Insane Hydraulics

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Absolute vs Kinematic Viscosity of Hydralic Oil

Today I will be talking about the viscosity of hydraulic oil. I bet all of my readers understand what the word viscosity means and know by heart the viscosity ranges of the hydraulic oil their equipment operates with, and in this regard, I won't be telling anything new, but I want to dive a bit deeper into this topic, and I if you finish this post - you'll never look at the term "viscosity" the same way as before, and will never be intimated or confused by phrases like mm squared per second, pascal-seconds, and even momentum diffusivity.

Let us consider for a moment the simple stuff every tech knows about the viscosity of hydraulic oil:

Practically speaking - you don't need to know more, really. You'll be OK and your oil viscosity choices (or recommendations) will be sound. Practice shows that for a given range of machinery in a given region two or three oil types will cover all the bases. For example, here, in Portugal, I would choose 32 for hand pumps and equipment that works cold, 46 for "normal" hydraulics, and 68 for mobile stuff that runs at slightly higher temperatures. Done!

But if you dig" a bit deeper, and curious tech always like digging deeper - a lot of questions arise, and there aren't many "feet on the ground" answers. You come about terms like absolute viscosity, dynamic viscosity, kinematic viscosity, poise (as /pwaz/), stokes... And then when you look into the scientific units - you find pascal-seconds, meters squared per second, millimeters squared per second, and other very correct, but unfortunately very un-intuitive units that don't help much.

Let me explain what I mean by "un-intuitive". People like intuitive units because they make sense. Take speed for example. Easy peasy - kilometers per hour, or meters per second, or any other measure of length divided by a measure of time. Easy to visualize and grasp. Now how do you visualize square meters divided by second and then wrap your head around the fact that this somehow indicates the viscosity index of a fluid?!! Then another manual will tell you that the viscosity of a fluid is measured in Pascal seconds. We work with pressures, so we get pascals, but pascal seconds?!!

But wait - there's more! So, you discover that your favorite grade 46 oil has a viscosity of 46 centistokes at 40 Cº. Then you dig a bit more and discover that centistokes are mm squared over second. Say what? But OK, we'll accept that. How about water? You look it up and find out that it's about 1 cSt at 20 Cº. Great - water is way thinner than oil, that's a given, we all know that, right? And then.. you look up the viscosity of air (in cSt, at sea level) and you discover that it is actually about 15 cSt, and now the whole viscosity concept is broken! Yep - that's right. Water is one measly centistoke and the air around us has 15 times more of it! The whole notion of thick and thin is upside down at this point!

So, in this post, I want to explain the viscosity in a simplified way that, at least for me and my very limited knowledge of elementary physics, seems to be intuitive, and hopefully it will be the same for you as well.

Let us start with the classic two planes, one stationary and the other one moving at a steady slow speed, with a Newtonian fluid between them:

Fluid flow between two plates

As the upper plane moves, it drags the fluid with it, and if we measured the speeds of the layers in the fluid, we would see that the speed distribution decreases linearly towards the stationary plane, which can be explained by the viscous friction between the fluid layers.

And we would also see that the force F necessary to move the upper plate at a steady speed is directly proportional to its area (A), its speed (v), and inversely proportional to the distance between the plates (d). Like so (the funny-looking ∝ sign means "is proportional to"):

F ∝ (A v) / d

By the way, another way to call the speed divided by separation distance would be "speed gradient", which in our system is constant across the layers, so if we, say, didn't know the separation distance between the plates, but could measure the speeds of two layers and the distance between them, we would get the same value.

Now, if we were to create a mathematically correct formula that would allow us to calculate the force necessary to move our plate at a constant speed, we would need to insert a proportionality factor (μ) in the formula above, and this factor would define on the shear-resisting property of our fluid. Like so:

F = μ (A v) / d

The factor (μ) that determines the shear resistance of our fluid is called absolute viscosity, and also very often - the dynamic viscosity. I prefer the name absolute one hundred times out of one hundred, and you'll see why in a minute, but in most sources it is called, unfortunately (once again, in my very subjective and personal opinion) the dynamic viscosity.

Now let us try to figure out the units of our "mystery factor" (N is for newtons, m is for meters, s is for seconds):

N = μ (m² m/s) / m

μ = N/((m² m/s) / m) = (N s)/m²

And if we recall that newton over a square meter is the pascal, we see that our viscosity unit boiled down to the pascal-second. But if you "think back" when you come across a dynamic viscosity of a fluid (when presented in Pa-s), you can think of it as a force in N required to "shear" it with a 1 square meter plane with the speed gradient of one meter per second per meter.

I like the standard meter-kilogram-second units, and thus have no problems with pascal-seconds, but you'll find that another unit is also widely used - the poise (pronounced as /pwaz/), which is basically the same thing from the centimeter-gram-second system of units. In our apparatus, one poise would be the viscosity of a fluid that required a shearing force of 1 dyne to move a square centimeter area over a 1-centimeter layer of fluid with a velocity of 1 centimeter per second. A dyne is a tiny force, by the way, about one milligram. If you do the math, you'll see that

1 poise = 0.1 pascal-second,

And since most fluids have very low numeric viscosity values, to make things easier for us, humans, it is very common to use the unit "centipoise", which is a hundredth of the poise,

so, or 1 cP = 1 mPa·s

Water at room temperature, for example, has an absolute viscosity of about one centipoise. Don't sweat too much about the conversion factors, though, there are calculators for that everywhere.

But... wait. How about them centistokes? When do these come in whit all this pascal-second nonsense? Be patient, I am getting there.

So, let us continue with our thought experiment, and imagine not one, but two(!) of the viscosity-measuring apparatuses we just used one next to the other. And now let us fill them with two different (and more extravagant) fluids - mercury and kerosene.

If we measure the force necessary to shear the layers, we'll see that both of the fluids have practically identical absolute (a.k.a dynamic) viscosity of about 1.6 cP. In other words - when we move our test plane at a steady speed, the resisting force will be equal both for kerosene and mercury, and of course, the speed distribution in the layers of fluid between the planes would be identical, but if we could measure the speeds of different layers in real-time, we would notice something strange when we changed the speed of the moving plane - for example - accelerated it. We would see that the kerosene layers pick up the speed change much faster than the mercury layers.

Now if we thought about it a little, we would quickly realize that this happens due to the fact mercury is much denser than kerosene (13.6 g/cm³ vs 0.82 g/cm³), so the heavier layers pick up speed much slower with the same moving (shearing) force.

But this also means that if we were to derive a factor that would reflect this behavior of a fluid, we would need to come up with a unit that describes the relation of absolute viscosity (μ) to the density of the fluid (ρ):

ν = µ/ρ

And this new and "improved" viscosity factor is called the kinematic viscosity of a fluid.

Let us consider its units before going further.

ν = ((N s)/m²) / (kg/m³) and if we recall that N is one kg per meter per second squared, we'll end up with m²/s.

So - there you have it - a very non-intuitive unit of square meters per second. Don't worry - I'll do my best to make it as intuitive for you as possible in a second. But before all, I must admit that our friends from the CGS were once again more successful in "advertising" their units, and so their unit of kinematic viscosity called stokes (centimeter squared over second) is what is used in the modern industry most of the time. Once again - in its centi-variant, i.e. centistokes, where 1 cSt equals 1 mm²/s.

Water at room temperature has a kinematic viscosity of about 1 cSt.

So now comes the "moment of truth": after having read all of the above, you can see that our beloved kinematic viscosity does not actually denote "how thick" a fluid is, but rather how fast speed changes propagate in it! With the more viscous fluid being the one that "conducts" the speed changes faster.

And now, finally, you should be able to see why the air (at sea level) has a kinematic viscosity of about 15 sCt, in other words, 15 times more than that of water! Simply because it is much less dense than water, and so it is capable of propagating the speed change that much faster.

The words "propagate speed changes" in a medium can be also translated as diffuse momentum - and that, my friend would be the real definition of the kinematic viscosity - as the fluid's momentum diffusivity!

Now for the intuitive visualization of this concept. This may be very simplified, or even downright incorrect, but the following visualization has always helped me wrap my head around the "area per second" units:

I imagine the cutaway view of the two-plane apparatus from our experiments, and I draw a mental line across the tips of arrows representing the speed of layers:

Fluid flow between two plates - visualisatoin of kinematic viscosity units

The line forms a triangle with the bases of the arrows, and as the speed changes the triangle becomes bigger or smaller (or a vertical line when the plane is stopped and the fluid is not moving). So the triangle represents the area that is filled when the speed of the plane changes, and it is filled at a certain rate of area/time, which is the kinematic viscosity of the fluid in the experiment.

That's my way of visualizing this concept. Maybe I am nuts.

There's obviously a ton more to all of these concepts, but I can tell you one thing - these simplifications did help me remember the units, and understand why the kinematic viscosity of a thin gas can be an order of magnitude higher than that of a thick fluid.

A question now - why do they use kinematic viscosity with industrial oils then? Wouldn't absolute viscosity be as good? And the answer is - yes, it actually would. However - if you look at the most common device used to measure the viscosity of fluid - it being a vessel with a calibrated hole that drains the fluid and evaluates its viscosity by measuring the amount of time it takes for the fluid to drain a certain volume - you will see that it measures exactly the kinematic viscosity because the thing that you are measuring - the time - is proportional to the fluid's absolute viscosity, and inversely proportional to its density (because the fluid is pushed out by gravity). So - there you have it - absolute viscosity over density equals kinematic viscosity! If we were to use the capillary viscometer with the two fluids from our second thought experiment (kerosene and mercury) we would see the heavy mercury slip out through the hole much faster because it is so much denser!

To conclude - a few words about why I don't like the term "dynamic viscosity". In my head, somehow, kinematic and dynamic have similar connotations. Like speed changes, or momentum propagation - it's all dynamic in my (primitive) brain. Absolute viscosity sounds way more correct to me - you shear a fluid and measure the resistance. Absolute. Simple. But that's just me.

Anyhow - now if someone winks at you and says something like "did you know that air is more viscous than water?" You'll be able to wink back and give an informed reply!