# 14.11.3: Hydraulics


Hydraulics is mechanics with liquids1 instead of solids (solid mechanics). Just like mechanics, hydraulics separates into hydrostatics and hydrodynamics2. The concepts are identical to solid mechanics. Statics when the system is not in motion, dynamics when it is in motion. Both work-energy concepts (Bernoulli) and force-momentum concepts (Archimedes) to describe motion are used in the hydraulics world. This is a matter of convenience, as each method can mostly produce the same results. For hydrostatics we still use the force-momentum concept, but in order to truly describe hydrostatics accurately we should do this in the context of the stress tensor3. Herein we will stick to Archimedes' principle named after Archimedes4 of Syracuse and Bernoulli's principle.

To describe motion using the work-energy concepts we will need to use pressure (P), volume (V), velocity $$\vec{v}$$, density ($$\rho$$), mass (m), drag coefficient ($$c_d$$), and height (z or h).

1Fluids come in two types: incompressible and compressible. Incompressible fluids are considered liquids and compressible fluids are gases. Hydraulics usually deals with the incompressible fluids, though that depends on the specific definition of hydraulics.

2Hydraulics can be defined as mechanics with fluids. In that case, hydraulics has an additional subject of aerodynamics (for compressible fluids).

3Not herein though as it is a little advanced for an introductory course. Though we will point you into that direction if you wish to do this on your own.

4There were many Archimedes in Ancient Greece with a number of them being noteworthy. This Archimedes is the polymath you know as the "Leonardo da Vinci of Ancient Greece."

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