sethoflagos

The total mass of the oceans slightly depresses the equilibrium level of the oceanic plates, thereby slightly increasing the underlying mantle pressure sufficient to raise the less dense continental plates by an (approximately) equivalent degree. The causal factors for the onset of plate tectonics, and its timing are currently major open questions. As @exchemisthas noted, it seems entirely plausible for the oceans to have supplied some chemical and lubricative effects to facilitate the process. As they still do.

A bit after the lord mayor's show,. However ... While thermal expansion must play some part in mantle convection, it seems that the primary driver is phase change (ref: https://authors.library.caltech.edu/25038/145/Chapter 5. The eclogite engine.pdf). This implies that most of the transported energy is locked up in the enthalpies of various sequences of crystal structural readjustments with depth (eg the olivine-wadsleyite-ringwoodite-perovskite sequence) rather than as thermal energy. Hence there is within the mantle a huge reservoir of energy bound up in high pressure mineral polymorphs, that may be released as heat at specific lower pressure locations (mid-ocean ridges. volcanic island arcs etc) moreorless independently of the overall thermal gradient. This localised heat release drives the processes of crustal magmatic fractionation, adding low density granitic material to the continents, and consequently increasing the density of the returning subduction slab. The excess of gravitational potential energy of this continental scale mass of dense material over and above the surrounding asthenosphere represents a second huge reserve of energy that is partially returned as heat back to the base of the mantle, but is mainly consumed in restoring the high pressure polymorphs of its constituent mineralogy. Overall, the process of continent building via magmatic convection and fractionation might be approximated as raising 3 billion km3 of granite (SG ~2.5) through 1,000 km of mantle (SG ~ 4) which looks like 4.5 x 10^28 Joules over a period of 4.5 billion years resulting in a heat output of 0.3 TW purely on isostatic considerations. Contrast this with the estimated total crustal heat flow of 47+/-2 TW (based on 38,000 measurements). If we were to consider the approach toward gravitational equilibrium of all structures within the earth (not just the surface ones), then the process of planetary differentiation (ref: https://en.wikipedia.org/wiki/Planetary_differentiation) would seem to amount to an appreciable percentage of the total. And that's based only on the isostatic aspect. We are as yet nowhere near full planetary chemical equilibrium either, and that must also factor into the balance sheet. I've seen figures of ~20 TW given for the heat produced by radioactive decay, and can only add the comment that it seems credible. More critically some authors have ascribed the balance to 'primordial heat'. I don't quite know what they mean by that. Or rather, I do. It's the heat generated during the initial accretionary growth of the planet, the sum total of initial gravitational potential energy of all its constituent parts and released as heat on impact. But isn't this just the initial phase of planetary differentiation? The phase where space was gravitationally displaced by matter? And has it been sat around doing nothing since? I think not. Rather its being doing what heat does - driving convection currents and fuelling endothermic reactions for the last 4.5 billion years. Seen in this light, I'm tending to lean towards there being an approximate balance between radiogenic heating and the nett release of gravitational and chemical potential energy arising from planetary differentiation.

Of course this is true. However centrifuges can work perfectly well in the absence of gravitational forces so for the purposes of the OP ... etc. Not that it's much of a complication. Gravity simply adds a vertical gradient to the pressure field caused by the fluid rotation, and the particles respond accordingly. Btw For some light reading, try 'Spray Drying of Detergents in Counter Current Towers', Victor Francia Garcia, School of Chem. Eng., University of Birmingham (2014). Link https://etheses.bham.ac.uk/id/eprint/5646/1/Francia-Garcia15EngD.pdf (if permitted) Interesting stuff on particle structures, density, porosity etc in Appendix II (page 260 and on)

Just reproduced the experiment with a capful of Ariel Original in a saucepan of freshly swirled water. The powder takes a significant time to wet thoroughly (about a minute). So while many of the individual components may well have densities equal to or exceeding that of water, under what I understand to be the OP's conditions, it appears that the detergent 'phase' while it exists retains a substantial air content, significantly suppressing its density. Putting numbers to this would be very difficult, but the proof of the pudding is in the eating. Until wetting and dissolution is complete, the detergent sits in the central vortex of the swirling liquid.

Best to consider this in terms of pressure gradients as concepts such as centrifugal force are artefacts of circular frames of reference and lead to misunderstandings. Suppose the fluid comprises x parcels all of equal volume. Each parcel is subject to an acceleration towards the centre of the bowl due to the rotational flow regime that you initially imposed on it. Each responds by generating a reactive inertial force (your 'centrifugal' force) in the opposite direction acting on their immediate outward neighbour. These reaction forces stack up to generate a pressure field that is a minimum at the centre of the bowl and a maximum at the outer wall. And it is this pressure field that gives a nett push toward the centre (ie, your 'centripetal' force) on each parcel causing the acceleration that maintains the rotational flow regime. Now consider a single parcel that is a little denser than its immediate neighbours. Due to its extra mass, the local pressure gradient is insufficient to accelerate it as much and so it tends to better maintain its course and moves outward, using its extra inertia to displace its outward neighbour(s). In turn, lower density (lower mass) parcels subject to the same pressure gradient will tend to accelerate toward the centre more readily, lacking the inertial punch necessary to prevent heavier neighbours from displacing them.

In principle, it should be possible to incorporate a micro Combined Cycle Gas Turbine power plant into the design of a large tractor unit. Modern designs of CCGT are routinely specified at >50% thermal efficiency, so it should represent a major advance on your historic baseline. Putting solid fuel through a GT is a bit problematic so you'd likely be looking at some version of liquid biofuel (biodiesel, ethanol etc) for base fuel as a practical proposition. Following combustion in the GT, the exhaust gas would pass to a HRSG (Heat Recovery Steam Generator) raising superheated mains steam to feed a condensing steam turbine, with condensate recovered from (perhaps) overhead air cooled condensers for return to the steam drum. The water circuit would therefore be closed cycle. The split of power output between the cycles would be of order 2:1 (GT:ST) so I guess it wouldn't quite be pure steam punkery.

Yes, thank you, Genady. Trial and error seems to indicate so. But how does one derive those values mathematically?

My scribblings came up with the following interesting function f(x1,x2,... xn) = -ln(x1^x1*x2^x2*,... xn^xn) Where: x1+x2+... xn = 1 0<xi<1 I suspect that this function ranges 0 to ln(n) but a proof is beyond me. Assistance would be most appreciated.

I'm more familiar with the sprung ball detent type wrench, so notwithstanding ... : As stated in my previous post, deflection angle is proportional to the applied moment for a given wrench length, so providing you dont try to apply load from somewhere other than the end grip, the two should be linearly correlated. I see no need to go any further than the static force balance here. Serious bolt tensioning is best done without significant dynamic loadings.

It's called the 'angle of deflection' and for an ideal weightless cantilever is proportional to the end load times the square of the cantilever length. Since this is a fixed displacement (the beam doesn't continue to move) mechanics in particular will tend to refer to the loading force as a moment rather than a torque. They are sort of the same thing, but torque is used more in the context of rotating bodies like crankshafts, and this can lead to confusion if the terms are applied haphazardly. Useful Wikipedia lpages to browse through may be Deflection (engineering) and Euler-Bernoulli beam theory.

No. At point A, the fluid is high pressure liquid phase at ambient temperature. At closure of valve B, it is low pressure mixed-phase stream at some lower temperature. Getting back to point A requires both recondensation (path B-C) and recompression stages (path C-A), which you have indicated on your P-V diagram, but failed to address in your process description.

On this sunny Lagos afternoon, the first thought that occurs is that liquid carbon dioxide in my ambient conditions would be in the neighbourhood of its critical point (78.3 bara, 31.1 deg C). Perhaps it's a shade cooler in most of Russia today, but even so, we need to be extremely wary of any processes that seek to gain advantage from assumed PV behaviour under gas-liquid phase changes. In the vicinity of the critical point, such leverage vanishes as gas and liquid become indistinguishable. Next thought is that the OP process schematics (Fig. 1-3) do not match the PV cycle shown in Fig. 4. Since no actual numbers are supplied, it's reasonable to take path AB (piston induced vapourisation/vapour expansion) at face value. However Figs 2&3 indicate a subsequent reversal of this process (piston induced compression/condensation). Even if it were possible to remove all thermodynamic inefficiencies from this cycle, the return PV path BA would simply overlie AB. No nett work, no nett cooling, no creation of the 'convenient' heat sink of tank B. By contrast, Fig 4 gives path BC, an isobaric contraction (~ideal condenser stage) followed by path CA, an isochoric compression (~ideal liquid pumping stage), both of which represent parasitic external energy inputs not disclosed by the OP. The implied external refrigeration plant (realising BC) is going to be a thermodynamically expensive item in particular.

If you read the quoted blog link to the end, you'll find: ... a point that was disputed by some when I raised it earlier. Nice have it confirmed!

40 years practice in fitting a chilled beer flash calc onto the back of a beer mat.

Sherwood & Prausnitz (1962) give the following relation: Enthalpy of Soln. (CO2) = 106.56 - 6.2634x10^4/T + 7.475x10^6/T^2 kJ/mol Plug in 273.15 for T, and this gives around -22.6 kJ/mol at normal water freezing point. So when you release the pressure, the heat of solution is lost to the escaping gas, and your drink autorefrigerates to a supercooled state, the released gas bubbles providing nucleation points for the formation of (typically) frazil ice. About 3g ice per litre of CO2 released as a rough estimate. This effect may be enhanced by the factors mentioned above by Swansont.

But my post wasn't about manuring, green or otherwise was it. It was about composting. Why the misdirection? Hydroponics may well be an improvement over some other earlier technology, but it does nothing I can see for the disposal of garden waste, animal bedding etc. The available alternatives for those duties are burning or landfill. These are not improvements imho, far from it. Incidentally, you may have seen the recent publicity push for post-mortem composting. An ancient solution to serious contemporary issues. Does 'straw man' have a collective noun? Seem to be gathering in flocks.

Moreorless exclusively by fungi as I recall. I think it's the lignin content that can cause nitrogen depletion so perhaps there's some variation with species. Also, unlike fresh leaves, the C-N ratio for typical autumn leaf fall is quite high at 50:1, double the 25:1 you typically look for in a good compost mix, so it doesn't bring much to the party nutrient-wise. Great soil conditioner though, at least when it's become leaf mould. Aren't forest soils typically high on organics, low on nutrients? Not entirely sure why. Back in the day, we had friends who kept horses, so my nitrogen supply never became an issue. Okay... So how do they dispose of surplus organic material?

If you deny yourself the benefits of a key neolithic technology that has not been substantially improved upon in the intervening millenia, what grounds do you have for anticipating anything beyond a pre-neolithic level of return on your labours? For what it's worth, most tree leaves take at least a year to break down fully in temperate climates, so they're usually composted separately. Using them for mulching before they're properly broken down will (if memory serves) rob the soil of available nitrogen.

The mathematics topics that caught me under-prepared as a new undergrad (nearly 50 years ago!) were set theory and matrix algebra which weren't in our school curriculum. On the calculus side, the major missing item appears to be Numerical Solutions to ODEs, but as stated by several previously, such advanced topics will be covered during your course.

To your excellent summary, I would stress the point that porous media - whatever the solid particle physical properties - make for first-class sound absorbers by their very nature. For a critical case scenario, google Hesco Bastions.

Thanks! For a CoM reference frame with scattering into an arbitrary xy plane, I now have vx1 = +/- sqrt(1 - k^2) ux1; vy1 = k ux1; vx2 = -/+ sqrt(1 - k^2) ux1 / r; vy2 = - k ux1 / r for k = -1 ... +1 (0 = 'head-on') which looks quite sufficient to fill in any gaps in the particle velocity distribution without recourse to anything exotic.

Quoting from https://en.wikipedia.org/wiki/Elastic_collision "Collisions of atoms are elastic, for example Rutherford backscattering. A useful special case of elastic collision is when the two bodies have equal mass, in which case they will simply exchange their momenta." Is this assertion mistaken? It does at least preserve both conserved quantities (momentum & energy), which your response appears to contradict.

I've not really studied noble gases before, but on general principles, I understand that for 2 particles with mass ratio r, and initial scalar speeds u1,u2, the following equations should hold: u1 + ru2 = v1 + rv2 (conservation of momentum) u1^2 + ru2^2 = v1^2 + rv2^2 (conservation of energy) Leaving aside the trivial no collision solution (v1 = u1, v2 = u2), the quadratic formula gives the change in momenta during collision as: v1 - u1 = 2r (u2 - u1) / (r+1) ; v2 - u2 = 2r (u1 - u2) / (r + 1) ... which yields some rather puzzling consequences: 1) For a pure noble gas isotope (r = 1), v1 = u2, v2 = u1 - particle momenta are simply swapped. 2) If all particles have a uniform initial scalar speed (u2 = u1), they maintain their initial momenta indefinitely. In both cases, there is no apparent trend from a disequilibrium particle velocity distribution toward equilibrium. Is my reasoning correct so far? If so then where does the main mechanism for establishing an equilibrium particle velocity distribution come from: a) rare 3-particle interactions? b) quantum fluctuations? c) something else?

Starting point without a doubt is Coulson and Richardson's Chemical Engineering: Volume 2A: Particulate Systems and Particle Technology, Sixth Edition. That's your broad brush introduction to the subject. But the range of application is extremely diverse - many, many specialist study areas with not so much common ground to unite them (or so it seems to me). If you have particular interest in some particular field, I may be able to give some relevant further references.

Nearly. But it isn't the properties of the medium that are changing: it is whether or not the medium is flowing away from you toward the trains, which would delay your detection of the whistles; or flowing toward you from the trains, which would advance the detection. If you had no information on airspeed, say for instance you were observing via a remote video camera and microphone, your measurements of the (apparent) speed of sound would vary according to wind speed and direction wouldn't they? This is an example of Galilean non-invariance. Now substitute 'speed of light' & 'luminiferous aether' for 'speed of sound' & 'air'. What happened when Mickleson & Morley tried looking for these telltale Galilean non-invariances in their measurements of the speed of light through the medium of the luminiferous aether? They found none! This is why there is a fundamental difference between the non-invariant measured speed of sound in air and the invariant measured speed of light in vacuum. No worries. We've all had to work our way through this some time or other.