Fluid mechanics is a branch of physics which concerns the study of fluids and the ways in which they interact with forces. Both liquids and gases are considered to be fluids for the purposes of this branch of science. Often, the field of fluid mechanics is divided into two more specific fields of study. These are fluid statics and fluid dynamics, which concern fluids at rest and fluids in motion, respectively. Fluid mechanics can involve highly complex mathematics, and the aid of modern computers has enhanced this science significantly.
The chronological roots of fluid mechanics go all the way back to at least the ancient Greeks. The Greek physicist and inventor Archimedes was the author of some of the first studies we know of which concern fluid statics, including the property of buoyancy. Persian philosophers in the Medieval time period coupled these ancient works with their own studies of fluid dynamics that acted as an early precursor to modern fluid dynamics. Such wellknown historical figures as Leonardo da Vinci and Sir Isaac Newton, as well as others, made notable contributions to our understanding of fluid mechanics.
Every type of science starts out with basic, fundamental assumptions that govern the course of their study. Fluid mechanics is typically defined as having three basic premises or assumptions at its root. The first is the conservation of mass, which means that mass can neither be spontaneously created nor destroyed, although it may change forms. The second assumption, the conservation of momentum, is somewhat similar. This law states that the total momentum in a closed system is constant, and cannot spontaneously appear or disappear.
The third basic assumption governing fluid mechanics is what is known as the continuum hypothesis. This is a way of seeing fluids that does not take into account the presence of discrete molecules. Instead, a fluid's properties are assumed to vary in a continuous way from one point to the next.
Because it ignores the actual nature of small particles of matter, the continuum hypothesis is only an approximation used as a tool in calculations. It can result in a slightly inaccurate solution, but also in solutions that are very accurate under ideal circumstances. Other, more exact methods exist, but this hypothesis is often quite useful as a preliminary assumption. Many times, it can also be assumed that a given fluid is incompressible, meaning it cannot be compressed. This is only actually true of liquids, however, and not gases.
NathanG Post 3 
@allenJo  The closest I’ve ever come to understanding fluid mechanics is the wave pool at the amusement park. All kidding aside, it’s fascinating to watch how waves crest and fall in response to pressure and realize that, despite the fluid nature of water, there are definite fluid mechanics equations behind these gentle tides.
While I don’t understand these equations myself, I have seen simulations of real world events that draw upon these principles. I was watching a program on tsunamis once on television and they created a simulated environment to mimic the behavior of these rogue waves.
They showed the water’s ebb and tide in a tub, along with animated fluid mechanics videos that explained the basic forces that were in operation.

allenJo Post 2 
@SkyWhisperer  Yeah, I took a physics class in college and studied fluid mechanics as well. It was more of a gentle introduction to fluid mechanics; I don’t remember a lot of the concepts like you did.
I do know there is a professional journal called the Journal of Fluid Mechanics; this is kind of the de facto peer reviewed journal on the subject. 
SkyWhisperer Post 1 
I ran into fluid mechanics when I had to help my daughter with her 12th grade AP physics class, although admittedly the chapter didn’t cover the material in a lot of detail.
Typical fluid mechanics problems deal with things like cylinders filled with fluid, where they ask you to determine either the amount of heat that is lost from the cylinder when it spins or its torque. The torque is the rotational force.
Other problems deal with oil viscosity; they ask, for example, how much viscosity is in the fluid when it’s spinning about at such and such a rate. I can see the practical applications of some of this material, especially when it comes to the viscosity of oil. I suppose that you can use that to determine how efficient your engine is, for example.
