Liquids are compressible however they have fairly high bulk modulus (or K factor) which means that they don’t compress much.
And there are a lot of water based hydraulic fluids usually a mixture of water and glycol to lower it’s freezing temperature.
The main reason why water isn’t commonly used is because of it’s thermal stability in the temperature ranges that hydraulic systems tend to usually operate.
Water freezes at 0 degrees and boils at 100, this isn’t good for anything that operates anywhere close to it’s freezing point or boiling point. The latter can be solved with anti-freeze but the former can’t be and the former also can generate steam which can introduce a lot of problems in a hydraulic system that wasn’t designed to handle it.
Additionally a lot of things are water soluble which can impact the fluid and lead to corrosion. And more importantly gasses are fairly well soluble in water which can cause a problem when pressure changes cause air bubbles to form and water has a relatively slow air release in general compared to other hydraulic fluids.
And lastly the viscosity index of the fluid is quite important especially for a high pressure system, which again water can be not ideal.
Oil is a very good hydraulic fluid for most cases since oil formulation can be made that still flow at -30c and have a smoke point of well over 200c which makes it pretty much perfect for nearly any application.
On the other hand water based fluids are commonly used in places where fire hazard is a real problem, these are very common in the mining industry, gas and oil refining and metal production and pretty much anywhere where you wouldn’t want a hydraulic fluid that could catch fire.
TLDR: Water has a very narrow temperature range which means that it’s out of the question for most applications without a lot of compensation in the design which would make the system more complex and expensive. Water is only used when oil and other synthetic fluids cannot be due to them being flammable.
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