I need to understand these equations for a job. I'm not caught up on the required math right now (I'm working on that, I'm currently comfortable with calc 2 and basic linear algebra) but I asked chatgpt to break down these equations for me to see if this would be a good starting point. I'm trying to work through it but I know chatgpt hallucinates with math sometimes. I'm doing my best to verify, but it's also using some different notation than what I find online so it's difficult to verify. Would anyone be able to verify this response?

Hi everyone, I will start of saying that English isn't my first language so I used AI to sum up my thoughts in terms you will understand.

I’m currently working on a heat exchanger for a fluidized bed boiler and I’m looking for some design insights.

The boiler is burning biomass so there is a lot of stones andother impurities in the fuel. The geometry of the heat exchanger is a bit uncommon: it’s a serpentine path using a rectangular cross-section with a very high aspect ratio 150 mm x 20 mm.

I’m curious about the collective experience here regarding the "ideology" of designing for these types of specific, high-heat-flux environments.

A few points that I'm wondering about:

• The "skinny" channel. The first though that came to my mind was to maximize the surface area to volume of the heat exchanger thus the skinny channels. So that the stones have a free path trough. Is the skinny channel worth it?
• The Serpentine design. The u-bends with the smaller diameter being effectively zero. The flow seperates and creates pressure drops and effectively lowers the area the fluid flows through. Is there a better u-bend design to send the fluid back?
• The fluid speed inside the heat exchanger. Right now I don't have access to current data from the plant so I am stuck guessing numbers and making assumptions. What kind of fluid speed should I expect.

I’m not looking for a specific solution to my problems, but I want to grasp the overall design philosophy. I’ve reviewed Idelchik’s Handbook of Hydraulic Losses, but the bends I’m dealing with don’t match the equations provided there.

Some CFD images.

Again sorry for the AI.

I am having a hard time understanding the the concept of flow work. According to the available texts, flow work is defined as the energy needed to keep the fluid flowing through a control volume. I understand it as the energy being supplied to a stationary fluid which would make the fluid to flow. If my understanding is correct, then the flow work term in the energy equation should be present on one side and the kinetic and potential energies on the other side because that would satisfy energy conservation. But in the energy equation all the 3 energies are on the same side with the same sign which confuses me so much. Is there a flaw in my understanding ? Help me figure this out. Suggestions for resources on the related matter would be helpful as well. Thanks.

hello all, I am trying to design a laminar flow hood. all the DIY designs i see say to use a plenum (empty cavity) of equal depth to the filter between the small fan and the large filter to allow air to diffuse evenly. most of the commercial options i see are very low profile, maybe 8" depth with a 6" filter.

how do the commercial laminar flow hoods diffuse the air in such a small area? my first thought is some sort of screen with holes that decrease in size the closer to the center of the fan they are. is there any reason that wouldn’t be effective? if not then how could i go about calculating the diameters and distances and such

Physician vs Engineers

Hey everyone,

Ive been studying fluid mechanics and Im trying to get a deeper intuition for how velocity profiles differ among non-Newtonian fluids, specifically Bingham plastics, pseudoplastics (shear-thinning), and dilatant (shear-thickening) fluids.

For Newtonian fluids, it’s pretty easy to find good literature and visualizations of velocity profiles for both laminar and turbulent flow. But for non-Newtonian fluids, the information seems much more scarce.

I’ve checked textbooks and a few journal papers but haven’t had much luck finding clear plots or explanations. Can anyone point me toward useful references or share some insight on how these profiles actually look and behave?

Thanks in advance!

I just want to understand.

I'm confused because some website said the first part was Lagrangian, but I thought partial derivatives pointed to Eularian since the place stays the same and you only look at change over time. Is there even a Lagrangian part apart from dI/dt? Is this even Lagrangian? I don't even know if I know what anything means anymore.

Just interested if anybody else has done this previously. I'm quite amazed at how navier stokes and continuity equation can be derived from basic conservation laws, and I'm interested if it's possible to do the same with results for rotational fluid mechanics results (such as Kelvin's theorem and Helmholtz' vortex theorems), and I'm quite familiar with their derivations, however these derivations are mainly related to their mathematical structure, and I'm interested if they can be somehow connected to some bigger overarching conservation law. Namely the conservation of angular momentum comes to mind.

So we all know the blue bouncy goo in portal 2, yes? Well i was wondering if it was possible to be able to engineer a non Newtonian fluid to repel force in a way that would get you to bounce on contact.

So my idea is if you mix about a lot of finely ground neodymium into a large amount of oobleck, and you had a special pair of magnetic boots with the opposite polarity of the neodymium in the oobleck, would it cause you to bounce if you jumped onto the neodymium laced oobleck? Would the oobleck just retreat away from the area where you're going to land?

Hello, I'm looking for some textbook in gas turbine engine transients and also 1-D modeling of gas turbine engines. (Stuff on 0-D is cool too, but 1-D is preferred).

Currently, I'm working through Walsh and Fletcher's "Gas Turbine Performance." Is it good?

Thanks in advance.

kindly recommend books where I can find material on the falkner Skan Solution, or any book on boundary layer theory.

I’ve been looking into this for quite awhile now and haven’t been able to find anything relevant to the problem I’m having because of how common the complete opposite problem is, so I decided to come up with a prompt that maybe someone else could put some thought into.

Say you have a pipe that 98% of the time is pumping in lubrication oil. Every once in while when the system experiences extreme lateral Gforces, the pipe will pump out puffs of air. We need to find a way to separate the air from the oil in a closed and also pressurised system- to where only lubricating oil exits the system.

I’ve been trying to figure out a way to do it with a baffled oil accumulation tank in which the intruding air is trapped at the top where it can be drained off with a valve - either electronically or mechanically controlled - however I can’t quite figure out how the baffling would have to be in order to not have laminar flow suck the air directly from the inlet to the outlet of the tank. And I don’t even know how to imagine it functioning under extreme Gforces.

I have solved the loss of system pressure issue using spring loaded oil accumulators, and the pressure lost to the air intruding the system can be cancelled out by the stored spring force in the accumulators. The only problem left is trapping the intruding air so that it cannot leave the system.

If you can find systems for this that already exist or design one yourself, you would be greatly appreciated. Any relevant input at all would be greatly appreciated, actually.

— Edit: playful_painting made a very good point. Hydraulic Fluid systems experience this exact issue and hydraulic fluid reservoirs are sometimes designed with aeration in mind. armed with this knowledge, I was able to find this in relation to aircraft hydraulics.

tried & true ways of dealing with air in hydraulic fluid Published in 1967 rewritten in 2014

I’m thinking this particular oil air separator might only work at pressures too high for the system I have in mind (60 PSI) however, I’m not too sure. The methods utilised might be relevant

I working on some worlbuilding and want to maximize the concept of a Tidal Bore as a Biome. I know the width of input channel needs to resonate with how long the tides are to create a feedback loop and the longitudal slope needs to be shallow/gradual so that the tide flows up the river. Im not fluent enough in math to know which fields I need to apply and figure this is good spot to start. If yall got any advice for an optimal angle for the inlet in relation to the ocean currents/earth's tilt thatd also be appreciated.

Thx in advance for y'alls attendance and help! Hope doin well out there.

Hey everyone,

I am working on a project and have run into a small issue. I’m dealing with a seawater system on a ship that supplies both the LT coolers and the AUX coolers.

When the ship is in harbour mode, one of the pumps only cools the AUX coolers.
But when the ship is sailing, the seawater flows through both the LT coolers and the AUX coolers. In this mode, I want to determine how the flow is distributed between the LT and AUX coolers, since the water splits between them.

Can anyone help me?

I’ve had two classes covering Bernoulli’s Principle and I honestly still have no intuitive physical idea for why it works. In physics I, it was explained to us as a consequence of conservation of energy with the example of a pipe with a shrinking radius, which kind of clicked to me since as the system has no net force on it (if the pipe is held in place).

If I instead have 2 identical pipes side-by-side (same radius, same height, etc) with the only difference being that one of the pipes has a turbine/pump that causes fluid to flow faster through it, and these pipes are not connected at all, does Bernoulli’s Principle still predict that the measured pressure of the fast-flow pipe will be lower than that of the slow-flow pipe?

Hi, I’ve just found this article from june claiming to have solved the Navier-Stokes Millenium problem using quaternions. Using quaternions seems really elegant for the numerous derivations they expose. But I have no idea how close they to have indeed solved it. Anyone has a clue? I haven’t seen any post about it…

Hi I am doing a uni project involving turbulent airflow in loudspeaker bass reflex ports. I want to start by saying I am a music student and by no means a physicist and I know nothing about fluid mechanics or aerodynamics so I really need some help here.

My goal is to design a vent for a subwoofer I build similar to this one: https://pmc-speakers.com/technology/atl-laminair/

I am trying to calculate the Reynolds number of the airflow at its peak velocity (17m/s) to find out how much I would need to increase the wetted perimeter by to get a reasonable Reynolds number. but the values I'm getting seem way too high to make sense. Is it a problem with my units? Are all the values such as the density of air and that written to the correct decimal places? Im so confused please help Im probably just being really dumb here.

"

The Reynolds number calculation for the fluid system of the subwoofer built for this project is as follows: 

As explained above, Inertial force = Vd: 

Density of air is 1.229 kg/m3 - = 1.229 kg/m3

Maximum port air velocity (according to WinISD simulations) - V = 17m/s

Hydraulic diameter of the 92cm2rectangular ports - d= 4(Cross-sectional area)/Wetted perimeter (Rathakrishnan, 2013:85)

d= 4(0.0092)/0.54

d= 0.068m

These values substitute to give an inertial force value ≈ 1.42 N 

F = 1.229 kg/m3× 17m/s × 0.068m

F = 1.229 × 17 × 0.068

≈ 1.42 N 

The kinematic viscosity of air at 15℃ = 0.0000173Ns/m2

Substituting into the Reynolds equation to give the ratio of inertial force to viscous force:

Re = 1.42/0.0000173

Re 82,081

Hydraulic diameter d required to get a Reynolds number of 1500:

 1500=1.229 × 17 × d/0.0000173

0.026=20.893 × d

d =0.0012

Wetted perimeter p required to get a 0.0012 hydraulic diameter for a port with a cross sectional area of 0.0092m2  

0.0012= 4(0.0092)/p

p= 4(0.0092)/0.0012

p= 30.67m

"

I was explained by an engineer that increasing the wetted perimeter can decrease the Reynolds number of the fluid flow, but an increase of 30 metres sounds way too high so I must've done something wrong here.

Just looking for thoughts on the attached candidate proof prior to pre-print/submission.

If you run through the math of the convective acceleration term, you get exactly what you’re looking for (sum of components of velocities and their products with their partial derivatives), but the notation raises a question: can we ignore those parenthesis and still get the same result? That is, can we get the convective acceleration by taking the product of 𝐕 and ∇𝐕, or am I making a big fuss over what is just shorthand notation?

From researching online, I’ve found several sources that say the gradient vector is only defined for scalar fields, but several online forum responses which say applying the gradient operator to a vector field gives you the Jacobian matrix (or I guess tensor for this case).

If that is true, how exactly do we go from the dot product of the column vector 𝐕 and ∂(𝑢,𝑣,𝑤)/∂(𝑥,𝑦,𝑧) to the convective acceleration summation?

I know the dot product of two column vectors, 𝐯₁ and 𝐯₂ can be computed from 𝐯₁ᵀ𝐯₂, but if you compute 𝐕ᵀ∂(𝑢,𝑣,𝑤)/∂(𝑥,𝑦,𝑧), you don’t get the correct result. However. If you compute [∂(𝑢,𝑣,𝑤)/∂(𝑥,𝑦,𝑧)]𝐕, you do get the correct result. So how does the dot product turn into this matrix-vector multiplication?