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(#90) Measuring Fluid Flow From Pitot to Shockwaves · Mechanical Engineering Made Simple

• 0:00
  Welcome back to Mechanical Engineering Made Simple.
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  Quick update before we dive in. We've officially launched paid
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  subscriptions. That means if you want deeper
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  directly. Today we are getting into
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  something really fundamental. We're going to be exploring how
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  we actually measure the invisible fluid flow.
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  Right, and this is a huge topic. It is.
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  We're going to cover everything from, you know, industrial pipes
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  that are governed by standards like British Standard 1042 all
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  the way to the really complex math you need to describe fluids
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  when they start misbehaving. Like hitting the sound barrier.
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  Exactly. We're looking at mechanical
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  versus optical measurement and then we'll dive into ideal flow
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  models against, well, what happens in the real world with
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  compressible effects. And that's really the dual
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  reality of fluid engineering, isn't it?
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  On one hand, you have to be able to put a real physical number on
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  a flow rate for safety, for efficiency, I mean for commerce.
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  That's the industrial standard. That's the industrial
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  imperative. But then to truly innovate, if
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  you're designing a pump or an aircraft wing, you need the
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  theoretical side of things. We start with this beautiful but
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  kind of flawed concept of an ideal fluid, and then we just
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  keep adding layers of complexity until we get to supersonic shock
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  waves. So the goal is to connect those
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  two worlds for everyone listening precisely.
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  OK, so let's start at the very beginning, pinpointing velocity.
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  I think the classic starting point has to be the Pluto tube
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  or the Pito static tube. It absolutely is.
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  And what's so fascinating about the Pito tube is how it uses
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  this direct, almost foolproof relationship between flow and
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  pressure. O how does it work mechanically?
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  Well, the velocity is calculated directly from the difference
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  between the total pressure, which we can call one, and the
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  static pressure P2. And if the fluid is
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  incompressible, you can often simplify the whole thing by
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  using a pittotube coefficient C that's just equal to 1.
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  Right, but real world pipes are huge and the velocity is never
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  perfectly uniform across the whole thing.
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  So how do you use a single point measurement to get a mean flow
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  rate? That's a great question, because
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  a single reading is, well, it's basically useless.
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  The trick, the real nugget here, is that you conceptually divide
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  the pipes cross section. Into smaller pieces.
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  Into concentric rings all of equal area.
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  Then you measure the velocity right at the center of each of
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  those rings and average them out.
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  It's a a really pragmatic way to get a highly accurate mean flow
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  velocity for the whole pipe. But the standard pedo tube is
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  really only for simple, one-dimensional flow.
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  What happens when things get messy, like flow swirling around
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  a turbine blade? Then you need specialized tools.
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  Tools that can sense direction as well as speed.
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  For two-dimensional flow, you'd upgrade to something like a
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  cylinder type pedo tube people often call a yameter.
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  And how does that work? You rotate the cylinder until 2
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  pressure ports on it shows 0 difference.
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  Once they do you find the flow direction.
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  Then you use a third port to get the total pressure and from that
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  the velocity. And for 3D.
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  For truly complex 3 dimensional flow, you'd move up to A5 five
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  whole spherical plateau tube. OK.
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  So that's the classic mechanical stuff, but sometimes you need
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  more speed, more precision. This is where things get really
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  interesting when we turn to electrical and optical
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  solutions. Let's start with the hot wire
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  anemometer. Yes, the principle here is just
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  elegant physics. It uses a very, very fine wire
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  that's heated electrically. And the fluid cools it down the.
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  Fluid flows past, whisks the heat away, and that changes the
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  wires electrical resistance, and that change in resistance tells
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  you the velocity. It's that simple.
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  We hear a lot about the constant temperature anemometer, the CTA.
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  Why did that model win out over the constant voltage type the?
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  Key engineering insight is all about thermal inertia.
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  You see, when you're studying turbulence, you want the system
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  to respond instantly to tiny, rapid fluctuations in the flow
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  to. Chaos.
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  To the chaos exactly. The CTA constantly adjusts the
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  current to keep the wire's temperature fixed.
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  By doing that, you drastically minimize the thermal inertia.
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  It gives you a phenomenal frequency response up to 100
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  kHz. 100 kHz. That's incredible, and that's
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  the speed you need to capture the smallest, most crucial
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  eddies in a turbulent jet stream.
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  It's non negotiable for optimizing something like
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  combustion efficiency. So if we push even further into
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  high tech, we get to the laser Doppler anemometer, the LDA.
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  How are we using light to measure flow here?
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  We're using the Doppler effect. First you had to see the fluid
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  with these microscopic tracer particles.
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  OK, When a laser beam hits one of those moving particles, the
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  light scatters. But because the particle is
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  moving, the frequency of that scattered light is slightly
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  shifted. That's the Doppler shift.
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  And the LDA just measures that shift.
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  It detects that frequency difference, which we call F sub
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  D, and that difference is directly proportional to the
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  particles velocity. You're basically using the speed
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  of light to measure the speed of a particle down to the
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  micrometer. And there are a few different
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  ways to set them up right. Exactly.
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  The main ones are the reference beam type, the interference
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  fringe type, and the single beam type.
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  They're complex to set up, sure, but once they're running they
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  give you the best spatial and temporal resolution you can
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  possibly get. So that covers pinpoint
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  velocity. Let's zoom out to the bigger
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  picture, measuring the total flow rate Q.
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  We're moving from point measurements to total system
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  throughput and the industrial workhorses.
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  Here are the restriction methods.
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  Right, to get the total flow rate you have to look at the
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  entire pipe cross section. This brings us the things like
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  the orifice plate, the nozzle and the venturi tube.
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  And they all work on the same basic idea.
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  They do. All three create a controlled
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  constriction which forces the fluid to accelerate.
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  By measuring the pressure difference across that
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  constriction delta P you can calculate the flow rate.
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  Q. So if they're all based on
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  Bernoulli's principle, why choose one over another?
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  I know the Venturi tube is the most efficient.
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  Theoretically it is. But the trade off is often
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  economic. A venturi tube has minimal flow
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  loss, but it's big and expensive.
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  Nozzles are a good middle groundless loss and bigger flow
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  coefficients than a simple orifice plate.
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  But the orifice plate is everywhere.
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  It is because even though it's inefficient and causes a big
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  permanent pressure drop, it often wins out.
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  Why? It's cheap to make, easy to
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  install, and you can just swap out the plate if you need to
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  measure a different flow range. It's a classic engineering trade
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  off. That's a great point.
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  Now let's flip the script. Let's talk about area flow
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  meters. Like the rhodameter, this one
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  works by keeping a constant pressure difference.
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  Yes, the constant pressure principle.
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  A rotameter has a float inside a vertical tapered tube.
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  As the flow increases, the flow rises, which increases the flow
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  area around. It and it finds an equilibrium.
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  It settles where the pressure and drag forces perfectly
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  balance the flow's weight, so the height of the float is a
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  direct linear visual measure of the flow rate.
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  Simple, cheap, perfect for low pressure stuff.
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  Beyond pressure and area, there are a bunch of other devices for
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  integrated volume. We have positive displacement
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  meters. These are basically mechanical
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  odometers for fluid. Things like Oval gear or roots
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  type meters physically trap and count a constant volume of fluid
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  over and over. They're fantastic for precise
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  batching. Then there's the turbine flow
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  meter. Right, that one uses the fluids
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  kinetic energy. The flow spins a small turbine
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  and the volume flow rate is just proportional to the pulse
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  frequency you get from the spinning blades.
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  What about the magnetic flow meter?
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  You see this in high purity or really corrosive applications.
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  Why is it so dominant there? It's dominance comes from its
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  principle, Faraday's law of electromagnetic conduction.
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  If you have a conducting fluid moving through a magnetic field,
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  it induces A voltage and electromotive force E across the
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  fluid. And that voltage tells you the
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  velocity. And it's directly proportional
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  to the mean flow velocity V. The magic though, is what it
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  doesn't depend on. It has zero moving parts, causes
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  zero pressure loss, and the reading is totally independent
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  of the fluid's viscosity, pressure, or specific gravity.
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  You just can't beat that for some industries.
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  Let's end this part with the vortex shedding flow meter.
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  This one always reminds me of the Carmen Vortex St. behind a
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  bridge pillar in a river. And that's exactly what it is.
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  You put a bluff body in the flow and Carmen Vortex shed
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  alternately behind it. The frequency F of that shedding
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  is directly proportional to the flow velocity U.
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  And that relationship is stable. Very stable.
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  It's described by the stroll hole number, which is about .2
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  for a huge range of industrial flows.
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  You just measure that shedding frequency and you've got your
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  velocity OK. That covers the brass tacks of
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  measurement. Let's leave the factory floor
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  and head into the theoretical workshop.
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  We have to start with ideal flow or potential flow.
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  Now everyone learns about velocity, potential, Fay and the
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  stream function. Yes, but be honest, is this
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  stuff still relevant when so much work is done with viscous
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  flow and CFD? That's a great challenge, and
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  the answer is yes, for two big reasons.
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  First, for many large scale flows where the Reynolds number
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  is huge, the bulk of the fluid behaves as if it's non viscous.
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  It's governed by Euler's equations. 2nd, and maybe more
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  imortantly, otential flow gives you an incredibly powerful
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  mathematical baseline for understanding things like lift
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  and drag. O tell us about those tools.
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  What's the real utility of the stream function size?
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  The screen function I saw is fantastic because it directly
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  shows you the fluid motion lines where PSI is constant.
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  Are the streamlines the actual paths the fluid particles
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  follow? And the real magic.
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  The real magic is that the volume flow rate Q between any 2
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  streamline, say PSI one and PSI 2, is just the difference.
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  Q equals PSI 2 minus PSI O1. Calculating a complex flow
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  volume becomes simple subtraction.
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  And what about the velocity potential Phi?
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  The velocity potential Phi gives you the velocity vector from its
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  gradient. A line where Phi is constant is
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  an equipotential line, and the beautiful part is that these
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  equal potential lines are always at perfect right angles to the
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  streamlines. And they're connected
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  mathematically. Deeply connected, both of them
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  satisfy Laplace's equation, which is Nabila squared Phi
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  equals zero, and they're linked through the Kaci Riemann
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  equations. Which brings us to complex
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  potential theory. W of Z equals Phi plus itsi.
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  The idea here is that you can build complex flows by adding
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  simple ones together. That's the power of
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  superposition. We can define basic flows like a
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  source where fluid flows out, or a sink where it's absorbed, but
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  the really clever component is the doublet.
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  And what is a doublet? Mathematically, you create a
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  doublet by taking a source and a sink of equal strength, moving
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  them infinitesimally close together and increasing their
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  strength to Infinity as they approach.
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  It sounds incredibly abstract. What's the payoff?
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  The payoff is huge. If you simply superimpose a
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  uniform parallel flow onto a doublet, you have just
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  mathematically modeled the flow around a perfect cylinder.
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  Just by adding two simple functions.
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  Just by adding them, it's an algebraic shortcut to
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  calculating pressure distribution and theoretical
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  lift and drag, avoiding a ton of complex calculus.
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  OK, let's move to the extreme end now.
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  Compressibility. When do we have to throw out the
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  assumption that density is constant?
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  You have to account for density changes when you're dealing with
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  gases moving very quickly or undergoing large pressure
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  changes. The whole game changes and it's
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  all quantified by the Mach number.
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  Which is based on the speed of sound a.
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  Exactly. Sonic velocity A is the speed a
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  pressure wave moves through the gas, and the math shows it's
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  proportional to the square root of the absolute temperature T.
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  Hotter gas, faster sound. The Mach number M is just the
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  ratio of your flow velocity you to that Sonic velocity.
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  A. And there's a rule of thumb for
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  when it starts to matter, right? If M is below about .3, the
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  compressive effects are pretty negligible.
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  You can usually get away with treating it as incompressible.
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  So what physically happens when you push past that and hit Mach
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  1? The way the flow communicates
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  with itself fundamentally changes in subsonic flow.
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  When M is less than one, pressure waves travel both
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  upstream and downstream. But in supersonic flow, where M
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  is greater than one, the fluid is outrunning its own pressure
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  waves. They can't travel upstream to
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  warn the fluid ahead. These trapped waves form a Mach
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  cone where the sign of the cones angle alpha equals 1 / m The
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  sound is literally trapped inside that cone.
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  Which is why you don't hear a supersonic jet until after it's
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  passed. That's the Sonic.
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  Boo. This is critical for nozzle
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  design. If I'm pushing air through a
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  simple convergent nozzle, can I get it to go supersonic?
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  No, you can only get it to Mach one and only right at the
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  throat. As you drop the downstream
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  pressure, the mass flow rate increases, but only up to a
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  point for air. That point is when the pressure
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  ratio hits .528. And then what happens?
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  At that exact point, the velocity hits the critical
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  velocity U star, which is equal to the local speed of sound a.
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  The flow is now choked. You can pull a complete vacuum
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  downstream and you will not get a single extra gram of air
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  through it. And that's what leads to the
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  classic shape for supersonic engines.
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  Precisely, to get flow to accelerate past Mach 1, you have
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  to add a divergent section after the convergent throat.
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  That's the Dilavel nozzle. Let's make one last jump from
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  steady state flow to the sudden chaotic world of unsteady flow.
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  We're talking about control systems, rapid changes.
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  Absolutely. A simple example is just the
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  vibration of a liquid column in a YouTube.
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  It's a simple harmonic motion Z = Z naughty cosine of Omega NT
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  at friction, and it becomes damped.
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  But the most critical unsteady safety issue is, without a
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  doubt, water hammer. And we're not just talking about
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  a calculation. This is about ruptured pipes,
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  millions in damage. This is a huge safety issue
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  caused by closing a valve too quickly.
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  It's incredibly violent. When you slam a valve shut, all
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  that fluid momentum is converted almost instantly into immense
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  pressure energy. You get a huge pressure spike
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  delta P. And you can calculate that
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  spike. You can delta P equals rho VA,
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  where A is the speed of the pressure wave, and crucially,
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  that wave speed. A isn't just the speed of sound
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  in the fluid, it's modified by the elasticity of the pipe
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  itself, the diameter, wall thickness, the Young's modulus
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  of the pipe material. And the timing of the closure is
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  everything. It's the difference between a
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  controlled stop and hitting a brick wall.
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  If you close the valve faster than the waves round trip time,
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  that's two L / a lay, you get the maximum catastrophic
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  pressure rise. If you close it slower, the
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  pressure rise is far more gradual, governed by a levy's
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  equation. What an incredible journey we
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  went, from practical tools like the magnetic flow meter which
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  causes zero pressure loss, the amazing precision of a hot wire
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  anemometer capturing turbulence at 100 kHz, all the way to the
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  pure theory of complex potential that lets us model an airfoil.
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  And then we finished with the dramatic physics of the Mott
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  cone and choked flow. The synthesis is what makes this
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  field so fascinating. And here's the final thought to
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  Mull over the same purely theoretical math.
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  I'm talking about conformal mapping techniques that we used
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  to model flow or and a perfect invisible cylinder to predict
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  its aerodynamic behavior. That is the exact same
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  mathematical tool we used to calculate the real messy
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  physical contraction coefficient to flow coming out of an orifice
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  in a giant industrial tank. The theory is never truly
• 15:22
  separate from reality. Fascinating stuff.
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  That's all the time we have for this deep dive, but if you
• 15:27
  haven't already, get over to our YouTube channel Mechanical
• 15:31
  Engineering Made Simple by Strike Vision Studio, where we
• 15:33
  post hands on how to videos, visual breakdowns, and practical
• 15:37
  engineering walkthroughs you can actually use.