Fluid Mechanics

Prerequisite: physics 1, algebra 2

All things "flowable" are fluids, which may be liquids, gases, plasmas, ion soups.. but for now, liquids and gases. Specific gravity is the ratio of two substances' densities, which comes in handy with buoyancy.

One main property that fluid mechanics considers is pressure. Here are two laws of fluid statics, regarding pressure of stationary fluid on an object:

The first one is quite understandable, since pressures need to be uniform in order for fluids to be stationary. The second one is somewhat confusing, but the logic is that since nothing is moving, the net force must be zero. Backwards reasoning. Sorry for the misleading picture, here is a better one:

There are many explanations out there from torque to average force, but my understanding is this: force is acceleration times mass, so if a fluid exerts a diagonal force as shown above, the fluid mass is accelerating with a y component and therefore moving. In order for the fluid to not be moving, it can only accelerate horizontally against the rigid bottle.

A more detailed formula for pressure can be derived as follows:

P = F / A
    = (mg) / A
    = (DV)g / A
    = D(l*w*h)g / (l*w)
    = Dhg
    = Dgh

This formula is for incompressible fluids, in other words, fluids that have the same density at any depth. For compressible fluids, ∆P = Dg∆h.

 Another common formula is this:

Atmospheric pressure is obviously pressure due to the atmosphere. Absolute pressure is the pressure inside a container regardless of the outside pressure. Gauge pressure is in a sense the "net pressure".

But I rather like to think of it as P(atm) - P(abs) = P(g), in which the pressure balance between the outside and inside determines the "apparent pressure" P(g). Dunno. Makes more intuitive sense to me.

Pascal's Principle is applied in the hydraulic lift in which since the pressure is the same at both ends, the out force increases with a maximized area so that the pressures match. The increased force can then be used to lift objects.

In terms of work, the in force is smaller but needs to cover a greater distance, in order for the greater out force to cover a short distance. No glitches, hacks, nor dirty tricks. Just physics.

Another property that fluid mechanics studies is buoyancy, the ability of an object to float. By Archimedes' Principle, an object's buoyant force is the weight of displaced fluid. If you divide constant g from both sides, you have D(fluid)V(displacement) = DV of object.

In fluid dynamics, flow rate can be expressed in mass over time, and if density does not vary, volume over time. The volume rate is easier to visualize while the mass rate uses density to convert volume units into mass units.

And here, Bernoulli's Principle: pressure is inversely proportional to pressure. I like to think of it as driving, or traffic. The cars are mashed up together in the slow lane but widely spaced out in the fast lane. Planes can fly because the bumps in their wings cause air to flow at a greater velocity over the wing than under, so the pressure is greater under than over, then lift off~ And there, the equation is derived by setting work and ∆PE equal to ∆KE.

So there, the basics of fluid mechanics~