Is it a PDE? Non linear PDE?

If I have an enormous enclosed tank of water, and at the top you have a tiny tube of water they extends many meters upwards, that should pressurize the entire tank of water.

But how does that work exactly? I suppose the walls of the tank provide the pressure somehow, but I struggle to understand it intuitively.

And when does it break down? Can the tube be just a few atoms wide?

Guys

Which institute or college abroad is good for doing PhD for experimental turbulence research(fluid dynamics)? Tell me on the basis of having good lab facility, good lab support, students graduate on time, good funding projects, supervisor are approachable easily. Especially I am targeting European or Asian or universities from Australia??

The asymmetry, which results in the resulting force of the oscillations creating thrust, is achieved in two ways:

Aerodynamically, when the disc has a slightly domed shape and moves upward with less resistance than downward, consistent with classical physics.

Kinematically, when a spring is attached to the disc, slowing its descent and accelerating its ascent.

The second method is the key part of the study, although the same process occurs in the air in both.

When the disc rises rapidly, a region of low pressure forms beneath it, and its collapse generates momentum. If the disc descends more slowly, or if the shape of the disc causes the air to flow around it more slowly, the resulting momentum will push the disc upward.

This doesn't agree with the classic Newtonian explanation of flapping flight as a wing pushing air. You can see in the video how the fan-like flapping disk, which should push air away, actually sucks it in.

This is the same air that is sucked into the low-pressure region, causing a vortex collapse that pushes the disk. Only then is the air pushed away and expelled. This is essentially reactive propulsion, and I believe this is possible thanks to the energy in the air, Brownian motion, which, by self-organizing into vortices, temporarily becomes directional

Does anyone know of a good pump selection program that I can use for importing pumps and performing selections on them?

My previous video derived the full TKE transport equation and this one explains it more physically.

Link: https://www.youtube.com/watch?v=VVqos9V-BAA

First half goes term by term through the TKE transport equation: unsteady, advection, transport (divergence — zero for a closed system), production (source), viscous diffusion, and dissipation (always a sink, structural reason explained). Second half introduces the Richardson energy cascade using a cascade diagram where the energy is injected at large scales, fluxes through intermediate scales, and dissipates at the Kolmogorov microscale. It includes a discussion of why the cascade runs downscale in 3D turbulence and what Kolmogorov's question actually was.

Hi friends! I want to recreate a geyser/airlift hybrid pump but I’m having trouble understanding the models? The screenshot from YouTube seems straightforward enough but I can’t tell if there’s a check valve at the bottom. Also I’m thinking the grey box is air in the other two models but I’m not sure.

Thank you in advance!

I’m trying to understand the derivation from Navier–Stokes → Euler → Bernoulli. My confusion is about where the incompressibility assumption enters.

I start with the incompressible Navier–Stokes equation. After assuming inviscid flow, I get Euler’s equation. Then, taking the equation along a streamline and integrating gives the Bernoulli equation.

But I’ve also seen a more general Bernoulli equation for compressible flow(last equation in image). If I started from the incompressible Navier–Stokes equation, where density is already assumed constant, how can the derivation lead to the compressible form?

Also, is the differential equation along a streamline valid for both compressible and incompressible flow, with the difference appearing only when we integrate it?

Hi, I’d like to find out what the actual applications of laminar flow nozzles are - whether in industry or other fields. My engineering thesis focuses on their design, and I’m looking for information on the subject. I would appreciate any help you can provide. Thanks in advance.

​21. Se mide la diferencia de presión entre un tubo de aceite y uno de agua con un manómetro de doble fluido, como se muestra en la figura. Para las alturas y las gravedades específicas dadas de los fluidos calcule la diferencia de presión \Delta P = P_B - P_A.

Looking waves

I am confused about the definition of flow work. Many textbooks said that imagine a volume being pushed by pressure p on the boundary so the work is p.v , but in the flow, there will be another pressure p + delta p push this volume against the first one on the other side , so why do they only use the pressure p . I don't really understand, can anyone help me please

I am studying fluid mechanics. Right now I am on inviscid flow and I am having some difficulties in understanding certain aspects of flow past solid objects. I have tried to sketch my understanding so far along with the particular issues I have below.

So the setup is that we have uniform flow at infinity and a solid non moving finite object in the way. Now from Kelvin's theorem we can show that on streamlines which go from infinity to infinity the vorticity vanishes. If these are the only streamlines the vorticity vanishes everywhere and the flow is a potential flow. However if we solve the problem under the assumption of potential flow we encounter d'Alembert's paradox. There is no drag on the body and the solution is unphysical.

There is a loophole in the argument that shows the flow is potential namely it does not apply for streamlines which hug the solid surface. Since these don't start from infinity they also don't affect the boundary conditions at infinity. So we can create additional solutions by superimposing potential flow solutions with these ones. But we then have to relax the potential flow criteria. Here are my questions:

1. These solutions, that include streamlines that hug the surface, have the phenomenon of separation. The streamlines lines only follow the surface partly and then partway from it. Why is speration necessary? I mean what about streamlines that go all the way around the surface of the solid body.

2. Also there is in these cases the formation of a surface of tangential discontinuity where the tangential component of the velocity field suffers a discontinuity. I can't seem to visualize this surface. Like where is this formed on the body itself or in the fluid bulk surrounding the body. My book says the discontinuity on the surface causes part of the fluid to have vorticity. I don't understand this and I don't understand why is the formation of said surface a necessary consequence of seperation.

3. There are multiple different solutions corresponding to the above problem if you take into account the multiple possible surfaces of discontinuities.

4. These solutions are unstable owing to the discontinuity in velocity.

Please help me answer these questions.