Welcome to the third episode of the Nutrient Podcast. I'm Trevor Walker and I'm Matthew Kidd.
And today we are going to provide a little intro into process hydraulics.
We're going to do a two or three episode arc on hydraulics covering the basic principles this episode and moving on to quantifying pressure drop in the next episode.
A lot of what we're going to talk about today can be applied across a range of different fields.
Flow in pipes, flow in ducts, flow around an object, even flow over an aircraft wing.
To try and keep all our ducks in a row, we'll talk about most things from the perspective
of fluid flowing in a circular pipe.
If you've never seen one before, take a minute to go and have a look in the cupboards of
your kitchen.
It'll be the ones connected to your faucets, or taps if you speak the Queen's English.
Today we're going to look at pressure, Bernoulli's equation, Torricelli's law, flow regimes,
and Reynolds number.
Before we rush off and start talking about flow, let's take a moment to delve into pressure.
After all, it's a key variable when discussing flow.
Pressure is defined as force per unit area and in the SI system is typically expressed
in the derived unit, Pascal, which is equivalent to Newtons per metre squared, or in base units,
kilograms per metre per second squared.
If you can't quite remember the difference between base and derived units you might have
to go and have another listen to episode 1.
Now pressure is a scalar quantity, which means it has no direction and therefore exerts an
equal force in all directions. This is why bubbles and balloons are round, because while
surface tension is trying to pull the surface of the bubble into a solid spherical droplet,
the pressure of the gas within the bubble is pushing outwards equally in all directions.
Okay, now circling back to hydraulics, imagine a pipe filled with your favourite hydrocarbon
that is open to a tank at one end and pressurised by a pump at the other. If we examine a thin
slice of the pipe, we would see all those hydrocarbon molecules colliding with the boundaries
of the slice which happen to be the pipe walls and the fluid in the adjacent slices.
Pipe wall is rigid and so assuming the pipe has an adequate design pressure, the molecules
will just bounce straight off the wall in what's called an elastic collision, meaning
they will rebound in exactly an opposite direction with the same speed.
This is not the case for collisions with the fluid in the adjacent slices.
The higher the pressure, the harder the molecules are colliding with the boundaries.
Therefore, molecules in the slice closer to the pump, which are at a higher pressure,
will impact the downstream slice, which is further from the pump a little harder than
they are hitting back.
This has the net effect of pushing the slice a little further down the pipe, during which
the slice will lose a little bit of pressure due to friction at the pipe walls.
The cumulative effect of this nudging is flow from high pressure to low pressure.
And you can see why it is the key variable in hydraulics, as it is a measure of how much
force there is pushing the fluid through a pipe. Now this rambling pseudo theory
is nice and all but you're probably all wondering what it all means for the
humble engineer. So Matt why don't you tell us a bit about Bernoulli's
principle. Bernoulli's equation or principle is fundamentally an application
of the first law of thermodynamics. Remember that the first law of
thermodynamics is about the conservation of energy. We can't destroy or create
energy we can only change the form. So Bernoulli's equation is a mathematical
formula to help us understand the forms of energy we find in our fluid systems and relate
them to each other. In other words, it is a mass and energy balance for a fluid system.
This gives us a nice framework with which to analyse a fluid system, as long as what
you're trying to do balances out Bernoulli's equation, you're probably on the right track.
When we consider fluid systems, we might find energy in the form of pressure, kinetic energy,
Work added or work removed, friction, elevation, temperature, enthalpy and some other minor
effects like sound and vibration.
So looking at each of those in a little bit more detail.
Pressure is that pushing power we talked about earlier.
Kinetic energy is the energy from the mass and velocity of the fluid.
Work added, which is usually in the form of a pump or compressor.
Typically in a simple system we have an electric motor taking electrical energy and driving
a pump which adds energy to the fluid.
Work removed, which could be through a turbine.
The reverse of our pump or compressor, we can use the work we take from the fluid to
make power like in a power station or hydroelectric dam.
We can also use it to directly pressure up a different fluid stream, like we talked about
last week with a turbo expander coupled to a compressor.
Friction is energy lost as the fluid pushes past a surface like the pipe wall.
There's no such thing as a perfectly smooth pipe, and as the fluid moves along, energy
is lost to the bumps it runs into along the way.
Elevation, also known as static head.
This is the energy it takes to elevate the fluid to a certain height, or the potential
energy it has once it's there.
Temperature.
For many systems you can ignore temperature changes for hydraulic purposes, but there
there are a couple where you need to factor it in.
If you're going to be putting gases through a big pressure change, it's something you'll
need to factor in, as we discussed last week, it can have pretty dramatic consequences.
Or if the system you are looking at goes through a heat exchanger, you'll probably want to
account for the effect of all that energy you added or took away.
Enthalpy, like temperature, enthalpy can often be ignored for simple systems, but for some
systems we might change conditions so dramatically that we cause a gas to condense or a liquid
to vaporize. Phase changes are big energy events that need to be accounted for in terms
of the enthalpy change of the fluid in our Bernoulli's equation.
Sound and vibration. These energy losses from the system are usually too small to impact
the energy balance on a practical level, so it's usually safe to ignore them, although
you probably want to think about them from a safety perspective.
So those are the elements that we might take into consideration in our Bernoulli's equation.
To be fair, what we have loosely described as Bernoulli's equation here is an expanded
form of Bernoulli's original work.
His equation was a bit more restrained, and didn't account for mechanical work or temperature
changes, but we add them to the expanded versions because they're useful for understanding fluid
systems.
The detail to which you take your Bernoulli's equation depends on what you're trying to
achieve, ranging from a simple summing up of components to size of pump in an incompressible
system to the super-sciencey multiple-component partial differential of everything version.
For practical purposes, when you get to a complicated liquid or gas system, you're probably
better off using a software package for your calculations, rather than trying to do anything
by hand.
One of the most useful forms of the Bernoulli's equation is a simple two-component liquid
system and expresses energy in the form of head.
For liquids, head is a concept that relates energy to the equivalent height you would
have to lift that liquid to get the equivalent potential energy.
So for our simple liquid system, we get something like
Change in pressure + change in static head + work added = change in velocity head + work
removed as friction.
The benefit of expressing everything in head is that pumps are usually specified this way,
or if you're in the water game, you now know the size of the water tower you should make.
So a side note about the creator of the Bernoulli principle, Daniel Bernoulli.
He's one of those annoying 18th century scientists who makes modern scientists look bad with
how much he got done in his career.
At one point he entered a scientific contest competing against his father and they tied
for first place, which really annoyed his father.
He also published a book on hydraulics called the Hydrodynamica, ahead of his father who
published a book called Hydraulica.
His father, presumably in his jealousy, backdated the book to before Daniel's book was published,
and plagiarised some of the content while he was at it.
So that chalks up a handy 300 years of making people jealous of his achievements for Bernoulli,
so not a bad effort there.
One practical and simple outcome of Bernoulli's principle is Torricelli's law.
It's a simplification which gives us the velocity at which a fluid will shoot out of a hole
in a vessel, depending on the height of the liquid above it.
Basically it's the velocity equals the square root of two times gravity times the height
of the liquid above the hole.
If you have a barrel of water sitting on a bench and you shoot a hole in the bottom of
it, Torricelli's law can tell you how fast the water will be going when it shoots out.
So that's something to think about next time you're watching a western movie.
It's also kind of interesting and surprising to me that in Torricelli's law the velocity
that liquid shoots out of the hole is not dependent on the density of the fluid.
You'd think that that change in weight would have some kind of impact.
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engineered network. So now that we are all experts in Bernoulli's principle we
know that in order to get some flow, i.e. increase the velocity of a fluid, we're
going to have to give up some pressure. Further to this we are also going to
have to provide some additional pressure to overcome the frictional resistance of
the pipe walls. So how do we go about calculating how much pressure needs to
be provided to achieve a certain flow rate? Well the first step is to try and
characterize the frictional losses which means we need to figure out the flow regime.
Flow regime is a concept which considers the way in which the fluid flows across a surface
and interacts internally.
There are three fluid flow regimes, laminar, transitional and turbulent.
Laminar flow, sometimes called streamline flow, is where the fluid flows along in straight
lines without much mixing, eddies or vortexes.
You could think of it like traffic driving down a multi-lane road without ever changing
lanes, nice and smooth, evenly flowing traffic.
The flow on the pipe will be slower near the edges, where the fluid is being slowed down
by the friction of the walls, and faster in the middle.
Like a multi-lane road, flow is faster in the middle, assuming slower drivers have politely
pulled into the edge lanes.
Laminar flow occurs at lower velocities and higher viscosities.
For fluids with very low viscosities like air, it is very unlikely that flow will be
laminar at any velocity where you would even notice that the air is moving.
For very viscous liquids like honey, it would take some impressive pumping to get out of
laminar flow regime.
If we look at the velocity of fluid flowing in a pipe, it changes from the edge of the
pipe to the centre.
For laminar flow, the fluid will be much slower or stop near the edge, and much faster in
the middle.
the whole pipe diameter, the profile will look sort of like a deep parabola.
Turbulent flow is the opposite to laminar flow. Streamlines have been broken down and
there is good mixing across the flow profile. Fluid near the edge may be swept right into
the middle and back again regularly and there are eddies swirling around through the fluid.
In our road analogy, this is about the worst road you can imagine driving on. People are
swerving in and out of lanes, some people have even stopped to do donuts in the middle
of the road or reverse up the road a bit. Turbulent flow occurs at high velocity and
lower viscosities. The velocity profile for turbulent flow is a much blunter curve. Across
most of the cross-sectional area the fluid is flowing at the same velocity, only slowing
down a little at the walls. You can see these velocity profiles in our Reynolds number article
on Nutrium.net that is linked in the show notes. And don't worry, we're going to get
onto Reynolds number shortly. Lastly we have transitional flow which is
sometimes called critical flow and is one of life's great mysteries. It exists
between the laminar and turbulent flow regimes and defies sensible engineering.
It may feature properties of both laminar and turbulent flow with smooth
streamlines in parts and eddies in the others. It can be difficult to quantify
the behavior of fluids in the transitional regime so when engineering
we usually try and avoid it by either staying in the laminar regime or really
punching through to the turbulent regimes. The flow regime of the fluid
will impact how we calculate frictional losses, so we have a nice little
dimensionless number that will help identify whereabouts on the flow regime
spectrum we sit. To figure out what kind of flow regime we have we can use the
Reynolds number, the king of dimensionless numbers, to a chemical
engineer at least. Reynolds number outshines lesser dimensionless numbers
like the Prandtl number, the Grashof number, the Froude number, the Mach number,
they're nothing. It's used as a breakpoint in numerous correlations due to its
ability to tell us where the flowing characteristics of a fluid will change.
Reynolds number is the ratio of inertial forces to viscous forces in a flowing
fluid. In its most basic form, Reynolds number is density times velocity times
pipe diameter divided by dynamic viscosity.
In the derivation of the number we have inertial forces in the numerator and viscous forces
in the denominator. At lower Reynolds numbers we have stronger viscous forces, and the fluid
flows in straighter lines with less mixing, so we find our fluid in the laminar flow regime.
At higher Reynolds numbers we have stronger inertial forces, so our fluids flow with eddies
and vortices, and we are in the turbulent flow regime.
Somewhere in the middle we're in the transitional flow regime, and all bets are off.
Typically, Reynolds numbers of less than 2100 are considered the laminar flow regime,
and Reynolds numbers of greater than 4000 are considered the turbulent flow regime,
though these criteria can change a little depending on who you talk to and the application.
As an example, when we look at a packed bed,
a packed bed is a vessel filled with particles or objects,
like a sand pool filter or imagine a tube filled with golf balls.
When we consider the Reynolds number of a packed bed, the laminar regime stops at a Reynolds number of 10
and the turbulent flow regime starts at a Reynolds number of around 2000.
This is probably because of all the shapes in the packed bed causing their own eddies
and so we cause the transitions to happen a bit earlier than they otherwise would.
So a Reynolds number is a very important number in knowing what flow regime we're in
and it pops up in most of the equations you find in fluid dynamics,
so we'll be looking at it a lot going forward when we talk about friction factors.
So recapping for this episode, we have learnt that pressure is a key variable for driving process hydraulics
and allows us to overcome frictional resistances in pipes.
Characterising these frictional resistances is an important part of process hydraulics
and its characterisation method is dependent on the flow regime.
Lastly, we can identify flow regime through the use of a dimensionless number called Reynolds
number.
Next episode we will look at using the Reynolds number to go ahead and calculate frictional
losses in pipes and fittings.
If you haven't already, subscribe to the podcast in your favourite podcast app and stay tuned.
Ok this has been another episode of the Nutrium Podcast.
As always, we have added links and related reading in the show notes, and have numerous
articles on process hydraulics available at www.nutrium.net
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