sethoflagos

Let's let this thread die a well deserved death. The well has been poisoned by those unable to yield ground in their turf wars.

= Kinetically Imparted Common Knowledge

Firstly a word about deriving the result from Newton's second law. Maybe you missed the details of my earlier post: Please read the first calculation line carefully. I begin with rate of change of momentum, just as @swansont recommends, but since I can't integrate that directly I use the chain rule to recast the ODE into a simple form I can integrate. This gives the correct answer. Attempting crude numerical integration of the raw momentum equation via left Riemann sum as we saw yesterday gave a 100% overestimate, to which I suggested you try the middle Riemann sum. You are right to maintain some doubt over the validity of this procedure. It gives the correct solution but only by accident. You're working with at least one assumption that is profoundly unphysical. I made a little explanatory sketch of how I see air flow over a wall. (A small one - let's keep it simple) Interactions between the wind and wall are mediated by a clockwise rotating prism of air that acts as a ramp to accelerate the incoming airstream up and over the wall. It is clear that the main flow retains much of its horizontal momentum throughout - it doesn't dump it all into wall in fact it mustn't (continuity). But it isn't total momentum that is in the equation - it's rate of change of momentum that counts. So what happens inside the prism. Wind shear transfers momentum into the angled face accelerating it up to near bulk velocity. And that momentum is transferred via an exchange of angular momentum with a flow parallel to the wall rather than linear momentum from direct impingement. A similar effect happens on the ground providing the necessary reaction to generate upwards momentum. Almost none of the main flow gets anywhere near the wall. Anyway, this model works for me and is pretty close to what I've seen from wind-tunnel tests of blast walls and the like. Hope it helps someone out there, though I suspect the OP is long gone after yesterday's sorry show.

I'm sorry Josh, I missed the last bit. I took a little time out from the dog-piling to check my facts. I read the OP as 'What is the stagnation pressure acting on a wall normal to a headwind'. The response I gave is simply textbook fluid mechanics and is correct given the stated assumptions. I find it strange for once being called on to defend the Bernoulli equation, but then lots of things seem strange to me these days. Both viewpoints expressed comply with conservation of momentum. The key difference is that I reduce momentum incrementally into a dynamic pressure field while others drop all the incoming momentum at the face of the wall. Now I have an easy way of propelling the fluid up and over the wall: it's accelerated up and away by the pressure field built with the momentum of the incoming stream. Others seem to have stationary gas stuck to the wall and no source of energy to move it away. I look forward to some imaginative explanations.

The calculations you presented specifically state 'The jet strikes the plate and does not rebound but spreads sideways over the surface of the plate. The momentum normal to the plate is destroyed.' Sounds pretty inelastic to me. It seems quite credible. Just inappropriate to the OP. In particular there is no mention of the jet being slowed by an adverse pressure gradient prior to impact. In fact no mention of pressure at all. Which at least then avoids having to explain away the infinite pressure necessary to bring a jet to a halt instantaneously. I provided my own simplified calculation of 'the force of the wind' some dozen or so posts back. Perhaps you could tell me where exactly the mistake is?

What a very curious idea. Why exactly are inelastic impacts relevant to the discussion?

No worries. Just adjust the first line of your calc to dL = (v/2) dt and I think everything else clicks into place.

Of course Bernoulli is an energy equation - that's what you get when you integrate a force balance. If kinetic energy is conserved as you say, then where does the work necessary to compress the air come from? These things do happen very quickly but they are not instantaneous. The momentum exchange does not occur at constant velocity v. It occurs gradually over the velocity range v to zero. On average that's v/2. This is why your results are double what they should be. You need to integrate over a valid path.

One problem with this approach is that the system is steady state so there is no clear timelime to integrate over. However we can proceed along the lines of: dP/dx = -p dv/dt = - p v dv/dx hence dP = - p v dv If we keep things simple and ignore air compressibility and elevation changes we get on integration P1 - P0 = pv^2 / 2 Which is a form of the Bernoulli equation.

Ask yourself what the phrase "went up 50 points" actually means. It means the narrator believes his audience is too stupid to understand the actual units, how the increase relates to a normal healthy range, and how that translates to a quantifiable increased risk of serious disease. I have fairly frequent blood tests for other reasons, but have never had my cholesterol level flagged despite getting most of my protein from eggs (I probably average about two a day). So I'm comfortable with dismissing this video as somewhat offensive, partisan rubbish. Those who do have high cholesterol levels should heed the advice of a qualified medical practitioner who has properly assessed their health condition.

If you work it through F = ma becomes F = density x area x velocity^2 / 2. Divide by area and you get the pressure rise acting on the windward side of the wall. On the downwind side the reverse happens, air is accelerated back up to wind speed creating a partial vacuum. The nett force on the wall is 2F (give or take).

Yes, though the full belt can be traced from the Algarve to Bohemia (see https://en.wikipedia.org/wiki/Variscan_orogeny)

The ophiolites I've personal experience of, the Lizard complex and Ballantrae complex are pre-Mesozoic (associated with the Hercynian and Caledonian orogenies respectively) and extensively altered. But some of the rocks are absolutely gorgeous, especially the serpentinites.

No I don't. The initial heating and cooling effects are one offs. A small amount of heat transferred between two bodies at the cost of some of your initial potential energy. If you try to make use of the temperature difference in any way, the machine will compensate until all its initial potential energy input has been consumed. And then it stops.

Cyprus has one of the world's best exposed ophiolite sequences (uplifted oceanic crust), the Troodos Ophiolite.

Absolute energy values are irrelevant - it's the changes that matter. The change in potential energy of the ball between highest and lowest points of travel determines the change in internal energy of the gas at those positions which in turn determines the maximum temperature change of the gas. dU + dEP = 0 is not a really hard sum to solve. Yes it's a sort of simple refrigerator. It's also a sort of simple harmonic oscillator with potentially minimal damping. So it's also a candidate for perpetual motion machine of the third kind. No, it won't run 'forever' but stating that there is finite limit to how long such a device could remain in motion would be a falsehood.

The little bit of energy you put in to get it running in the first place. If you deny the necessity of this then fine. Just produce a refrigerator that operates continuously with no energy input and we can continue the conversation. Until that happens then words are just words. No science here.

Okay, we're agreed that with a little initial energy input we can cycle indefinitely between two temperature states. Okay, I'll accept that obscure terminology can be a bit confusing. Let's avoid the unnecessary and cut to the important bit. I accept 100% that starting at uniform ambient temperature and given that little initial energy input, it is possible to produce a hot body and a cold body. Not impossible at all. Most of us have access to a refrigerator.

Many wind musicians (especially trumpets) are occasionally called on to 'fluttertongue' which is produced by rolling the tongue. Some find it harder than others (depending on their mothertongue as much as anything else) but most seem to get the hang eventually.

To the extent that if a machine exists that lost half it's 'bounce energy' in a week, there's every reason to suspect that with a little more investment that performance could be extended. And so on. You're adding heat to a closed system so the temperature rises throughout the cycle until there's no more incoming heat. And the expansion has hit your compression ratio so you don't see on the hot side what you've lost on the cold side.

Focus on the 'bouncing ball' assembly in the middle of the apparatus. If there are no losses from the system, the cycle can be described by the equation: U + EP + EK = constant where U is the instantaneous internal energy of the gas and proportional to it's temperature; EP is the instantaneous potential energy primarily due to the height of the ball in the tube, and EK is the system bulk kinetic energy realised in the instantaneous velocity of the ball. At rest, everything is at ambient temperature, the ball is stationary with no kinetic energy, and at some intermediate position where its mass is supported by the air pressure beneath. To start the process either the ball must be raised to the maximum height, minimum temperature position, or depressed to the minimum height maximum temperature position, and subsequently released. Both these actions require a significant input of work. The system can in principle then continue to oscillate between these points cycling between high and low temperature (either side of ambient) moreorless indefinitely. No physics is being broken so far. The problems happen when you try adding or removing heat to/from the device. The stored energy used to start the machine runs down. There is no free lunch.

No. The 1st Law treats W & Q as equivalent. The 2nd Law was introduced to help explain their observed differences. eg why it is possible to convert W into Q completely while the reverse is not true.

You claim to derive the 2nd Law from the 1st Law in this (unreviewed?) reference. However to do this you rely on the relation dU = dQrev = TdS, which is a 2nd Law statement. Therefore your claim is undermined by a very obvious fallacy.

One picture that I found comfortable is to firstly accept that the paths taken are simply governed by a form of least action (via Fermat's Principle of least time) - which I think is one way of saying that any potential deviation from Snell's law would be corrected by wave interference. Then taking a first law view, the total energy of the incoming light is transformed at the interface into a composite package of equal energy that now includes some level of induced motion in the local lattice electrons. This package, if viewed as a particle in its own right, now has some albeit small mass and therefore must adopt a sublight speed appropriate to the amount of 'baggage' it's now carrying. When leaving the medium the lattice field reclaims its baggage and returns its borrowed energy back to the reconstituted photon which continues on its way. I'm sure there's some phrasing here that I've got wrong but at least it's a process I can picture.

Much of what you say is correct which is why they got ignored for over a century. Compared to IC engines, they're more amenable to renewable energy resources (such as solar collectors etc); they can be very quiet; and as static devices they're quite competitive in cost with IC up to ~100 kW.