Insane Hydraulics
Bold and audacious blog about fluid power
After looking into how the pressure drop across an orifice is calculated, I wouldn't be myself if I didn't put the theory to the test using the example from last week's post: a flow rate of 30 liters per minute of mineral oil and an orifice with a diameter of 2 mm.
The goal is to see if the commonly recommended value of the discharge coefficient (0.62) is anywhere close to reality, to verify if a change in the orifice length (depth) affects the pressure drop significantly, and also to confirm my suspicion that the discharge coefficient varies with flow rate (after all, nothing is constant or linear in real life).
Let me demonstrate the "supplies."" For my variable-length 2-mm orifice, I'll use these pennies, which I will be stacking inside a DIN fitting:
A euro cent has a diameter of 16.2 mm and is 1.6 mm thick, so it fits quite nicely in a slightly widened and deepened 16S metric fitting. Believe it or not, I once saved a cylinder-based mold turning system from self-excited oscillations with such a coin (only it was Escudos back then).
As you can see, one of the coins has a hole with a wide chamfer. This is my attempt at creating the thinnest possible sharp-edged orifice, which I will be progressively 'making worse' by stacking the other coins on top. I've read publications stating that a chamfer lead or a radius lead on an orifice tends to increase its discharge coefficient, which is why I tried to make the chamfer wide. However, I can't thin out the orifice plate too much, because otherwise the pressure drop will simply rip through it.
It is very important for such a test to measure the flow rate with the least amount of error - and here's how I did it:
First, I marked five distinct positions on the knob of the flow-regulating needle valve of our test bench, approximately corresponding to flow rates of 5, 10, 15, 20, and 30 liters per minute.
Then, I measured the flow rates with a volumetric flow meter and a stop watch with the oil at room temperature (the beginning of the test) and with the oil at about 40ºC (the end of the test). There is a slight but noticeable increase in flow rate as the temperature rises and the oil gets thinner. This happens because the LS system of the bench keeps the pressure drop across the flow regulator (and the lines) constant. I am extrapolating the flow rates between these two values in the tables below.
The test is composed of four parts:
This is the test setup:
I am using my wireless pressure sensors here because of the convenience of the app that calculates and displays the pressure drop in real time.
A trick question now: You have the description of the test and you see the test arrangement (mind you - the oil flows from left to right). It is about to fail. Catastrophically. Can you guess why? (A hint: it's all in the picture!) And no, it is not the orifice being ripped from its place by the flow or the test bench suffering a severe pressure spike - it is something else...
I will let you think about it for a while as I disclose the test logs:
| Flow, l/min | 5.85 | 9.35 | 14.25 | 20.75 | 29.3 |
| Pressure drop, bar | 8.6 | 23.9 | 54.5 | 117 | 243 |
| Discharge coeff. | 0.699 | 0.699 | 0.675 | 0.671 | 0.658 |
| Flow, l/min | 6.22 | 9.73 | 14.7 | 20.95 | 29.47 |
| Pressure drop, bar | 9.1 | 25.3 | 57.8 | 125 | 252 |
| Discharge coeff. | 0.721 | 0.677 | 0.677 | 0.656 | 0.65 |
| Flow, l/min | 6.59 | 10.11 | 15.15 | 21.15 | 29.64 |
| Pressure drop, bar | 9.6 | 27.6 | 60.5 | 130 | 260 |
| Discharge coeff. | 0.744 | 0.673 | 0.682 | 0.649 | 0.643 |
| Flow, l/min | 6.95 | 10.5 | 15.6 | 21.35 | 29.8 |
| Pressure drop, bar | 8.9 | 25.1 | 58 | 122.6 | 247 |
| Discharge coeff. | 0.816 | 0.733 | 0.717 | 0.675 | 0.663 |
OK, so the first thing that stands out to me here is the fact that my sharp-edged orifice fails as a sharp-edged orifice under 20 l/min - the pressure drop and the discharge coefficient vary greatly between cold and hot oil. However, above 20 liters per minute, the lines converge almost perfectly, which is interesting.
You can also clearly see in all four tests that the discharge coefficient is dynamic - it gets "worse" (decreases) as the flow rate increases.
The pressure drop does grow as I stack up the coins, but I actually thought that the increase in drag would be much more noticeable.
I made this graph that plots the pressure/flow lines for the four tests, the respective values of the discharge coefficient, and on top of that, I put three theoretical lines that use the formula we derived last week and the flow coefficients of 0.62, 0.65, and 0.72:
The theoretical 0.65 coefficient seems to be the "sweet spot" for my makeshift orifices, especially for the three-coin version.
In any case, what I can see is this - if you need an orifice that secures a certain flow at a given pressure differential, you will have to test it, and you will have to do so across the expected range of working oil temperature. If you skip the test, you may get a surprisingly inadequate result, especially if you are aiming for a lower flow rate.
What else? Oh yes, I almost forgot - the catastrophic failure!
So yes, there I am, fully invested in testing this contraption, when all of a sudden, some five minutes after I began the "experiment", I hear a "s-s-s-s" and see a stream of oil jetting out of the side of the hose downstream the orifice:
Any guesses on how a hose with a static pressure that was never higher than one bar could fail like that? I'll tell you how. Even better - I'll show you!
Here's what I found inside the hose when I cut it open:
The hose was bending pretty hard right downstream the orifice, and this allowed the high-speed jet coming out of the orifice to slice through the inner tube like a hot knife through butter! Notice how the jet managed to make multiple cuts as the orientation of the hose changed slightly on every "coin stack".
So, now you know: if you ever need to assemble a similar "orifice situation," make absolutely sure that the flexible hose run right downstream the orifice is straight!
One last thing now - here's what the coins turned into after this "high pressure abuse:"
All three of them! I guess they don't use the hardest of steels to make Euro cent cores after all (in case you didn't know, these coins are actually bi-metallic)!