How do you apply classical mechanics to turbulence?

>not knowing this intuitively
Why haven't you dropped out yet?

>> who cares about the vortexes
But HOW DO WE GET THE DESIRED FLOW?

Trial and error. Build a few prototypes, test it in the envelope you want it to perform and call it a day.

Start with Bernoulli's laws. Then determine the friction losses by testing every single pipe material and every type of minor losses (valves, fittings, etc) in existence and slapping a "friction factor" on each of them. Bam, fluid mechanics.

that sounds shoddy as fuck. what if the friction losses are imprecise and you end up blowing up your piping and killing all your clients?

you don't know that.

That just means you didn't do the testing properly

You literally can't be incorrect, because you measure the energy before and after flowing through a known length of pipe, and that's the friction factor of the pipe.

>things just randomly explode
>safety margins and testing don't exist

continuum mechanics -> equations of motion -> non dimensionalize the equations -> observe equations get freaky in high Reynolds number domain because of the non-linear term of vi*dvj/dxi

Therefore they came up with RANS. Continuum mechanics is pretty much the only link between classical mechanics and turbulence since fluids are easier to be viewed as a continuum (Eulerian) than discrete particles (Lagrangian). The rest is math.

That's too expensive for some things
Ok now do that for something new that doesn't exist yet

You make a pipe sample and you test it :)

Friction coefficients are based on pipe material alone. The total friction loss is a function of both the friction coefficient and length. So a small sample can be extrapolated to any length of pipe.

I'm finishing off my mech B.S this summer with a specialization in fluids and I still don't know why turbulence occurs.
Why do those eddy currents suddenly appear?
Suppose we have air flowing in a wind tunnel, this flow is almost uniform at locations far away from the walls, at a certain speed (Reynolds number), vortices start to appear. Now for a fluid element to change course in these vortices, a force must have been applied on it. Where did that pressure differential come from?

The drag from the walls creates a low pressure region enough to pull some fluid back, and it just gets ridiculous from there.

I don't think that's it, the vortices appear in the approximately inviscid region in the core.

Yeah, it's like a domino effect in the fluid. The pressure fluctuations eventually take up the whole pipe.

increase number of particles (or cells if you are a meshcuck) to infinite.

You use the Navier-Stokes equations. The problem is they're very non-linear as there are momentum variations due to viscous shear stresses which produce force as a function of its gradient and the shear forces are also in turn functions of the gradient of the velocity field (the velocity gradient tensor). The material derivative is also a non-linear in the advection term. If you want to solve them then there are special cases where direct solutions exist (incompressible, steady state, fully developed flow), or you can use special algoirthms and complex linear algebra to solve it.

Asking the 'why' questions are what win people nobel prizes. Heisenberg once said that he would ask god once he got to heaven "Why turbulence?" It isn't so simple as a 'why' question, if we know the answers to 'why gravity' or 'why electricity' in the sense of attaining an understanding into the fundamental reason for their existence, we would inevitably be led to ask 'well then why does THIS phenomena cause gravity, or EM, or etc.' It's difficult to answer the 'why' question from a scientific perspective on a fundamental level because alot of it is just classifying phenomena. The reason religion exists is rooted in the fundamental human uncertainty; in truth, we probably will never reach a complete answer to the question 'why turbulence?' other than it being a consequence of fluid dynamics.

d_Pressure over distance from origin?
There should also be a coefficient of pressure for each gas.
Also something about temperature of gasses at origin, temperature gradients of inner surface of tube, and of course, radius if tube.

That's too expensive for something that is really big like an airplane or big waterslide

How is it expensive to make a small pipe?

>fluid with low viscosity
classical mechanics -> material derivatives -> Euler's fluid equations -> Bernoulli's equations

>fluid with high viscosity
>Euler's fluid equations -> Navier Stokes equations

>The issue is the equations just explode and require huge amounts of computational effort.

that's not even the main problem. the real problem is that you need a huge amount of boundary conditions

See:
-Reynolds averaging
-Kolmogorov cascade and power spectral density of turbulent fluctuations
-Momentum integral equation
-Self similarity of turbulence
-Boundary layers and their subparts: Viscous sublayer, buffer layer, log layer, outer layer and the Blasius solution
-Direct numerical simulation
-Turbulence models (such as k epsilon, LES, Boussinesq eddy viscosity)

Assume some perturbation (e.g. Wall notch) causes a perturbation in the laminar flow. This perturbation has a certain size and therefore a wave number and therefore can be expressed as a Fourier mode. The nonlinear term in the N-S equations cause this single fourier mode to quickly expand into infinitely many modes-a cascade. The largest modes are result of the excitation (Integral length scale) while the smallest sizes are determined by molecular forces-i.e. Dissipation.

Search for the Turbulence power spectral density.

braid theory + algebraic topology + stochastic partial differential equations = homotopic turbulence theory

Seriously, this was like, van Karman's thesis: "There is no way to precisely describe turbulences with formulas and shit."

This is why most modern turbulence research focuses on pipe flow, because its a huge industrial application.

See: Princeton Superpipe; European Long Pipe Experiments; etc

>small pipe
>turbulence experiments

Pick one. At low Reynolds numbers, just do a DNS. At high Reynolds numbers, prepare to have millions of dollars. Industrial pipe flows regularly exceed Re=10,000,000 (eg: 2 meter pipe flowing at 5 m^3/s).

Modern pipe experiments in this flow regime are few and far between. And extremely expensive.

Here's such an experiment. 110m long, 1m diameter carbon fiber pipe with surface roughness of 200 nanometers, temperature maintained within 0.1C (for a facility of this size that's crazy), flows at 60m/s (working fluid is air), using a 500 hp fan. All this just to get such friction factors, and for fundamental research into wall-bounded turbulence.

Most applications don't really need that though.

mind of god

Industrial pipe flows do, and that's where a lot of the money for turbulence research comes from.

>making pipe samples to measure their friction loss
Just measure the roughness of the material, brainlet.

Start here

probably as a noisy pressure wave.

in classical mechanics the vacuum is a standard departation from unified field theory; the quantized approach means from a single standpoint of view you have to have a single unical dynamicized mode of thinking. someone grab the operator for the thinking it's a thought already

You put this equation into a computer that was designed by someone smarter than you

Gotta discretize

>computer engineers are now smarter than physicists

lol?

Can anyone explain turbulence using only Newton's second law?

Navier-Stokes is Newton's second law applied to a continuum.

You could with a super quantum computer and an unholy tensor grid, with a scope down to molecular level.

Use diffusion transfer equations

EZPZ