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How viscous forces affect force transmission in hydraulic systems

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Hi everyone,

I have a question that I am struggling and need your help. So I am working on a project which is essentially two syringes, A & B, with different cross-sectional areas, A1 & A2, connected via a tube filled with water. If we assume loss-less system, Pascal's law, the input force ,F1 ,will be transmitted to the second syringe and the output force, F2, will be a multiplication of the two cross-sectional areas [F2=F1*(A2/A1)].

So my question is if that is the case because in real life?

Hydraulic systems are affected by viscous forces (minor and major losses) which cause a pressure gradient in the system. In simple words the efficiency is not 100% but something else. Is there a way to calculate that efficiency and what would be the actual output force (F2) in such a system. Is Bernoulli's equation including losses a suitable equation?

Thank you very much.

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