sethoflagos

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.

In what circumstance would a medium be not at rest with respect to itself? Perhaps you intended "... at rest with respect to the observer", ie. a restatement of our 'still air' constraint. Could another restatement of this constraint be that observer and medium must be in the same Galilean reference frame? If so, then if the constraint was a necessary precondition, wouldn't this imply that the apparent speed of sound was not invariant under a Galilean transformation? I stress the word 'apparent' to distinguish between transmission over a measured distance in a measured time interval, as distinct from a physical property of the medium itself. These are two different quantities. Whether the latter is invariant to Galilean transformation is a moot point.

Meteorites survive passage through the atmosphere, so perhaps you intend 'audible fireballs'. Even so, these propagate, initially at least, as supersonic bow shocks (sudden pressure discontinuities) rather than sound waves - at velocities dependent on their initial trajectories, and independent (for a while at least) of atmospheric properties. If one bolide were travelling towards the observer, and one away, they would be experienced as two blast wave fronts, the first perhaps considerably more powerful than the second. 'Pitch' is meaningless here. There may be some reflected aftershocks, but not necessarily in any ordered sequence. Perhaps your enquiries would be better served with a simpler less energetic case, such as two locomotives in still air, sounding their steam whistles as they passed each other in opposing directions. In the absence of relatavistic effects, and if the locomotives were perfectly streamlined (ie they weren't dragging a large envelope of air with them) an observer on the station platform would hear two perfectly simultaneous sounds pitched according to their respective Doppler shifts.

'Robotic skin' is a highly active area of current research, and your OP seems to require a relatively low resolution, planar version of the same thing. I'm puzzled why you pick impedance as the sensed property for this. Most work in this field has been focused on traditional resistance strain gauges, piezoresistance, and capacitance methods though Fibre Bragg Gratings (FBGs) seem to have received a lot of attention recently. The EU Roboskin Project is funded to the tune of about 5 million Euros: details at https://cordis.europa.eu/project/id/231500

I clearly remember my grandmother starting the fire like that as the family gathered for christmas dinner. The sudden updraught caught her pet budgie by surprise and... it didn't end well.

Natural draught is used extensively as a power source, but not in an obvious way. It doesn't provide enough power to pull combustion air through a commercial power station, but it contributes significantly in reducing the power requirement of the forced- & induced-draught fans. Similarly, natural draught cooling towers (and domestic coal fires for those old enough to remember them) don't need forced ventilation in order to maintain air flow.

Thanks!