Tag Archives: fluid flow

Einstein’s theory of diffusion in liquids, and my extension.

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In 1905 and 1908, Einstein developed two formulations for the diffusion of a small particle in a liquid. As a side-benefit of the first derivation, he demonstrated the visible existence of molecules, a remarkable piece of work. In the second formulation, he derived the same result using non-equilibrium thermodynamics, something he seems to have developed on the spot. I’ll give a brief version of the second derivation, and will then I’ll show off my own extension. It’s one of my proudest intellectual achievements.

But first a little background to the problem. In 1827, a plant biologist, Robert Brown examined pollen under a microscope and noticed that it moved in a jerky manner. He gave this “Brownian motion” the obvious explanation: that the pollen was alive and swimming. Later, it was observed that the pollen moved faster in acetone. The obvious explanation: pollen doesn’t like acetone, and thus swims faster. But the pollen never stopped, and it was noticed that cigar smoke also swam. Was cigar smoke alive too?

Einstein’s first version of an answer, 1905, was to consider that the liquid was composed of atoms whose energy was a Boltzmann distribution with an average of E= kT in every direction where k is the Boltzmann constant, and k = R/N. That is Boltsman’s constant equals the gas constant, R, divided by Avogadro’s number, N. He was able to show that the many interactions with the molecules should cause the pollen to take a random, jerky walk as seen, and that the velocity should be faster the less viscous the solvent, or the smaller the length-scale of observation. Einstein applied the Stokes drag equation to the solute, the drag force per particle was f = -6πrvη where r is the radius of the solute particle, v is the velocity, and η is the solution viscosity. Using some math, he was able to show that the diffusivity of the solute should be D = kT/6πrη. This is called the Stokes-Einstein equation.

In 1908 a French physicist, Jean Baptiste Perrin confirmed Einstein’s predictions, winning the Nobel prize for his work. I will now show the 1908 Einstein derivation and will hope to get to my extension by the end of this post.

Consider the molar Gibbs free energy of a solvent, water say. The molar concentration of water is x and that of a very dilute solute is y. y<<1. For this nearly pure water, you can show that µ = µ° +RT ln x= µ° +RT ln (1-y) = µ° -RTy.

Now, take a derivative with respect to some linear direction, z. Normally this is considered illegal, since thermodynamic is normally understood to apply to equilibrium systems only. Still Einstein took the derivative, and claimed it was legitimate at nearly equilibrium, pseudo-equilibrium. You can calculate the force on the solvent, the force on the water generated by a concentration gradient, Fw = dµ/dz = -RT dy/dz.

Now the force on each atom of water equals -RT/N dy/dz = -kT dy/dz.

Now, let’s call f the force on each atom of solute. For dilute solutions, this force is far higher than the above, f = -kT/y dy/dz. That is, for a given concentration gradient, dy/dz, the force on each solute atom is higher than on each solvent atom in inverse proportion to the molar concentration.

For small spheres, and low velocities, the flow is laminar and the drag force, f = 6πrvη.

Now calculate the speed of each solute atom. It is proportional to the force on the atom by the same relationship as appeared above: f = 6πrvη or v = f/6πrη. Inserting our equation for f= -kT/y dy/dz, we find that the velocity of the average solute molecule,

v = -kT/6πrηy dy/dz.

Let’s say that the molar concentration of solvent is C, so that, for water, C will equal about 1/18 mols/cc. The atomic concentration of dilute solvent will then equal Cy. We find that the molar flux of material, the diffusive flux equals Cyv, or that

Molar flux (mols/cm2/s) = Cy (-kT/6πrηy dy/dz) = -kTC/6πrη dy/dz -kT/6πrη dCy/dz.

where Cy is the molar concentration of solvent per volume.

Classical engineering comes to a similar equation with a property called diffusivity. Sp that

Molar flux of y (mols y/cm2/s) = -D dCy/dz, and D is an experimentally determined constant. We thus now have a prediction for D:

D = kT/6πrη.

This again is the Stokes Einstein Equation, the same as above but derived with far less math. I was fascinated, but felt sure there was something wrong here. Macroscopic viscosity was not the same as microscopic. I just could not think of a great case where there was much difference until I realized that, in polymer solutions there was a big difference.

Polymer solutions, I reasoned had large viscosities, but a diffusing solute probably didn’t feel the liquid as anywhere near as viscous. The viscometer measured at a larger distance, more similar to that of the polymer coil entanglement length, while a small solute might dart between the polymer chains like a rabbit among trees. I applied an equation for heat transfer in a dispersion that JK Maxwell had derived,

where κeff is the modified effective thermal conductivity (or diffusivity in my case), κl and κp are the thermal conductivity of the liquid and the particles respectively, and φ is the volume fraction of particles. 

To convert this to diffusion, I replaced κl by Dl, and κp by Dp where

Dl = kT/6πrηl

and Dp = kT/6πrη.

In the above ηl is the viscosity of the pure, liquid solvent.

The chair of the department, Don Anderson didn’t believe my equation, but agreed to help test it. A student named Kit Yam ran experiments on a variety of polymer solutions, and it turned out that the equation worked really well down to high polymer concentrations, and high viscosity.

As a simple, first approximation to the above, you can take Dp = 0, since it’s much smaller than Dl and you can take Dl to equal Dl = kT/6πrηl as above. The new, first order approximation is:

D = kT/6πrηl (1 – 3φ/2).

We published in Science. That is I published along with the two colleagues who tested the idea and proved the theory right, or at least useful. The reference is Yam, K., Anderson, D., Buxbaum, R. E., Science 240 (1988) p. 330 ff. “Diffusion of Small Solutes in Polymer-Containing Solutions”. This result is one of my proudest achievements.

R.E. Buxbaum, March 20, 2024

The straight flush

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I’m not the wildest libertarian, but I’d like to see states rights extended to Michigan’s toilets and showers. Some twenty years ago, the federal government mandated that the maximum toilet flush volume could be only 1.6 gallons, the same as Canada. They also mandated a maximum shower-flow law, memorialized in this Seinfeld episode. Like the characters in those shows, I think this is government over-reach of states rights covered by the 10th amendment. As I understand it, the only powers of the federal government over states are in areas specifically in the constitution, in areas of civil rights (the 13th Amendment), or in areas of restraint of trade (the 14th Amendment). None of that applies here, IMHO. It seems to me that the states should be able to determine their own flush and shower volumes.

If this happen to you often, you might want to use more water for each flush, or at least a different brand of toilet paper.

If your toilet clogs often, you might want to use more flush water, or at least a different brand of toilet paper.

There is a good reason for allowing larger flushes, too in a state with lots of water. People whose toilets have long, older pipe runs find that there is insufficient flow to carry their stuff to the city mains. Their older pipes were designed to work with 3.5 gallon flushes. When you flush with only 1.6 gallons, the waste only goes part way down and eventually you get a clog. It’s an issue known to every plumber – one that goes away with more flush volume.

Given my choice, I’d like to change the flush law through the legislature, perhaps following a test case in the Supreme court. Similar legislation is in progress with marijuana decriminalization, but perhaps it’s too much to ask folks to risk imprisonment for a better shower or flush. Unless one of my readers feels like violating the federal law to become the test case, I can suggest some things you can do immediately. When it comes to your shower, you’ll find you can modify the flow by buying a model with a flow restrictor and “ahem” accidentally losing the restrictor. When it comes to your toilet, I don’t recommend buying an older, larger tank. Those old tanks look old. A simpler method is to find a new flush cistern with a larger drain hole and flapper. The drain hole and flapper in most toilet tanks is only 2″ in diameter, but some have a full 3″ hole and valve. Bigger hole, more flush power. Perfectly legal. And then there’s the poor-man solution: keep a bucket or washing cup nearby. If the flush looks problematic, pour the extra water in to help the stuff go down. It works.

A washing cup.

A washing cup. An extra liter for those difficult flushes.

Aside from these suggestions, if you have clog trouble, you should make sure to use only toilet paper, and not facial tissues or flushable wipes. If you do use these alternatives, only use one sheet at a flush, and the rest TP, and make sure your brand of wipe is really flushable. Given my choice, I would like see folks in Michigan have freedom of the flush. Let them install a larger tank if they like: 2 gallons, or 2.5; and I’d like to see them able to use Newman’s Serbian shower heads too, if it suits them. What do you folks think?

Dr. Robert E. Buxbaum, November 3, 2016. I’m running for Oakland county MI water resources commissioner. I’m for protecting our water supply, for better sewage treatment, and small wetlands for flood control. Among my less-normative views, I’ve also suggested changing the state bird to the turkey, and ending daylight savings time.

just water over the dam

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Some months ago, I posted an engineering challenge: figure out the water rate over an non-standard V-weir dam during a high flow period (a storm) based on measurements made on the weir during a low flow period. My solution follows. Weir dams of this sort are erected mostly to prevent flooding. They provide secondary benefits, though by improving the water and providing a way to measure the flow.

A series of weir dams on Blackman Stream, Maine. These are thick, rectangular weirs.

A series of compound, rectangular weir dams in Maine.

The problem was stated as follows: You’ve got a classic V weir on a dam, but it is not a knife-edge weir, nor is it rectangular or compound as in the picture at right. Instead it is nearly 90°, not very tall, and both the dam and weir have rounded leads. Because the weir is of non-standard shape, thick and rounded, you can not use the flow equation found in standard tables or on the internet. Instead, you decide to use a bucket and stopwatch to determine the flow during a relatively dry period. You measure 0.8 gal/sec when the water height is 3″ in the weir. During the rain-storm some days later, you measure that there are 12″ of water in the weir. Give a good estimate of the storm-flow based on the information you have.

A V-notch weir, side view and end-on.

A V-notch weir, side view and end-on.

I also gave a hint, that the flow in a V weir is self-similar. That is, though you may not know what the pattern will be, you can expect it will be stretched the same for all heights.

The upshot of this hint is that, there is one, fairly constant flow coefficient, you just have to find it and the power dependence. First, notice that area of flow will increase with height squared. Now notice that the velocity will increase with the square root of hight, H because of an energy balance. Potential energy per unit volume is mgH, and kinetic energy per unit volume is 1/2 mv2 where m is the mass per unit volume and g is the gravitational constant. Flow in the weir is achieved by converting potential height energy into kinetic, velocity energy. From the power dependence, you can expect that the average v will be proportional to √H at all values of H.

Combining the two effects together, you can expect a power dependence of 2.5 (square root is a power of 0.5). Putting this another way, the storm height in the weir is four times the dry height, so the area of flow is 16 times what it was when you measured with the bucket. Also, since the average height is four times greater than before, you can expect that the average velocity will be twice what it was. Thus, we estimate that there was 32 times the flow during the storm than there was during the dry period; 32 x 0.8 = 25.6 gallons/sec., or 92,000 gal/hr, or 3.28 cfs.

The general equation I derive for flow over this, V-shaped weir is

Flow (gallons/sec) = Cv gal/hr x(feet)5/2.

where Cv = 3.28 cfs. This result is not much different to a standard one  in the tables — that for knife-edge, 90° weirs with large shoulders on either side and at least twice the weir height below the weir (P, in the diagram above). For this knife-edge weir, the Bureau of Reclamation Manual suggests Cv = 2.49 and a power value of 2.48. It is unlikely that you ever get this sort of knife-edge weir in a practical application. Be sure to measure Cv at low flow for any weir you build or find.

Robert Buxbaum, vote for me for water commissioner. Here are some thoughts on other problems with our drains.

Weird flow calculation

Here is a nice flow problem, suitable for those planning to take the professional engineers test. The problem concerns weir dams. These are dams with a notch in them, somethings rectangular, as below, but in this case a V-shaped notch. Weir dams with either sort of notch can be used to prevent flooding and improve the water, but they also provide a way to measure the flow of water during a flood. That’s the point of the problem below.

A series of weir dams on Blackman Stream, Maine. These are thick, rectangular weirs.

A series of weir dams with rectangular weirs in Maine.

You’ve got a classic V weir on a dam, but it is not a knife-edge weir, nor is it rectangular or compound as in the picture at right. Instead it is nearly 90°, not very tall, and both the dam and weir have rounded leads. Because the weir is of non-standard shape, thick and rounded, you can not use the flow equation found in standard tables or on the internet. Instead, you decide to use a bucket and stopwatch to determine that the flow during a relatively dry period. You measure 0.8 gal/sec when the water height is 3″ in the weir. During the rain-storm some days later, you measure that there are 12″ of water in the weir. The flow is too great for you to measure with a bucket and stopwatch, but you still want to know what the flow is. Give a good estimate of the flow based on the information you have.

As a hint, notice that the flow in the V weir is self-similar. That is, though you may not know what the pattern of flow will be, you can expect it will be stretched the same for all heights.

As to why anyone would use this type of weir: they are easier to build and maintain than the research-standard, knife edge; they look nicer, and they are sturdier. Here’s my essay in praise of the use of dams. How dams on drains and rivers could help oxygenate the water, and to help increase the retention time to provide for natural bio-remediation.

If you’ve missed the previous problem, here it is: If you have a U-shaped drain or river-bed, and you use a small dam or weir to double the water height, what is the effect on water speed and average retention time. Work it out yourself, or go here to see my solution.

Robert Buxbaum. May 20-Sept 20, 2016. I’m running for drain commissioner. send me your answers to this problem, or money for my campaign, and win a campaign button. Currently, as best I can tell, there are no calibrated weirs or other flow meters on any of the rivers in the county, or on any of the sewers. We need to know because every engineering decision is based on the flow. Another thought: I’d like to separate our combined sewers and daylight some of our hidden drains.

Weir dams to slow the flow and save our lakes

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As part of explaining why I want to add weir dams to the Red Run drain, and some other of our Oakland county drains, I posed the following math/ engineering problem: if a weir dam is used to double the depth of water in a drain, show that this increases the residence time by a factor of 2.8 and reduces the flow speed by 1/2.8. Here is my solution.

A series of weir dams on Blackman Stream, Maine. Mine would be about as tall, but somewhat further apart.

A series of weir dams on Blackman Stream, Maine. Mine would be about as tall, but wider and further apart. The dams provide oxygenation and hold back sludge.

Let’s assume the shape of the bottom of the drain is a parabola, e.g. y = x2 , and that the dams are spaced far enough apart that their volume is small compared to the volume of water. We now use integral calculus to calculate how the volume of water per mile, V is affected by water height:  V =2XY- ∫ y dx = 2XY- 2/3 X3 =  4/3 Y√Y. Here, capital Y is the height of water in the drain, and capital X is the horizontal distance of the water edge from the drain centerline. For a parabolic-bottomed drain, if you double the height Y, you increase the volume of water per mile by 2√2. That’s 2.83, or about 2.8 once you assume some volume to the dams.

To find how this affects residence time and velocity, note that the dam does not affect the volumetric flow rate, Q (gallons per hour). If we measure V in gallons per mile of drain, we find that the residence time per mile of drain (hours) is V/Q and that the speed (miles per hour) is Q/V. Increasing V by 2.8 increases the residence time by 2.8 and decreases the speed to 1/2.8 of its former value.

Why is this important? Decreasing the flow speed by even a little decreases the soil erosion by a lot. The hydrodynamic lift pressure on rocks or soil is proportional to flow speed-squared. Also, the more residence time and the more oxygen in the water, the more bio-remediation takes place in the drain. The dams slow the flow and promote oxygenation by the splashing over the weirs. Cells, bugs and fish do the rest; e.g. -HCOH- + O2 –> CO2 + H2O. Without oxygen, the fish die of suffocation, and this is a problem we’re already seeing in Lake St. Clair. Adding a dam saves the fish and turns the run into a living waterway instead of a smelly sewer. Of course, more is needed to take care of really major flood-rains. If all we provide is a weir, the water will rise far over the top, and the run will erode no better (or worse) than it did before. To reduce the speed during those major flood events, I would like to add a low bicycle path and some flood-zone picnic areas: just what you’d see on Michigan State’s campus, by the river.

Dr. Robert E. Buxbaum, May 12, 2016. I’d also like to daylight some rivers, and separate our storm and toilet sewage, but those are longer-term projects. Elect me water commissioner.

The Gift of Chaos

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Many, if not most important engineering systems are chaotic to some extent, but as most college programs don’t deal with this behavior, or with this type of math, I thought I might write something on it. It was a big deal among my PhD colleagues some 30 years back as it revolutionized the way we looked at classic problems; it’s fundamental, but it’s now hardly mentioned.

Two of the first freshman engineering homework problems I had turn out to have been chaotic, though I didn’t know it at the time. One of these concerned the cooling of a cup of coffee. As presented, the coffee was in a cup at a uniform temperature of 70°C; the room was at 20°C, and some fanciful data was presented to suggest that the coffee cooled at a rate that was proportional the difference between the (changing) coffee temperature and the fixed room temperature. Based on these assumptions, we predicted exponential cooling with time, something that was (more or less) observed, but not quite in real life. The chaotic part in a real cup of coffee, is that the cup develops currents that move faster and slower. These currents accelerate heat loss, but since they are driven by the temperature differences within the cup they tend to speed up and slow down erratically. They accelerate when the cup is not well stirred, causing new stir, and slow down when it is stirred, and the temperature at any point is seen to rise and fall in an almost rhythmic fashion; that is, chaotically.

While it is impossible to predict what will happen over a short time scale, there are some general patterns. Perhaps the most remarkable of these is self-similarity: if observed over a short time scale (10 seconds or less), the behavior over 10 seconds will look like the behavior over 1 second, and this will look like the behavior over 0.1 second. The only difference being that, the smaller the time-scale, the smaller the up-down variation. You can see the same thing with stock movements, wind speed, cell-phone noise, etc. and the same self-similarity can occur in space so that the shape of clouds tends to be similar at all reasonably small length scales. The maximum average deviation is smaller over smaller time scales, of course, and larger over large time-scales, but not in any obvious way. There is no simple proportionality, but rather a fractional power dependence that results in these chaotic phenomena having fractal dependence on measure scale. Some of this is seen in the global temperature graph below.

Global temperatures measured from the antarctic ice showing stable, cyclic chaos and self-similarity.

Global temperatures measured from the antarctic ice showing stable, cyclic chaos and self-similarity.

Chaos can be stable or unstable, by the way; the cooling of a cup of coffee was stable because the temperature could not exceed 70°C or go below 20°C. Stable chaotic phenomena tend to have fixed period cycles in space or time. The world temperature seems to follow this pattern though there is no obvious reason it should. That is, there is no obvious maximum and minimum temperature for the earth, nor any obvious reason there should be cycles or that they should be 120,000 years long. I’ll probably write more about chaos in later posts, but I should mention that unstable chaos can be quite destructive, and quite hard to prevent. Some form of chaotic local heating seems to have caused battery fires aboard the Dreamliner; similarly, most riots, famines, and financial panics seem to be chaotic. Generally speaking, tight control does not prevent this sort of chaos, by the way; it just changes the period and makes the eruptions that much more violent. As two examples, consider what would happen if we tried to cap a volcano, or provided  clamp-downs on riots in Syria, Egypt or Ancient Rome.

From math, we know some alternate ways to prevent unstable chaos from getting out of hand; one is to lay off, another is to control chaotically (hard to believe, but true).

 

What causes the swirl of tornadoes and hurricanes

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Some weeks ago, I presented an explanation of why tornadoes and hurricanes pick up stuff based on an essay by A. Einstein that explained the phenomenon in terms of swirling fluids and Coriolis flows. I put in my own description that I thought was clearer since it avoided the word “Coriolis”, and attached a video so you could see how it all worked — or rather that is was as simple as all that. (Science teachers: I’ve found kids love it when I do this, and similar experiments with centrifugal force in the class-room as part of a weather demonstration).

I’d like to now answer a related question that I sometimes get: where does the swirl come from? hurricanes that answer follows, though I think you’ll find my it is worded differently from that in Wikipedia and kids’ science books since (as before) I don’t use the word Coriolis, nor any other concept beyond conservation of angular momentum plus that air flows from high pressure to low.

In Wikipedia and all the other web-sits I visited, it was claimed that the swirl came from “Coriolis force.” While this isn’t quite wrong, I find this explanation incomprehensible and useless. Virtually no-one has a good feel for Coriolis force as such, and those who do recognize that it doesn’t exist independently like gravity. So here is my explanation based on low and high pressure and on conservation of angular momentum.  I hope it will be clearer.

All hurricanes are associated with low pressure zones. This is not a coincidence as I understand it, but a cause-and-effect relationship. The low pressure center is what causes the hurricane to form and grow. It may also cause tornadoes but the relationship seems less clear. In the northern hemisphere, the lowest low pressure zones are found to form over the mid Atlantic or Pacific in the fall because the water there is warm and that makes the air wet and hot. Static air pressure is merely the weight of the air over a certain space, and as hot air has more volume and less density, it weighs less. Less weight = less pressure, all else being equal. Adding water (humidity) to air also reduces the air pressure as the density of water vapor is less than that of dry air in proportion to their molecular weights. The average molecular weight of dry air is 29 and the molecular weight of water is 18. As a result, every 9% increase in water content decreases the air pressure by 1% (7.6 mm or 0.3″ of mercury).

Air tends to flow from high pressure zones to low pressure zones. In the northern hemisphere, some of the highest high pressure zones form over northern Canada and Russia in the winter. High pressure zones form there by the late fall because these regions are cold and dry. Cold air is less voluminous than hot, and as a result additional hot air flows into these zones at high altitude. At sea level the air flows out from the high pressure zones to the low pressure zones and begins to swirl because of conservation of angular momentum.

All the air in the world is spinning with the earth. At the north pole the spin rate is 360 degrees every 24 hours, or 15 degrees per hour. The spin rate is slower further south, proportionally to the sine of the latitude, and it is zero at the equator. The spin of the earth at your location is observable with a Foucault pendulum (there is likely to be one found in your science museum). We normally don’t notice the spin of the air around us because the earth is spinning at the same rate, normally. However the air has angular momentum, and when air moves into into a central location the angular speed increases because the angular momentum must be conserved. As the gas moves in, the spin rate must increase in proportion; it eventually becomes noticeable relative to the earth’s spin. Thus, if the air starts out moving at 10 degrees per hour (that’s the spin rate in Detroit, MI 41.8° N), and moves from 800 miles away from a low pressure center to only 200 miles from the center, the angular momentum must increase four times, or to 40 degrees per hour. We would only see 30 degrees/hr of this because the earth is spinning, but the velocity this involves is significant: V= 200 miles * 2* pi *30/360 = 104 mph.

To give students a sense of angular momentum conservation, most science centers (and colleges) use an experiment involving bicycle wheels and a swivel chair. In the science centers there is usually no explanation of why, but in college they tend to explain it in terms of vectors and (perhaps) gauge theories of space-time (a gauge is basically a symmetry; angular momentum is conserved because space is symmetric in rotation). In a hurricane, the air at sea level always spins in the same direction of the earth: counter clockwise in the northern hemisphere, clockwise in the southern, but it does not spin this way forever.

The air that’s sucked into the hurricane become heated and saturated with water. As a result, it becomes less dense, expands, and rises, sucking fresh air in behind it. As the hot wet air rises it cools and much of the water rains down as rain. When the, now dry air reaches a high enough altitude its air pressure is higher than that above the cold regions of the north; the air now flows away north. Because this hot wet air travels north we typically get rain in Michigan when the Carolinas are just being hit by hurricanes. As the air flows away from the centers at high altitudes it begins to spin the opposite direction, by the way, so called counter-cyclonally because angular momentum has to be consevered. At high altitudes over high pressure centers I would expect to find cyclones too (spinning cyclonally) I have not found a reference for them, but suspect that airline pilots are aware of the effect. There is some of this spin at low altitudes, but less so most of the time.

Hurricanes tend to move to the US and north through the hurricane season because, as I understand it, the cold air that keeps coming to feed the hurricane comes mostly from the coastal US. As I understand it the hurricane is not moving as such, the air stays relatively stationary and the swirl that we call a hurricane moves to the US in the effective direction of the sea-level air flow.

For tornadoes, I’m sorry to say, this explanation does not work quite as well, and Wikipedia didn’t help clear things up for me either. The force of tornadoes is much stronger than of hurricanes (the swirl is more concentrated) and the spin direction is not always cyclonic. Also tornadoes form in some surprising areas like Kansas and Michigan where hurricanes never form. My suspicion is that most, but not all tornadoes form from the same low pressure as hurricanes, but by dry heat, not wet. Tornadoes form in Michigan, Texas, and Alabama in the early summer when the ground is dry and warmer than the surrounding lakes and seas. It is not difficult to imagine the air rising from the hot ground and that a cool wind would come in from the water and beginning to swirl. The cold, damp sea air would be more dense than the hot, dry land air, and the dry air would rise. I can imagine that some of these tornadoes would occur with rain, but that many the more intense?) would have little or none; perhaps rain-fall tends to dampen the intensity of the swirl (?)

Now we get to things that I don’t have good explanation for at all: why Kansas? Kansas isn’t particularly hot or cold; it isn’t located near lakes or seas, so why do they have so many tornadoes? I don’t know. Another issue that I don’t understand: why is it that some tornadoes rotate counter cyclonicly? Wikipedia says these tornadoes shed from other tornadoes, but this doesn’t quite seem like an explanation. My guess is that these tornadoes are caused by a relative high pressure source at ground level (a region of cold ground for example) coupled with a nearby low pressure zone (a warm lake?). My guess is that this produces an intense counter-cyclonic flow to the low pressure zone. As for why the pressure is very low in tornadoes, even these that I think are caused by high pressure, I suspect the intense low pressure is an epee-phenomenon caused by the concentration of spin — one I show in my video. That is, I suspect that the low pressure in the center of counter-cyclonic tornadoes is not the cause of the tornado but an artifact of the concentrated spin. Perhaps I’m wrong here, but that’s the explanation that seems to fit best with the info I’ve got. If you’ve got better explanations for these two issues, I’d love to hear them.

Why tornadoes and hurricanes lift up cars, cows, etc.

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Here’s a video I made for my nieces and any other young adults on why it is that tornadoes and hurricanes lift stuff up. It’s all centrifugal forces — the same forces that generate the low pressure zone at the center of hurricanes. The explanation is from Albert Einstein, who goes on show why it is that rivers don’t run straight; before you read any more of it, I’d suggest you first watch the video here. It’s from my Facebook page, so it should be visible.

If can’t see, you may have to friend me on Facebook, but until then the video shows a glass coffee cup with some coffee grounds and water in it. Originally, the grounds are at the bottom of the cup showing that they are heavier than the water. When I swirl the water in the cup, you’ll see that the grounds are lifted up into a heap in the center with some flowing all around in a circle — to the top surface and then to the walls of the cup. This is the same path followed by light things (papers for example) in a tornado. Cows, houses and cars that are caught up in real tornadoes get sucked in and lifted up too, but they never get to the top to be thrown outward.

The explanation for the lifting is that the upper layers of liquid swirl faster than the lower layers. As a result there is a low pressure zone above the middle of the swirl. The water (or air) moves upward into this lower pressure area and drags along with it cows, cars, houses and the like (Here’s another post on the subject of where the swirl comes from). The reason the swirl is faster above the bottom of the cup is that the cup bottom adds drag to the flow (the very bottom isn’t swirling at all). The faster rotating, upper flows have a reasonable amount of centrifugal force and thus a lower pressure in the middle of the swirl, and a higher pressure further out. The non-rotating bottom has a more uniform pressure that’s relatively higher in the middle, and relatively lower on the outside. As a result there is a secondary flow where air moves down around the outside of the flow and up in the middle. You can see this secondary flow in the video by following the lighter grounds.

Robert. E. Buxbaum. Weather is not exactly climate, but in my opinion both are cyclic and chaotic. I find there is little evidence that we can stop climate change, and suspect there is no advantage to wanting the earth colder. There was a tornado drought in 2013, and a hurricane draught too. You may not have heard of either because it’s hard to report on the storms that didn’t happen.