly, but they are a nightmare
• 14:47
  to build in the field. The manual talked about the
• 14:49
  orange peel method, yes. Forming steel plates into
• 14:53
  tapered segments like an orange peel or the soccer ball method.
• 14:57
  But think about the fabrication you are welding curved plates
• 15:01
  high in the air. And then the hardest part, you
• 15:06
  have to hold it up. Gravity is the problem.
• 15:08
  Always. You can't just set a sphere on
• 15:09
  the ground. You need legs.
• 15:11
  But attaching a vertical straight leg to a curved
• 15:13
  spherical shell is a geometric mismatch.
• 15:16
  It's a discontinuity. The leg wants to go straight up,
• 15:19
  the shell curves away. Exactly.
• 15:20
  When you put weight on those legs, they try to punch through
• 15:22
  the shell. You get massive local stresses
• 15:24
  right at the attachment points. So the sphere is perfect for
• 15:27
  pressure, but terrible for gravity.
• 15:29
  Now inside these vessels we sometimes put pipe coils for
• 15:32
  heating or cooling. And you found a detail here that
• 15:35
  creates a very specific type of flow.
• 15:37
  The double AD effect or the Dean effect?
• 15:39
  This is fluid dynamics at its finest.
• 15:41
  Walk us through it. OK, when water flows through a
• 15:43
  straight pipe, it's lazy. The water in the middle moves
• 15:47
  fast. The water near the walls move
• 15:49
  slow. But when you curve that pipe
• 15:51
  into a coil, centrifugal force kicks in.
• 15:54
  The faster moving water in the center of the pipe gets thrown
• 15:57
  to the outside of the curve. Like a car taking a turn.
• 16:00
  But the water has to go somewhere, so it hits the
• 16:03
  outside wall, splits, travels along the walls back to the
• 16:05
  inside of the curve and pushes into the center again.
• 16:09
  It creates 2 counter rotating swirls inside the tube.
• 16:12
  So the water spirals while it flows.
• 16:14
  Yes, it's turning itself inside out constantly, and that
• 16:18
  turbulence is fantastic for heat transfer in a coil.
• 16:22
  The Dean effect constantly mixes the hot and cold fluid.
• 16:25
  It scrubs the heat off the walls.
• 16:27
  So you get much better efficiency just by bending the
• 16:29
  pipe. You do, you pay for it.
• 16:31
  In friction you need a bigger pump, but for heat exchanger
• 16:34
  it's brilliant. It's amazing how much complexity
• 16:36
  is hidden inside a curved pipe. It really is.
• 16:39
  So let's unpack this entire deep dive.
• 16:42
  We started with a simple cylinder, but by the time we're
• 16:44
  done we've got a system where the wind is trying to shake it
• 16:48
  apart with vortices. The internal mixer is trying to
• 16:51
  shear the baffles off the wall with low speed torque.
• 16:53
  The. Heat is trying to crack the
• 16:55
  lining through differential expansion.
• 16:58
  And if it's a silo, the friction of the contents is trying to
• 17:01
  crush the walls vertically like a soda can.
• 17:04
  A pressure vessel isn't just a container, it's a battlefield of
• 17:07
  forces. It is a complex system of
• 17:09
  conflicting requirements. You solve one problem, like
• 17:12
  adding a stiffener for wind, and you create a new problem like
• 17:17
  local stress concentrations. Design is about balancing those
• 17:20
  conflicts. And that leads us to the final
• 17:22
  thought. What's the one thing you want
• 17:24
  the listener to take away from this?
• 17:25
  For me, it's the concept of scale and the reality of field
• 17:29
  fabrication. We aren't talking about
• 17:31
  precision lab equipment here, we are talking about massive
• 17:34
  structures built outdoors in the mud by guys with welders.
• 17:38
  Right, It's not a watch, it's a monument.
• 17:40
  Think about the thermal calculations we discussed.
• 17:42
  If you are off by a single degree in your thermal expansion
• 17:45
  calculation on a 300 foot tower, that translates to inches of
• 17:50
  steel moving where it. Shouldn't.
• 17:52
  Inches. In a rigid metal structure, a
• 17:55
  movement of 1 inch is catastrophic.
• 17:58
  It shears bolts, it buckles, supports, it rips, piping
• 18:01
  flanges apart. The math we look at on paper,
• 18:04
  the sigmas and the deltas. They represent massive physical
• 18:07
  forces. That is a sobering thought.
• 18:10
  The math is real and the consequences are heavy.
• 18:12
  Absolutely. If you respect the
• 18:14
  discontinuities, you'll be fine. If you ignore them, they will
• 18:17
  find you. Well, that is all the time we
• 18:19
  have for today's deep dive into the crunch of metal and the flow
• 18:22
  of stress. It was a pleasure.
• 18:23
  If you haven't already, get over to our YouTube channel
• 18:25
  Mechanical Engineering Made Simple, where we post hands on
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• 18:30
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