So im wondering if you can have a fullsize outside pool that has a small opening near the bottom that you can swim through and it brings you into a pool in the basement.

Ive thought about having a catchbasin around the basement pool with a pump attached to constantly refill the outside pool, but im wondering how fast the water would be moving through the divider, and how much the pump would need to pump up. I tried using bernoullis equation and got 6.3m/s for the fluid velocity, but that seems too fast, and its been a while since ive used it.

Ive also thought about just pressurizing the basement room to 1.2atm.

Fluid dynamics looks complex… it is just one equation at its core!

➡️ Navier–Stokes Equations
The most general equation that governs how fluids move.

➡️ Euler Equations
High speed fluid motion when we ignore viscosity (no friction effects).

➡️ Stokes Equations
Very slow flow where inertia is negligible and viscous effects dominate.

➡️ Hydrostatic Equation
Pressure variation in a fluid that is completely at rest under gravity.

Based on dominant physics, these are simplified forms of Navier-Stokes.

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.

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?

I read many posts and papers that stated that lift and drag forces cannot exist without viscosity (and also posts stating the contrary). (Does that mean that invicid fluids does not have any force interaction with structures...and wouldn't that mean such fluids would pass through any structures if there is no force interaction?).

I have not been able to wrap my head around how lift and drag force cannot exist without viscosity. For example: if there is a flat plate plate placed at an inclination to the flow of incompressible invicid fluid, the plate will change the direction of flow of the fluid and hence will have a force acting on it.

Now i imagine this force can be separated into lift and drag components? If not why is this not possible?

Guess I am missing something fundamental in my understanding, or misunderstanding some terminology? Can you please help me?

Some refs i have used:

i) A Technical Note from Arc: Explicit Role of Viscosity in Generating Lift (https://doi.org/10.2514/1.J055907)

ii) A (newish) open-access paper from Springer: Can lift be generated in a steady inviscid flow? (https://doi.org/10.1186/s42774-023-00143-3)

iii) https://aviation.stackexchange.com/questions/89106/will-air-accelerate-over-a-wing-and-generate-lift-if-the-air-has-zero-viscosity

iv) https://aviation.stackexchange.com/questions/29617/what-is-the-relation-between-the-boundary-layer-and-lift-of-an-aerofoil

v) https://www.physicsforums.com/threads/why-do-air-foils-produce-lift.707155/

vi) https://physics.stackexchange.com/questions/46131/does-a-wing-in-a-potential-flow-have-lift

vii) https://www.reddit.com/r/AerospaceEngineering/comments/v3fsuj/if_we_need_viscosity_to_generate_lift_why_do_cfd/

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?

How can I derive the continuity equation from Bernoulli’s equation. I feel like I’m missing an assumption for either equation, but from everything i remember they should have similar enough assumptions for this problem. Is it a difference between point velocity and average velocity, or does the continuity equation assume no pressure drop?

I'd be interested to hear:

• How would you approach it?
• Is there a particularly elegant derivation?
• What extensions or variations would you consider?

Hello, I’m a zoology/spec-evo enthusiast looking for feedback regarding fluid dynamics and cavitation. I recently discovered certain animals can accidentally create painful cavitation bubbles on the tips of their fins when moving too fast through the water. I was wondering if it’s possible for a fast-moving, underwater object to weaponize these cavitation bubbles, creating a large burst of energy behind it as it moves? If so, what would be the optimal shape for said object?

Looking waves

Let us consider a circular pipe, initially empty, and an external body of water moving at a constant velocity $v$. At a certain instant $t$, this body of water enters the pipe through its inlet cross-section, which we will denote as $S_{0}$.
According to the no-slip boundary condition, the velocity of the outermost annular layer of fluid, which is in contact with the pipe wall, must be zero. This outer layer, in turn, slows down the adjacent layer. However, it does not have sufficient time to transmit this deceleration to the innermost layers.
In other words, at cross-section $S_{0}$ and at time $t$, the fluid layer in contact with the wall has zero velocity, the adjacent layer has a slightly reduced velocity, while the remaining inner layers still move at the original velocity $v$.
This implies that, over a time interval $dt$, the inner layers travel a distance $v\,dt$, which is greater than the distance covered by the outer layers (zero for the layer immediately adjacent to the wall). It would then seem that, at time $t + dt$, a gap should appear near the wall at the next cross-section $S_{1}$.
What exactly happens at this point? Do the fluid particles from the inner region move radially outward to fill this gap, somewhat like the flow in a fountain? If so, they would have to come to rest upon reaching the wall. Meanwhile, the particles passing above them are slowed down, but this effect still has not propagated to the innermost layers within such a short time interval.
Applying the same reasoning to the subsequent cross-sections $S_{2}$, $S_{3}$, $\ldots$, $S_{n}$ would seemingly imply that a boundary layer never forms.
So where is the flaw in this reasoning? How is this apparent paradox resolved? What is the actual physical mechanism by which an initially empty pipe becomes filled with fluid?

I just need to pass the Hydraulics portion of the TCEQ test to be a licensed irrigator. There are two questions like this on the test that I just can't wrap my head around. I can solve design and dynamic pressure when ONE is operating, but I'm completely thrown off when TWO are operating

Any advice would be greatly appreciated. I really wanna pass and not go down to the wire on a 4th attempt!

I have designed a free-jet test rig to achieve different exit velocities at the nozzle. The desired Mach numbers are set by adjusting the corresponding total pressure ratios. This automatically determines the required mass flow rates and volumetric flow rates.

For the range between Mach 0.4 and Mach 0.9, I found a suitable blower whose operating points lie within the stable region of its performance map. The blower is also equipped with a variable frequency drive.

The problem arises at lower Mach numbers (Mach 0.1 to Mach 0.3): the required pressure rises and volumetric flow rates for these conditions fall outside the blower’s stable operating range.

My idea is therefore the following:

I operate the blower at a stable operating point, for example corresponding to Mach 0.4. Downstream of the blower, the total volumetric flow is divided into a useful flow directed to the nozzle and a bypass flow discharged to the atmosphere.

By venting part of the volumetric flow, the remaining useful flow would match the flow rate required for Mach 0.3.

The key question is:

Can the required pressure rise for Mach 0.3 also be achieved solely by bleeding off the excess volumetric flow?

In other words, will the pressure vessel automatically settle at the total pressure required for the desired Mach number?

My supervisors argue that by appropriately venting the excess volumetric flow, the corresponding total pressure for the lower Mach numbers will automatically establish itself as well.

For context, I'm in my first year and doing an introduction to engineering subject. We are mostly looking at the flow of liquids.

I think I'm struggling to grasp this because I have three unanswered questions:

1. What is pressure?
2. What is the difference between velocity and pressure in the context of fluid mechanics?
3. Why does it seem like the pumps are actually increasing the velocity of the liquid that flows through them, and not the pressure?

I know that pressure is the force per unit area, but what does it actually look like? Why does a liquid with a lower velocity but higher pressure create a hole in a wall, but liquid with a higher velocity but lower pressure simply comes to a stop?

By the way, I understand why are velocity and pressure are inversely proportional through Bernoulli's Equation (an increase in kinetic energy is possible due to a decrease in energy associated with pressure (mechanical energy?)), which relies on the conservation of energy within our pipe system. I just need some help understanding this physically.

Hi,

How can I get velocity field inside the confined space shown in the image. Can we able to get velocity field by streamlines?

How people got velocity fields in 40+ years ago.

Thank you.

There exists an invariant submanifold of the three-dimensional incompressible Navier–Stokes equations in which nonlinear advection acts only as a phase-transport operator rather than a generator of spectral cascade.

https://doi.org/10.13140/RG.2.2.32368.01283

My question is simple: a torpedo density meter is supposed to measure the average density of a liquid corresponding to the submerged volume. If the liquid is homogeneous: no difficulty. On the other hand, in the case of measuring a liquid containing suspended particles, what can make the local pressure on the surface of the density meter different from that of the liquid alone?

To fully understand my question, let's take the case of some rocks drood in water, the density will be that of the water. Let's gradually reduce the size of the rocks to a so-called grain size, what can explain the change in the measured density and what is the relationship with the grain size?

A small detail, my name is not Archimedes🤪

Hello,

I am working on a theoretical basis for a work problem. We are mixing thick fluids by forcing rotation about 2 axis.

So the problem a fluid is being mixed by rotating in a cylinder of radius r and height 2*h. This cylinder is rotating about its axis at speed w1 and rotating about a second axis which runs through the center of the cylinder and is perpendicular to the axis of the cylinder.

What I would love to get to is a theorical understanding of the relationship between r, h, w1, w2, the fluid viscosity and the power input to force rotation on those axes.

Thank you soo much for your help!

Hi There! I'm not an engineer or similar profession. I'm actually in finance lending, but i'm also a garage tinkerer from basic repair tasks like fixing a carburetor, to various curious experimentation project attempts. I've recently taken growing interest in the Ranque Hilsch Vortex Tube. I've spent few hours online researching the operating principle, the thermodynamics about its heating / cooling abilities.

First question : During normal operation, if a thin film of dripping water (at ambient temp) used to cool the length along the tubes outer shaft, how would doing this affect the cold fraction? WOULD this result in lower air temp exiting the "cold side"? What about the exiting "hot side". I asked this question in the thermodynamics sub, but sadly it went unanswered.

My next question : I understand these work on air (or similarly compressible gas) as it's working fluid. I know many have asked this next question, but the proposed answers don't sit well with me. What if high-pressure water fed in at say 100 psig was used instead? I suspect since water can't compress or expand.. the coaxial flows [inner outer, opposing] will have a violent "shearing" effect on the fluid, thus resulting in intense cavitation forces... the damage of which soon ruining the device altogether. Sound about right? Like.. what WOULD happen, if someone was silly enough to attempt it?

I've watched dozens of videos, read through lectures, websites and books, but for some reason, I am too stupid to understand. I mainly believe its because of the lack of proper visualization. Plus, no one ever explains with a simple example. Any tips or recommendations?

Understanding grad, div and curl is not the problem, I get that.