Author Archives: R.E. Buxbaum

About R.E. Buxbaum

Robert Buxbaum is a life-long engineer, a product of New York's Brooklyn Technical High School, New York's Cooper Union to Science and Art, and Princeton University where he got a PhD in Chemical Engineering. From 1981 to 1991 he was a professor of Chemical Engineering at Michigan State, and now runs an engineering shop in Oak Park, outside of Detroit, Michigan. REB Research manufactures and sells hydrogen generation and purification equipment. He's married with 3 wonderful children who, he's told, would prefer to not be mentioned except by way of complete, unadulterated compliments. As of 2016, he's running to be the drain commissioner/ water resources commissioner of Oakland county.

Sewage reactor engineering, Stirred tank designs

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Over the past few years, I’ve devoted several of these essays to analysis of first-stage sewage treatment reactors. I described and analyzed the rotating disc reactor found at the plant is Holly here, and described the racetrack,“activated sludge” plug reactor found most everywhere else here. I also described a system without a primary clarifier found near Cincinatti. All of these were effective for primary treatment; soluble organics are removed by bio-catalyzed oxidation:

2 H-C-O-H + O2 –> CO2 + H2O.

A typical plant in Oakland county treats 2,000,000 gallons per day of this stuff, with the bio-reactor receiving liquid waste containing about 200 ppm of soluble and colloidal biomass. That’s 400 dry gallons for those interested, or about 3200 dry lbs./day. About half of this will be oxidized to CO2 and water. The rest (cell bodies) are removed with insoluble components, and applied to farmers fields or buried, or burnt in an incinerator.

There is another type of reactor used in Oakland County. It’s mostly used for secondary treatment, converting consolidated sludge to higher-quality sludge that can be sold or used on farms with less restriction, but it is a type of reactor used at the South Lyon treatment plant, for primary treatment. It is a Continually stirred tank reactor, or CSTR, a design that is shown in schematic below.

As of some years ago, the South Lyon system involved a single largish pond lined with plastic with a volume about 2,000,000 gallons total. About 700,000 gallons per day of sewage liquids went into the lagoon, at 200 ppm soluble organics. Air was bubbled through the liquid providing a necessary reactant, and causing near-perfect mixing of the contents. The aim of the plant managers is to keep the soluble output to the, then-acceptable level of 10 ppm; it’s something they only barely managed, and things got worse as the flow increased. Assume as before, a value V and a flow Q.

We will call the concentration of soluble organics C, and call the initial concentration, the concentration that enters,  Ci. It’s about 200 ppm. We’ll call the output concentration Co, and for this type of reactors, Co = C.  The reaction is first order, approximately, so that, if there were no flow into or out of the reactor, the concentration of organics would decrease at the rate of

dC/dt = -kC.

Here k is a reaction constant, dependent on temperature oxygen and cell content. It’s typically about 0.5/hour. For a given volume of tank the rate of organic removal is VkC. We can now do a mass balance on soluble organics. Since the rate of organic entry is QCi and the rate leaving by flow is QC. The difference must be the amount that is reacted away:

QCi – QC = VkC.

We now use algebra, to find that

Co = Ci/(1 + kV/Q).

V/Q is sometimes called a residence time; for the system. At normal flow, the residence time of the South Lyon system is about 2.8 days or 68.6 hours. Plugging these numbers in, we find that the effluent from the reactor leaves at 1/35 of the input concentration, or 5.7 ppm, on average. This would be fine except that sometimes the temperature drops, or the flow increases, and we start violating the standard. A yet bigger problem was that the population increased by 50% while the EPA standard got more stringent to 2 ppm. This was solved by adding another, smaller reactor, volume = V2. Using the same algebraic analysis, as above you can show that, with two reactors,

Co = Ci/ [(1 + kV/Q)(1+kV2/Q)].

It’s a touchy system, but it meets government targets, just barely, most of the time. I think it is time to switch to a plug-flow reactor system, as used in much of Oakland county. In these, the fluid enters a channel and is reacted as it flows along. Each gallon of fluid, in a sense moves by itself as if it were its own reactor. In each gallon, we can say that dC/dt = -kC. We can thus solve for Co in terms of the total residence time, where t again is V/Q. We can rearrange this equation and integrate: ∫dC/C = – ∫kdt. We then find that, 

      ln(Ci/Co) = kt = kV/Q

To convert 200 ppm sewage to 2 ppm we note that Ci/Co = 100 and that V = Q ln(100)/k = Q (4.605/.5) hours. An inflow of 1000,000 gallons per day = 41,667 gal/ hour, and we find the volume of tank is 41,667 x 9.21 = 383,750 gallons. This is quite a lot smaller than the CSTR tanks at South Lyon. If we converted the South Lyon tanks to a plug-flow, race-track design, it would allow it to serve a massively increased population, discharging far cleaner sewage. 

Robert Buxbaum, November 17, 2019

Maximum height of an NYC skyscraper, including wind.

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Some months ago, I demonstrated that the maximum height of a concrete skyscraper was 45.8 miles, but there were many unrealistic assumptions. The size of the base was 100 mi2, about that of Sacramento, California; the shape was similar to that of the Eiffel tower, and there was no wind. This height is semi-reasonable; it’s about that of the mountains on Mars where there is a yellow sky and no wind, but it is 100 times taller than the tallest skyscraper on earth. the Burj Khalifa in Dubai, 2,426 ft., shown below. Now I’d like to include wind, and limit the skyscraper to a straight tower of a more normal size, a city-block square of manhattan, New York real-estate. That’s 198 feet on a side; this is three times the length of Gunther’s surveying chain, the standard for surveying in 1800.

Burj Khalifa, the world’s tallest building, Concrete + glass structure. Dubai tourism image.

As in our previous calculation, we can find the maximum height in the absence of windby balancing the skyscrapers likely strength agains its likely density. We’ll assume the structure is made from T1 steel, a low carbon, vanadium steel used in bridges, further assume that the structure occupies 1/10 of the floor area. Because the structure is only 1/10 of the area, the average yield strengthener the floor area is 1/10 that of T1 steel. This is 1/10 x 100,000 psi (pounds per square inch) = 10,000 psi. The density of T1 steel is 0.2833 pounds per cubic inch, but we’ll assume that the density of the skyscraper is about 1/4 this; (a skyscraper is mostly empty space). We find the average is 0.07 pounds per cubic inch. The height, is the strength divided by the density, thus

H’max-tower = 10,000psi / 0.07 p/in3 = 142, 857 inches = 11, 905 feet = 3629 m,

This is 4 1/4 times higher than the Burj Khalifa. The weight of this structure found from the volume of the structure times its average density, or 0.07 pounds per cubic inch x 123 x 1982x 11,905 = 56.45 billion pounds, or, in SI units, a weight of 251 GNt.

Lets compare this to the force of a steady wind. A steady wind can either either tip over the building by removing stress on the upwind side, or add so much extra stress to the down-wind side that the wall fails. The force of the wind is proportionals to the wind’s energy dissipation rate. I’ll assume a maximum wind speed of 120 mph, or 53.5 m/s. The force of the wind equals the area of the building, times a form factor, ƒ, times the rate of kinetic energy dissipation, 1/2ρv2. Thus,

F= (Area)*ƒ* 1/2ρv2, where ρ is the density of air, 1.29kg/m3.

The form factor, ƒ, is found to be 1.15 for a flat plane. I’ll presume that’s also the form factor for a skyscraper. I’ll take the wind area as

Area = W x H,

where W is the width of the tower, 60.35 m in SI, and the height, H, is what we wish to determine. It will be somewhat less than H’max-tower, =3629 m, the non-wind height. As an estimate for how much less, assume H = H’max-tower, =3629 m.
For this height tower, the force of the wind is found to be:

F = 3629 * 60.35* 2123 = 465 MNt.

This is 1/500 the weight of the building, but we still have to include the lever effect. The building is about 60.1 times taller than it is wide, and as a result the 465 MNt sideways force produces an additional 28.0 GNt force on the down-wind side, plus and a reduction of the same amount upwind. This is significant, but still only 1/9 the weight of the building. The effect of the wind therefore is to reduce the maximum height of this New York building by about 9 %, to a maximum height of 2.05 miles or 3300 m.

The tallest building of Europe is the Shard; it’s a cone. The Eiffel tower, built in the 1800s, is taller.

A cone is a better shape for a very tall tower, and it is the shape chosen for “the shard”, the second tallest building in Europe, but it’s not the ideal shape. The ideal, as before, is something like the Eiffel tower. You can show, though I will not, that even with wind, the maximum height of a conical building is three times as high as that of a straight building of the same base-area and construction. That is to say that the maximal height of a conical building is about 6 miles.

In the old days, one could say that a 2 or 6 mile building was inconceivable because of wind vibration, but we’ve found ways to deal with vibration, e.g. by using active damping. A somewhat bigger problem is elevators. A very tall building needs to have elevators in stages, perhaps 1/2 mile stages with exchanges (and shopping) in-between. Yet another problem is fire. To some extent you eliminate these problems by use of pre-mixed concrete, as was used in the Trump tower in New York, and later in the Burj Khalifa in Dubai.

The compressive strength of high-silica, low aggregate, UHPC-3 concrete is 135 MPa (about 19,500 psi), and the density is 2400 kg/m3 or about 0.0866 lb/in3. I will assume that 60% of the volume is empty and that 20% of the weight is support structure (For the steel building, above, I’d assumed 3/4 and 10%). In the absence of wind,

H’max-cylinder-concrete = .2 x 19,500 psi/(0.4 x.0866  lb/in3) = 112,587″ = 9,382 ft = 1.77 miles. This building is 79% the height of the previous, steel building, but less than half the weight, about 22,000,000,000 pounds. The effect of the wind will be to reduce the above height by about 14%, to 1.52 miles. I’m not sure that’s a fire-safe height, but it is an ego-boost height.

Robert Buxbaum. December 29, 2019.

The dangers of political humor

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One big danger of political humor is that some folks just don’t get the joke. You say something outrageous and they don’t get that you were exaggerating, but think you were lying, or ignorant, or worse yet they take you at your word, and think you were telling the truth.

Daniel Boone liked to claim things that were not true; he claimed he jumped the Mississippi and that he lassoed a tornado and that he killed a bear (with his bear hands) when he was three. The joke was on anyone who took him seriously, and I’m sure there were those who did: “Why that’s not true!” “You’re a liar!” or worse yet “Wow, how did you do that!” It’s a sort of brag-joke that, today is called “trolling.”

H.L. Menken on the fake news of the early – mid 20th century.

But there is a bigger danger with political jokes, and that happens when you’re not quite making a joke and folks realize you are telling the truth, or at least that there is a dagger of threat thats being passed off within a joke, or as part of an exaggeration. Basically, they realize that this joke was no joke at all.

A recent case in point, two weeks ago Trump was speaking to Jewish businessmen, and told them about his troubles building the US embassy in Jerusalem (read the whole speech here), but within the funny story is a hook:

Bob Hope told the truth but hid it in a funny delivery.

“And I called David Friedman.  I said, “David, I need some help.  I just approved an embassy, and they want to spend $2 billion to build the embassy.  And I know what that means: You’re never going to get it built.  It’ll take years and years.”  I said, “You know what’s going on here? …. So we’re going to spend 2 billion, and one of them was going to buy a lousy location.  A lot of you are in the real estate business because I know you very well.  You’re brutal killers.  (Laughter.)  Not nice people at all.  But you have to vote for me; you have no choice.  You’re not going to vote for Pocahontas, I can tell you that.  (Laughter and applause.)  You’re not going to vote for the wealth tax.  “Yeah, let’s take 100 percent of your wealth away.”  No, no.  Even if you don’t like me; some of you don’t.  Some of you I don’t like at all, actually.  (Laughter.)  And you’re going to be my biggest supporters because you’ll be out of business in about 15 minutes, if they get it.  So I don’t have to spend a lot of time on that. But David calls me back and he goes, “Sir” — he always used to call me “Donald.”

The press claimed the above was vile and anti-semitic. It almost sounds otherwise when quoted in context, but they are not totally off. There is truth inside that jest. Such truths lose the humor, but they do get the message across. A lot has to do with the delivery. Ideally the folks that you want to get the point will, and the rest will think you mean nothing by it. It’s a hard act.

Robert Buxbaum December 23, 2019.

A mathematical approach to finding Mr (or Ms) Right.

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A lot of folks want to marry their special soulmate, and there are many books to help get you there, but I thought I might discuss a mathematical approach that optimizes your chance of marrying the very best under some quite-odd assumptions. The set of assumptions is sometimes called “the fussy suitor problem” or the secretary problem. It’s sometimes presented as a practical dating guide, e.g. in a recent Washington Post article. My take, is that it’s not a great strategy for dealing with the real world, but neither is it total nonsense.

The basic problem was presented by Martin Gardner in Scientific American in 1960 or so. Assume you’re certain you can get whoever you like (who’s single); assume further that you have a good idea of the number of potential mates you will meet, and that you can quickly identify who is better than whom; you have a desire to marry none but the very best, but you don’t know who’s out there until you date, and you’ve an the inability to go back to someone you’ve rejected. This might be he case if you are a female engineering student studying in a program with 50 male engineers, all of whom have easily bruised egos. Assuming the above, it is possible to show, using Riemann Integrals (see solution here), that you maximize your chance of finding Mr/Ms Right by dating without intent to marry 36.8 % of the fellows (1/e), and then marrying the first fellow who’s better than any of the previous you’ve dated. I have a simpler, more flexible approach to getting the right answer, that involves infinite serieses; I’ll hope to show off some version of this at a later date.

Bluto, Popeye, or wait for someone better? In the cartoon as I recall, she rejects the first few people she meets, then meets Bluto and Popeye. What to do?

With this strategy, one can show that there is a 63.2% chance you will marry someone, and a 36.8% you’ll wed the best of the bunch. There is a decent chance you’ll end up with number 2. You end up with no-one if the best guy appears among the early rejects. That’s a 36.8% chance. If you are fussy enough, this is an OK outcome: it’s either the best or no-one. I don’t consider this a totally likely assumption, but it’s not that bad, and I find you can recalculate fairly easily for someone OK with number 2 or 3. The optimal strategy then, I think, is to date without intent at the start, as before, but to take a 2nd or 3rd choice if you find you’re unmarried after some secondary cut off. It’s solvable by series methods, or dynamic computing.

It’s unlikely that you have a fixed passel of passive suitors, of course, or that you know nothing of guys at the start. It also seems unlikely that you’re able to get anyone to say yes or that you are so fast evaluating fellows that there is no errors involved and no time-cost to the dating process. The Washington Post does not seem bothered by any of this, perhaps because the result is “mathematical” and reasonable looking. I’m bothered, though, in part because I don’t like the idea of dating under false pretense, it’s cruel. I also think it’s not a winning strategy in the real world, as I’ll explain below.

One true/useful lesson from the mathematical solution is that it’s important to learn from each date. Even a bad date, one with an unsuitable fellow, is not a waste of time so long as you leave with a better sense of what’s out there, and of what you like. A corollary of this, not in the mathematical analysis but from life, is that it’s important to choose your circle of daters. If your circle of friends are all geeky engineers, don’t expect to find Prince Charming among them. If you want Prince Charming, you’ll have to go to balls at the palace, and you’ll have to pass on the departmental wine and cheese.

If you want Prince Charming, you may have to associate with a different crowd from the one you grew up with. Whether that’s a good idea for a happy marriage is another matter.

The assumptions here that you know how many fellows there are is not a bad one, to my mind. Thus, if you start dating at 16 and hope to be married by 32, that’s 16 years of dating. You can use this time-frame as a stand in for total numbers. Thus if you decide to date-for-real after 37%, that’s about age 22, not an unreasonable age. It’s younger than most people marry, but you’re not likely to marry the fort person you meet after age 22. Besides, it’s not great dating into your thirties — trust me, I’ve done it.

The biggest problem with the original version of this model, to my mind, comes from the cost of non-marriage just because the mate isn’t the very best, or might not be. This cost gets worse when you realize that, even if you meet prince charming, he might say no; perhaps he’s gay, or would like someone royal, or richer. Then again, perhaps the Kennedy boy is just a cad who will drop you at some time (preferably not while crossing a bridge). I would therefor suggest, though I can’t show it’s optimal that you start out by collecting information on guys (or girls) by observing the people around you who you know: watch your parents, your brothers and sisters, your friends, uncles, aunts, and cousins. Listen to their conversation and you can get a pretty good idea of what’s available even before your first date. If you don’t like any of them, and find you’d like a completely different circle, it’s good to know early. Try to get a service job within ‘the better circle’. Working with people you think you might like to be with, long term, is a good idea even if you don’t decide to marry into the group in the end.

Once you’ve observed and interacted with the folks you think you might like, you can start dating for real from the start. If you’re super-organized, you can create a chart of the characteristics and ‘tells’ of characteristics you really want. Also, what is nice but not a deal-breaker. For these first dates, you can figure out the average and standard deviation, and aim for someone in the top 5%. A 5% target is someone whose two standard deviations above the average. This is simple Analysis of variation math (ANOVA), math that I discussed elsewhere. In general you’ll get to someone in the top 5% by dating ten people chosen with help from friends. Starting this way, you’ll avoid being unreasonably cruel to date #1, nor will you loose out on a great mate early on.

Some effort should be taken to look at the fellow’s family and his/her relationship with them. If their relationship is poor, or their behavior is, your kids may turn out similar.

After a while, you can say, I’ll marry the best I see, or the best that seems like he/she will say yes (a smaller sub-set). You should learn from each date, though, and don’t assume you can instantly size someone up. It’s also a good idea to meet the family since many things you would not expect seem to be inheritable. Meeting some friends too is a good idea. Even professionals can be fooled by a phony, and a phony will try to hide his/her family and friends. In the real world, dating should take time, and even if you discover that he/ she is not for you, you’ll learn something about what is out there: what the true average and standard deviation is. It’s not even clear that people fall on a normal distribution, by the way.

Don’t be too upset if you reject someone, and find you wish you had not. In the real world you can go back to one of the earlier fellows, to one of the rejects, if one does not wait too long. If you date with honesty from the start you can call up and say, ‘when I dated you I didn’t realize what a catch you were’ or words to that effect. That’s a lot better than saying ‘I rejected you based on a mathematical strategy that involved lying to all the first 36.8%.’

Robert Buxbaum, December 9, 2019. This started out as an essay on the mathematics of the fussy suitor problem. I see it morphed into a father’s dating advice to his marriage-age daughters. Here’s the advice I’d given to one of them at 16. I hope to do more with the math in a later post.

Samuel Johnson and British elitism during the revolution.

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A common opinion of Samuel Johnson was that “No man but a blockhead ever wrote except for money”. It’s recorded by Boswell on April 5, 1776 well into the revolution, and applied equally to the American revolutionaries and all other unpaid enthusiasts. Johnson wrote for money. He wrote sermons for priests, he wrote political speeches for Troys, he wrote serialized travel logs, and at one point a tearful apology for a priest about to be hanged for forgery. That he was paid was proof that he was good at writing, though not 100% convincing. The priest was forgiven and acquitted in the public eye, but he was hanged for the forgery none-the-less. 

Some Samuel Johnson Quotes about America

Johnson was unequivocal in his opinion of American independence. His pamphlet ,”Taxation no Tyranny” 1775 (read it here) makes a semi-convincing Tory argument that taxation without representation is in no way tyranny, and is appropriate for America. America, it’s argued, exists for the good of the many, and that’s mainly for the good of England. He notes that, for the most part, Americans came to the land willingly, and thus gave up their rights: “By his own choice he has left a country, where he had a vote and little property, for another, where he has great property, but no vote.” Others left other lands or were sent as criminals. They “deserved no more rights than The Cornish people,” according to Johnson. Non-landed people, in general had no vote, and he considered that appropriate. Apparently, if they had any mental value, they’d be able to afford an estate. His views of Irish Catholics were somewhat similar , “we conquered them.” By we, Johnson meant Cromwell over a century earlier, followed by William of Orange. Having beat the Irish Catholics at the battle of the Boyne meant that that the Protestants deserved to rule despite the Catholics retaining a substantial right to land. I am grateful that Johnson does not hide his claim to rulership in the will of God, or in some claim to benefit the Irish or Americans, by the way. It is rule of superior over inferior, pure and simple. Basically, ‘I’m better than you, so I get to rule.’

One must assume that Johnson realized that the US founders wrote well, as he admitted that some Whigs (Burke) wrote well. Though he was paid for writing “Taxation no Tyranny”, Johnson justifies the rejection of US founding fathers’ claims by noting they are motivated by private gain. He calls American leaders rascals, robbers, and pirates, but is certain that they can be beat into submission. The British army , he says, is strong enough that they can easily “burn and destroy them,” and advises they should so before America gets any stronger. He tells Boswell, “Sir, they are a race of convicts, and ought to be thankful for anything we allow them short of hanging.” Even after a treaty was signed, he confides, “I am willing to love all mankind, except an American.”

I’ve come to love Johnson’s elitism, his justification for rule and exploitation based purely on his own superiority and that of his fellow British. It allows him to present his prejudices uncommonly clearly, mixing in enough flattery to be convincing to those who accept his elitist perspective. That makes his words eminently quotable. It doesn’t make them right, nor does it mean that his was a useful way to deal with people or problems. Adam Smith was willing to admit that the Americans had a gripe, and suggests the simple remedy of giving Americans a voice in Parliament. His solution might have kept the empire whole. Edward Gibbon, an expert on Rome who opposed rights for Americans, at least admitted that we might win the war. Realistic views like this are more productive, but far less marketable. If you are to sell your words, it helps to be a pig-headed bigot and a flatterer of those who agree with you. This advantage of offending your opponents was not lost on Johnson as the quote below shows.

Johnson writing about notoriety, a very American attitude.

I’m left to wonder about the source of Johnson’s hatred for Americans though — and for the Irish, Cornish, and Scots. In large part, I think it stems from a view of the world as a zero-sum game. Any gain for the English servant is a loss to the English gentleman. The Americans, like the Irish and Cornish, were subject peoples looking for private benefit. Anything like low taxes was a hurt to the income of him and his fellows. The zero sum is also the view of Scrooge in a Christmas Carol; it is a destructive view.

As for those acted in any way without expectation of pay, those who would write for posterity, or would fight the Quixotic fight, such people were blockheads in his view. He was willing to accept that there were things wrong in England, but could not see how an intelligent person would favor change that did not help him. This extended to his beliefs concerning education of children: “I would not have set their future friendship to hazard for the sake of thrusting into their heads knowledge of things for which they might not perhaps have either taste or necessity. You teach your daughters the diameters of the planets, and wonder when you have done that they do not delight in your company. No science can be communicated by mortal creatures without attention from the scholar; no attention can be obtained from children without the affliction of pain, and pain is never remembered without resentment.” This is more of Johnson’s self-interest: don’t teach anything that will bring resentment and no return benefit. Teach the sons of the greats that they are great and that they are to lead. Anything more is a waste or an active harm to the elite.

But what happens when America succeeds? Johnson was still alive and writing in 1783. If the Americans could build an army and maintain prosperous independence, they would have to be respected as an equal or near-equal. Then what of the rest of the empire? How do you admit that this one servant is your equal and not admit that your other servants may be too? This is the main source of his hatred, I think, and also of the hatred the Scrooge has for mankind. It’s the hatred of the small soul for the large, of the sell-out for the enthusiast. If the other fellow’s sacrifice produces a great outcome, that suggests a new order in the stars — it suggests that everything you’ve done was wrong, or soon will be. The phrase “novus ordo seclorum” on our dollars alludes to just that idea, ‘there is a new order in the heavens.’. He must have realized the possibility, and trembled. Could there be something to the rabble, something beyond cash, safety and rule by the elite? I suspect the very thought of it insulted and angered poor Samuel. At his death, he could be comforted that, at least the Irish, Indians, and Canadians remained subservient.

Robert Buxbaum, December 2, 2019. This essay started out as a discussion of paid writing. But I’ve spent many years of my life dealing with elitists who believed that being paid proved they were right. I too hope that my writing will convince people, and maybe I’ll be paid as an expert (Water commissioner?) To hope for personal success, while trying to keep humble is the essential glorious folly of man.

The main route of lead poisoning is from the soil by way of food, dust, and smoke.

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While several towns have had problems with lead in their water, the main route for lead entering the bloodstream seems to be from the soil. The lead content in the water can be controlled by chemical means that I reviewed recently. Lead in the soil can not be controlled. The average concentration of lead in US water is less than 1 ppb, with 15 ppb as the legal limit. According to the US geological survey, of lead in the soil, 2014., the average concentration of lead in US soil is about 20 ppm. That’s more than 1000 times the legal limit for drinking water, and more than 20,000 times the typical water concentration. Lead is associated with a variety of health problems, including development problems in children, and 20 ppm is certainly a dangerous level. Here are the symtoms of lead poisoning.

Several areas have deadly concentrations of lead and other heavy metals. Central Colorado, Kansas, Washington, and Nevada is particularly indicated. These areas are associated with mining towns with names like Leadville, Telluride, Silverton, Radium, or Galena. If you live in an areas of high lead, you should probably not grow a vegetable garden, nor by produce at the local farmer’s market. Even outside of these towns, it’s a good idea to wash your vegetables to avoid eating the dirt attached. There are hardly any areas of the US where the dust contains less than 1000 times the lead level allowed for water.

Lead content of US soils, from the US geological survey of soils, 2014. Michigan doesn’t look half bad.

Breathing the dust near high-lead towns is a problem too. The soil near Telluride Colorado contains 1010 mg/kg lead, or 0.1%. On a dust-blown day in the area, you could breath several grams of the dust, each containing 1 mg of lead. That’s far more lead than you’d get from 1000 kg of water (1000 liters). Tests of blood lead levels, show they rise significantly in the summer, and drop in the winter. The likely cause is dust: There is more dust in the summer.

Recalled brand of curry powder associated with recent poisoning.

Produce is another route for lead entering the bloodstream. Michigan produce is relatively safe, as the soil contains only about 15 ppm, and levels in produce are generally far smaller than in the soil. Ohio soils contains about three times as much lead, and I’d expect the produce to similarly contain 3 times more lead. That should still be safe if you wash your food before eating. When buying from high-lead states, like Colorado and Washington, you might want to avoid produce that concentrates heavy metals. According Michigan State University’s outreach program, those are leafy and root vegetables including mustard, carrots, radishes, potatoes, lettuce, spices, and collard. Fruits do not concentrate metals, and you should be able to buy them anywhere. (I’d still avoid Leadville, Telluride, Radium, etc.). Spices tend to be particularly bad routes for heavy metal poisoning. Spices imported from India and Soviet Georgia have been observed to have as much as 1-2% lead and heavy metal content; saffron, curry and fenugreek among the worst. A recent outbreak of lead poisoning in Oakland county, MI in 2018 was associated with the brand of curry powder shown at left. It was imported from India.

Marijuana tends to be grown in metal polluted soil because it tolerates soil that is too polluted fro most other produce. The marijuana plant concentrates the lead into the leaves and buds, and smoking sends it to the lungs. While tobacco smoking is bad, tobacco leaves are washed and the tobacco products are regulated and tested for lead and other heavy metals. If you choose to smoke cigarettes, I’d suggest you chose brands that are low in lead. Here is an article comparing the lead levels of various brands. . Better yet, I’s suggest that you vape. There are several advantages of vaping relative to smoking the leaf directly. One of them is that the lead is removed in the process of making concentrate.

Some states test the lead content of marijuana; Michigans and Colorado do not, and even in products that are tested, there have been scandals that the labs under-report metal levels to help keep tainted products on the shelves. There is also a sense that the high cost encourages importers to add lead dust deliberately to increase the apparent density. I would encourage the customer to buy vape or tested products, only.

Here is a little song, “pollution” from Tom Lehrer, to lighten the mood.

Robert Buxbaum, November 24, 2019. I ran for water commissioner in 2016 and lost. I may run again in 2020. Who knows, this time I may win.

The chemistry of lead in drinking water

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Our county, like many in the US and Canada, is served by thousands of miles of lead pipes. Some of these are the property of the government, others sit beneath our homes and are the property of the home-owner. These pipes are usually safe, but sometimes poison us. There is also problem of lead-tin solder. It was used universally to connect iron and copper pipes until it was outlawed in 1986. After years of sitting quietly, this lead caused a poisoning crisis in DC in 2004, and in Flint in 2015-16. Last month my town, Oak Park, registered dangerous lead levels in the drinking water. In an attempt to help, please find the following summary of the relevant lead chemistry. Maybe people in my town, or in other towns, will find some clue here to what’s going on, and what they can do to fix it.

lead pipes showing the three oxides: brown, yellow, and red, PbO2, PbO, and Pb2O3.

Left to itself, lead and solder pipe could be safe; lead is not soluble in clean water. But, if the water becomes corrosive, as happens every now and again, the lead becomes oxidized to one of several compounds that are soluble. These oxides are the main route of poisoning; they can present serious health issues including slow development, joint and muscle pain, memory issues, vomiting, and death. The legal limit for lead content in US drinking water is 15 ppb, a level that is far below that associated with any of the above. The solubility of PbO, lead II oxide, is more than 1000 times this limit 0.017 g/L, or 17,000 ppb. At this concentration serious health issues will show up.

PbO is the yellow lead oxide shown in the center of the figure above, right; the other pipes show other oxides, that are less-soluble, and thus less dangerous. Yellow lead oxide and red lead oxides on the right were used as paint colors until well into the 20th century. Red lead oxide is fairly neutral, but yellow PbO is a base; its solubility is strongly dependent on the PH of the water. In neutral water, its solution can be described by the following reaction.

PbO + H2O(l) –> Pb2+(aq) + 2 OH–(aq).

In high pH water (basic water), there are many OH–(aq) ions, and the solubility is lower. In low pH, acidic water the solubility is even higher. For every 1 point of lower pH the lowubility increases by a factor of 10, for every 1 point of higher pH, it decreases by a factor of ten. In most of our county, the water is slightly basic, about pH 8. It also helps that our water contains carbonate. Yellow lead forms basic lead carbonate, 2PbCO3·Pb(OH)2, the white lead that was used in paint and cosmetics. Its solubliity is lower than that of PbO, 110 ppb, in pure water, or within legal limit in water of pH 8. If you eat white lead, though, it reacts with stomach acid, pH 2, and becomes quite soluble and deadly. Remember, each number here is a factor of ten.

A main reason lead levels a very low today are essentially zero, even in homes with lead solder or pipe, involves involves the interaction with hypochlorite. Most water systems add hypochlorite to kill bacteria (germs) in the water. A side benefit is significant removal of lead ion, Pb2+(aq).

Pb2+(aq) + 2 ClO–(aq) –> Pb(ClO)2(s). 

Any dissolved lead reacts with some hypochlorite ion reacts to form insoluble lead hypochlorite. Lead hypochlorite can slowly convert to Lead IV oxide — the brown pyrophilic form of lead shown on the left pipe in the figure above. This oxide is insoluble. Alkaline waters favor this reaction, decreasing solubility, but unlike with PbO, highly alkaline waters provide no significant advantage.

PbClO+(aq) + H2O(l) –> PbO2(s) + 2 H+(aq) + Cl–(aq)

Lead IV oxide, PbO2 was used in old-fashioned matches; it reacts violently with phosphorus or sulfur. People were sometimes poisoned by sucking on these matches. In the stomach, or the presence of acidic drinking water, PbO2 is decomposed forming soluble PbO:

PbO2(s) +2 H+(aq) + 2 e– –> PbO(s) + H2O(l).

You may wonder at the presence of the two electrons in the reaction above. A common source in water systems is the oxidation of sulphite:

SO3-2(aq)–> SO4-2(aq) + 2 e–.

The presence of sulphite in the water means that hypochlorite is removed.

ClO–(aq) + 2 H+(aq) + 2 e– —> Cl–(aq) + H2O(l).

Removal of hypochlorite can present a serious danger, in part because the PbO2(s) slowly reverts to PbO and becomes soluble, but mostly because bacteria start multiplying. In the Flint crisis of 2016, and in a previous crisis in Washington DC, the main problem, in my opinion was a lack of hypochlorite addition. The lead crisis was preceded by an uptick in legionnaires disease; It killed 12 people in Flint in 2014 and 2015, and 87 were sickened, all before the lead crisis. Eventually, it was the rise of legionaries disease that alerted water officials in Virginia that there was something seriously wrong in Flint. Most folks were unaware because Flint water inspectors seem to have been fudging the lead numbers to make things look better.

Most US systems add phosphate to remove lead from the water. Flint water folks could have stopped the lead crisis, but not the legionnaires, by adding more phosphate. Lead phosphate solubility is 14 ppb at 20°C, and my suspicion is that this is the reason that the legal limit in the US is 15 ppb. Regulators chose 15 ppb, I suspect, not for health reasons, but because the target could be met easily through the addition of phosphate. Some water systems in the US and Canada disinfect with chloramine, not hypochlorite, and these systems rely entirely on phosphate to keep lead levels down. Excess phosphate is used in Canada to lower lead levels below 10 ppb. It works better on systems with hypochlorite.

Chloramine is formed by reacting hypochlorite with ammonia. It may be safer than hypochlorite in terms of chlorite reaction products, a real problem when the water source is polluted. But chloramine is not safe. It sickened 72 soldiers, 36 male and 36 female in 1998. They’d used ammonia and bleach for a “cleaning party” on successive days. Here’s a report and first aid instructions for the poisoning. That switching to chloramine can expose people to lead is called “the chloramine catch”.

Unlike PbO, PbO2 is a weak acid. PbO2 and PbO can react to form red lead, PbO•PbO2(s), the red stuff on the pipe at right in the picture above. Red lead can react with rust to form iron plumbable, an insoluble corrosion resister. A simple version is:

PbO•PbO2(s) + Fe2O3(s) —> 2FePbO3(s).

This reaction is the basis of red-lead, anti-rust compounds. Iron plumbable is considered to be completely insoluble in water, but like PbO it is soluble in acid. Bottom line, slightly basic water is good, as are hypochlorite in moderation, and phosphate.

Robert Buxbaum, November 18, 2019. I ran for water commissioner, and might run again. Even without being water commissioner, I’ll be happy to lend my expertise, for free, to any Michigan town or county that is not too far from my home.

Ladder on table, safe till it’s not.

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via GIFER

Two years ago I wrote about how to climb a ladder safely without fear. This fellow has no fear and has done the opposite. This fellow has chosen to put a ladder on a table to reach higher than he could otherwise. That table is on another table. At first things are going pretty well, but somewhere about ten steps up the ladder there is disaster. A ladder that held steadily, slips to the edge of the table, and then the table tips over. It’s just physics: the higher he climbs on the ladder the more the horizontal force. Eventually, the force is enough to move the table. He could have got up safely if he moved the tables closer to the wall or if he moved the ladder bottom further to the right on the top table. Either activity would have decreased the slip force, and thus the tendency for the table to tip.

Perhaps the following analysis will help. Lets assume that the ladder is 12.5′ long and sits against a ten foot ledge, with a base 7.5′ away from the wall. Now lets consider the torque and force balance at the bottom of the ladder. Torque is measured in foot-pounds, that is by the rotational product of force and distance. As the fellow climbs the ladder, his weight moves further to the right. This would increase the tendency for the ladder to rotate, but any rotation tendency is matched by force from the ledge. The force of the ledge gets higher the further up the ladder he goes. Let’s assume the ladder weighs 60 lbs and the fellow weighs 240 pounds. When the fellow has gone up ten feet up, he has moved over to the right by 7.5 feet, as the diagram shows. The weight of the man and the ladder produces a rotation torque on the bottom of 60 x 3.75 + 240 x 7.5 = 1925 foot pounds. This torque is combatted by a force of 1926 foot pounds provided by the ledge. Since the ladder is 12.5 feet long the force of the ledge is 1925/12.5 = 154 pounds, normal to the ladder. The effect of this 154 lbs of normal force is to push the ladder to the left by 123.2 lbs and to lift the ladder by 92.4lbs. It is this 123.2 pounds of sideways push force that will cause the ladder to slip.

The slip resistance at the bottom of the ladder equals the net weight times a coefficient of friction. The net weight here equals 60+240-92.4 = 217.6 lbs. Now lets assume that the coefficient of friction is 0.5. We’d find that the maximum friction force, the force available to stop a slip is 217.6 x 0.5 = 108.8 lbs. This is not equal to the horizontal push to prevent rotation, 123.2 lbs. The net result, depending on how you loot at things, is either that the ladder rotates to the right, or that the ladder slips to the left. It keeps slipping till, somewhere near the end of the table, the table tips over.

Force balance of man on ladder. Based on this, I will go through the slippage math in gruesome detail.

I occasionally do this sort of detailed physics; you might as well understand what you see in enough detail to be able to calculate what will happen. One take home from here is that it pays to have a ladder with rubber feet (my ladders do). That adds to the coefficient of friction at the bottom.

Robert Buxbaum, November 6, 2019.

Water Towers, usually a good thing.

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Most towns have at least one water tower. Oakland county, Michigan has four. When they are sized right, they serve several valuable purposes. They provide water in case of a power failure; they provide increased pressure in the morning when people use a lot of water showering etc.; and they allow a town to use smaller pumps and to pump with cheaper electricity, e.g. at night. If a town has no tower, all these benefits are gone, but a town can still have water. It’s also possible to have a situation that’s worse than nothing. My plan is to show, at the end of this essay, one of the ways that can happen. It involves thermodynamic properties of state i a situation where there is no expansion headspace or excess drain (most towers have both).

A typical water tower — spheroidal design. A tower of the dimensions shown would contain about 1/2 million gallons of water.

The typical tower stands at the highest point in the town, with the water level about 170 feet above street level. It’s usable volume should be about as much water as the town uses in a typical day. The reason for the height has to do with the operating pressure of most city-level water pipes. It’s about 75 psi and each foot of water “head” gives you about 0.43 psi. You want pressures about 75 psi for fire fighting, and to provide for folks in apartment buildings. If you have significantly higher pressures, you pay a cost in electricity, and you start losing a lot of water to leaks. These leaks should be avoided. They can undermine the roads and swallow houses. Bob Dadow estimates that, for our water system the leakage rate is between 15 and 25%.

Oakland county has four water towers with considerably less volume than the 130 million gallons per day that the county uses. I estimate that the South-east Oakland county tower, located near my home, contains, perhaps 2 million gallons. The other three towers are similar in size. Because our county’s towers are so undersized, we pay a lot for water, and our water pressure is typically quite low in the mornings. We also have regular pressure excursions and that leads to regular water-boil emergencies. In some parts of Oakland county this happens fairly often.

There are other reasons why a system like ours should have water towers with something more like one days’ water. Having a large water reserve means you can benefit from the fact that electric prices are the lowest at night. With a days’ volume, you can avoid running the pumps during high priced, day times. Oakland county loses this advantage. The other advantage to having a large volume is that it gives you more time to correct problems, e.g. in case of an electric outage or a cyber attack. Perhaps Oakland thinks that only one pump can be attacked at one time or that the entire electric grid will not go out at one time, but these are clearly false assumptions. A big system also means you can have pumps powered by solar cells or other renewable power. Renewable power is a good thing for reliability and air pollution avoidance. Given the benefits, you’d expect Oakland county would reward towns that add water towers, but they don’t, as best I can tell.

Here’s one way that a water column can cause problems. You really need those pressure reliefs.

Now for an example of the sort of things that can go wrong in a water tower with no expansion relief. Every stand-pipe is a small water tower, and since water itself is incompressible, it’s easy to see that a small expansion in the system could produce a large pressure rise. The law requires that every apartment hose water system has to have expansion relief to limit these increases; The water tower above had two forms of reliefs, a roof vent, and an overflow pipe, both high up so that pressure could be maintained. But you can easily imagine a plumber making a mistake and installing a stand pipe without an expansion relief. I show a system like that at left, a 1000 foot tall water pipe, within a skyscraper, with a pump at the bottom, and pipes leading off at the sides to various faucets.

Lets assume that the pressure at the top is 20 psi, the pressure at the bottom will be about 450 psi. The difference in pressure (430 psi) equals the weight of the water divided by the area of the pipe. Now let’s imagine that a bubble of air at the bottom of the pipe detaches and rises to the top of the pipe when all of the faucets are closed. Since air is compressible, while water is not, the pressure at the bubble will remain the same as the bubble rises. By the time the bubble reaches the top of the pipe, the pressure there will rise to 450 psi. Since water has weight, 430 psi worth, the pressure at the bottom will rise to 880 psi = 450 + 430. This is enough to damage pump and may blow the pipes as well. A scenario like this likely destroyed the New Horizon oil platform to deadly consequences. You really want those pressure reliefs, and you want a competent plumber / designer for any water system, even a small one.

Robert Buxbaum, September 28- October 6, 2019. I ran for water commissioner is 2016.

Recycle nuclear waste

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In a world obsessed with stopping global warming by reducing US carbon emissions, you’d think there would be a strong cry for nuclear power, one of the few reliable sources of large-scale power that does not discharge CO2. But nuclear power produces dangerous waste, and I have a suggestion: let’s recycle the waste so it’s less dangerous and so there is less of it. Used nuclear fuel rods, in particular. We burn perhaps 5% of the uranium, and produce a waste that is full of energy. Currently these, semi-used rods are stored in very expensive garbage dumps waiting for us to do something. Let’s recycle.

I’ve called nuclear power the elephant in the room for clean energy. Nuclear fuel produces about 25% of America’s electricity, providing reliable baseline generation along with polluting alternatives: coal and natural gas, and less-reliable renewables like solar and wind. Nuclear power does not emit CO2, and it’s available whether or not the sun shines or the wind blows. Nuclear power uses far less land area than solar or wind too, and it provides critical power for our navy aircraft carriers and submarines. Short of eliminating our navy, we will have to keep using nuclear.

Although there are very little nuclear waste per energy delivered, the waste that there is, is hard to manage. Used nuclear fuel rods in particular. For one thing, the used rods are hot, physically. They give off heat, and need to be cooled. At first they give off so much heat that the rods must be stored under water. But rod-heat decays fractally. After ten years or so, rods can be stored in naturally cooled concrete; it’s still a headache, but a smaller one The other problem with the waste rods is that they contain about 1.2% plutonium, a material that can be used for atomic bombs. A major reason that you can’d just dump the waste into the ocean or into a salt mine is the fear that someone will dig it up and extract the plutonium for an a- bomb. The extraction is easy compared to enriching uranium to bomb-grade, and the bombs work at least as well. Plutonium made this way was used for the bomb that destroyed Nagasaki.

The original plan for US nuclear power had been that we would extract the plutonium, and burn it up by recycling it to the nuclear reactor. We’d planned to burry the rest, as the rest is far less dangerous and far less, long-term radioactive. We actually did some plutonium recycling of this sort but in the 1970s a disgruntled worker named Silkwood stole plutonium and recycling was shut down in the US. After that, political paralysis set in and we’ve come to just let the waste sit in more-or-less guarded locations. There was a thought to burry everything in a guarded location (Yucca Mountain, Nevada) but the locals were opposed. So the waste sits waiting to leak out or be stolen. I’d like to return to recycling, but not necessarily of pure plutonium as we did before Silkwood: there is no guarantee that there won’t be other plutonium thieves.

Instead of removing the plutonium for recycling, I’d like to suggest that we remove about 40% of the uranium in the rod, and all of the “ash”, this is all of the lighter atom elements created from the split uranium atoms. This ash is about 5% of the total. The resultant rods would have about 2% plutonium, 97.5% enriched uranium (about 1% enriched at this stage) plus about 0.5% higher transuranics. This composition would be a far less dangerous than purified plutonium. It would be less hot and it would not be possible to use it directly for atom bombs. It would still be fissionable, though, at the same energy content as fresh rods.

There is an uncommonly large amount of power available in nuclear fuel

Several countries recycle by removing the ash. Because no uranium is removed, the material they get has about half the usable life of a fresh rod. After one recycle, there is not much more they could do. If we remove uranium material is a lot more easily used, and more easily recycled again. If we keep removing ash and uranium, we could get many, many recycles. The result is a lot less uranium mining, and more power per rod, and fewer rods to store under guard.

The plutonium of multiply recycled rods is also less-usable for fission bombs. With each recycle, the rods build up a non-fisionabl isotope of plutonium: Pu 240. This isotope is not readily separated from the fissionable isotope, Pu 239, making multiply used rods relatively useless for fission bombs.

Among the countries that do some nuclear waste recycling are Canada, France, Russia, China, and Germany. Not a bad assortment. I would be happy to see us join them.

Robert Buxbaum September 9, 2019