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I feel silly asking because deep down, it just seems that a simple hydraulic pump (such as two syringes connected via a fluid-filled tube) has to be considered a simple machine... with two different-sized syringes, you can multiply force to gain mechanical advantage, or you can sacrifice a greater input force to gain range of motion.

My question is, why is it that hydraulic pumps aren't included in the classical "six" (lever, pulley, inclined plane, screw, wedge, wheel & axle)?

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    $\begingroup$ Probably because the ancient Greeks didn't have hydraulic pumps. $\endgroup$
    – Jon Custer
    Commented Nov 13 at 13:54

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It doesn’t matter. That list has no physics criteria that distinguishes machines which are on the list from machines which are off the list. Nothing about being on or off that list changes any equation or prediction or derivation.

If you want to write your own list of simple machines then do so. Your opinion-based list is every bit as valid as their opinion-based list.

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    $\begingroup$ I would agree entirely. Though, I'm currently teaching middle school engineering for the first time (I've taught university and AP physics for 15 years) and I'm certain I'll be asked why there's such particular focus on The Six (which, clearly, are primarily levers, inclined planes, and then variations of those). My best attempt was to say that hydraulic pumps are just "fluid levers". $\endgroup$
    – Brandon Fleming
    Commented Nov 13 at 15:52
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    $\begingroup$ @BrandonFleming that is perfectly reasonable $\endgroup$
    – Dale
    Commented Nov 13 at 15:58
  • $\begingroup$ @BrandonFleming I really think you might be onto something. Why not introduce something like what Angius shows as a simple machine. It's useful and relevant and will prime (no pun intended) young minds. Maybe say something like: "this isn't usually included in the list of simple machines but ..." $\endgroup$
    – JimmyJames
    Commented Nov 14 at 22:41
  • $\begingroup$ @BrandonFleming Where is the focus on these 6 coming from? I think this may have been mentioned in passing during one engineering lecture I had, but it's more historical than it is practical. $\endgroup$
    – JMac
    Commented Nov 15 at 13:10
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    $\begingroup$ "their opinion-based list" is a good way to frame it. It is as arbitrary as the "5 senses" (humans have way more than 5). It's not fundamental like the 5 platonic solids, the elements of the periodic table, or the particles in the standard model. $\endgroup$
    – Alexander
    Commented Nov 16 at 19:01
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That classical list is not something that is studied in the engineering school curriculum. It's basically a historical curiosity, like Aristotle's elements of Earth, Water, Air and Fire.

I agree with you that a set of pistons could be added to the list, or gears, and others. It's better to simply study the laws of conservation of momentum and energy, including statics and dynamics, to allow one to analyze any mechanism.

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    $\begingroup$ Like the 'seven wonders' of the world. Good point. $\endgroup$
    – JimmyJames
    Commented Nov 14 at 22:23
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    $\begingroup$ Something to think about along those lines: The Greeks did not have our well-refined mathematics of motion. The rigorous handling of Force took a few thousand years after their reign! As a result, many physical systems we now know are linked (via the conservation laws) were distinct for them, and investigated separately. $\endgroup$
    – Cort Ammon
    Commented Nov 15 at 14:30
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Well, to be honest all simple machines belongs to the same classical mechanics branch, which analyzes behavior or lays foundations for mechanical devices, while your proposed enter image description here

device is Hydraulic machinery, which uses fluid power (or fluid pressure) to "achieve things" and as such belongs to the branch of hydrodynamics, which in turn is a subdiscipline of fluid mechanics, which is concerned about mechanics of fluids.

In short, because hydraulics uses fluids laws, concept of pressure, which usually is associated with fluids (albeit one can generate pressure without fluid at all), and as such it is not a simple machine, because for good understanding of it's operation you need to grasp at least some fluid mechanics, which is kind of different beast.

I don't know if such distinguishing line was being made by some ancient Greek philosophers or Renaissance scientists, but it's an actual borderline between those subjects. (Even when ancient Egyptians knew some rules of hydrodynamics, because they were able to build Great pyramids using same sort of Hydraulic machinery).

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  • $\begingroup$ What about pipes, gradients, bellows, chimneys and that famous bathtub those are all machines used in various ways to achieve specific applied results? $\endgroup$
    – civitas
    Commented Nov 15 at 12:00
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Today with modern materials it is a very simple machine. However the seal is quite difficult to achieve so it would have been much harder to do using materials available in ancient times, so in those times it was not "simple".

Water suction pumps have been in use at least since Roman times but it does not matter for them (as much) is there is a bit of leakage. In the 17th Century the first vacuum pumps were produced which probably marks the time at which the seal started to become good enough for hydraulic pumps to become feasible.

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