Category Archives: Engineering

A very clever hydrogen pump

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I’d like to describe a most clever hydrogen pump. I didn’t invent it, but it’s awfully cool. I did try to buy one from “H2 Pump,” a company that is now defunct, and I tried to make one. Perhaps I’ll try again. Here is a diagram.

Electrolytic membrane H2 pump

Electrolytic membrane H2 pump

This pump works as the reverse of of a PEM fuel cell. Hydrogen gas is on both sides of a platinum-coated, proton-conducting membrane — a fuel cell membrane. As in a PEM fuel cell, the platinum splits the hydrogen molecules into H atoms. An electrode removes electrons to form H+ ions on one side of the membrane; the electrons are on the other side of the membrane (the membrane itself is chosen to not conduct electricity). The difference from the fuel cell is that, for the pump you apply a energy (voltage) to drive hydrogen across the membrane, to a higher pressure side; in a fuel cell, the hydrogen goes on its own to form water, and you extract electric energy.

As shown, the design is amazingly simple and efficient. There are no moving parts except for the hydrogen itself. Not only do you pump hydrogen, but you can purify it as well, as most impurities (nitrogen, CO2) will not go through the membrane. Water does permeate the membrane, but for many applications, this isn’t a major impurity. The amount of hydrogen transferred per plate, per Amp-second of current is given by Faraday’s law, an equation that also shows up in my discussion of electrolysis, and of electroplating,

C= zFn.

Here, C is the current in Amp-seconds, z is the number or electrons transferred per molecule, in this case 2, F is Faraday’s constant, 96,800, n is the number of mols transferred.  If only one plate is used, you need 96,800 Amp-seconds per gram of hydrogen, 53.8 Amp hours per mol. Most membranes can operate at well at 1.5 Amp per cm2, suggesting that a 1.1 square-foot membrane (1000 cm2) will move about 1 mol per minute, 22.4 slpm. To reduce the current requirement, though not the membrane area requirement, one typically stacks the membranes. A 100 membrane stack would take 16.1 Amps to pump 22.4 slpm — a very manageable current.

The amount of energy needed per mol is related to the pressure difference via the difference in Gibbs energy, ∆G, at the relevant temperature.

Energy needed per mol is, ideally = ∆G = RT ln Pu/Pd.

where R is the gas constant, 8.34 Joules per mol, T is the absolute temperature, Kelvins (298 for a room temperature process), ln is the natural log, and Pu/Pd is the ratio of the upstream and downstream pressure. We find that, to compress 2 grams of hydrogen (one mol or 22.4 liters) to 100 atm (1500 psi) from 1 atm you need only 11400 Watt seconds of energy (8.34 x 298 x 4.61= 11,400). This is .00317 kW-hrs. This energy costs only 0.03¢ at current electric prices, by far the cheapest power requirement to pump this much hydrogen that I know of. The pump is surprisingly compact and simple, and you get purification of the hydrogen too. What could possibly go wrong? How could the H2 pump company fail?

One thing that I noticed went wrong when I tried building one of these was leakage at the seals. I found it uncommonly hard to make seals that held even 20 psi. I was using 4″ x 4″ membranes so 20 psi was the equivalent of 320 pounds of force. If I were to get 200 psi, there would have been 3200 lbs of force. I could never get the seals to stay put at anything more than 20 psi.

Another problem was the membranes themselves. The membranes I bought were not very strong. I used a wire-mesh backing, and a layer of steel behind that. I figured I could reach maybe 200 psi with this design, but didn’t get there. These low pressures limit the range of pump applications. For many applications,  you’d want 150-200 psi. Still, it’s an awfully cool pump,

Robert E. Buxbaum, February 17, 2017. My company, REB Research, makes hydrogen generators and purifiers. I’ve previously pointed out that hydrogen fuel cell cars have some dramatic advantages over pure battery cars.

Rethinking fluoride in drinking water

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Every now and again, it pays to rethink what everyone knows is so. As it happens I was asked to rethink fluoride in the drinking water. So here goes.

Fluoride is a poison, toxic for a small child in doses of 500 mg, and toxic to an adult in doses of a few thousand mg. It is a commonly used rat poison that kills by robbing the brain of its ability to absorb oxygen. In the form of hydrofluoric acid, it is responsible for the deaths of more famous chemists than any other single compound: Humphrey Davy died trying to isolate fluorine; Paul Louyet and Jerome Nickles, too. Thomas Knox nearly died, and Henri Moissan’s life was shortened. Louis-Joseph Gay Lussac, George Knox, and Louis- Jacques Thenard suffered burns and similar, George Knox was bedridden for three years. Among the symptoms of fluoride poisoning is severe joint pain and that your brain turns blue.

In low doses, though, fluoride is thought to be safe and beneficial. If true, this would be an example of hormesis. It’s found that many things that are toxic at high doses are beneficial at low. Most drugs fall into this category; chemotherapy works this way. Sunshine and radioactivity show hormesis too. Fluoride seems to be like this. In small doses, Fluoride is associated with strong teeth, and few cavities, and no obvious health risks. It is found at ppm levels many well water systems, and has shown no sign of toxicity, either for humans or animals at these ppm levels. Following guidelines set by the AMA, most US cities have been putting fluoride in drinking water since the 1960s, typically at concentrations between 0.7 and 1.2 ppm. We have seen no deaths or clear evidence of any injury from this, but there has been controversy. Much of the controversy stems from a Chinese study that links fluoride to diminished brain function, and passivity (Anti-fluoriders falsely attribute this finding to a Harvard researcher, but the Harvard study merely cites the Chinese). The American dental association strongly maintains that worries based on this study are groundless, and that the advantage in lower cavities more than off-sets any other risks. Notwithstanding, I thought I’d take another look. The typical US adult consumes 1-3 mg/day the result of drinking 1-3 liters of fluoridated water (1 ppm = 1 mg/liter). This < 1/1000 the toxic dose,

While there is no evidence that people who drink high-fluoride well water are any less-healthy than those who drink city water, or distilled / filtered water, that does not mean that our city levels are ideal. Two months ago, while running for water commissioner, I was asked about fluoride, and said I would look into it. Things have changed since the 1960s: our nutrition has changed, we have vitamin D milk, and our toothpastes now contain fluoride. My sense is we can reduce the water concentration. As shown below, many industrial countries that don’t add fluoride have similar tooth decay rates to the US.

World Health Organization data on tooth decay and fluoridation.

World Health Organization data on tooth decay and fluoridation.

This chart should not be read to suggest that fluoride doesn’t help; all the countries shown use fluoride toothpaste, and some give out fluoride pills, too. And some countries that don’t add fluoride have higher levels of cavities. Norway and Japan, for example. They don’t add fluoride and have 50% more cavities than we do. Germany doesn’t add fluoride, and has fewer cavities, but they hand out fluoride pills, To me, the chart suggests that our levels should be lower than the AMA guidance, though not zero. In 2015, the Department of Health recommend lowering the fluoride level to 0.7 ppm, the lower end of the previous range, but based on the experience of Europe, I’d pick 1/2 the original dose: 0.6 to 0.35 ppm. I’d then revisit the data in another 15 years.

Having picked my target fluoride concentration, I checked to see what the levels we use in my county, Oakland county, MI. I was happy to discover that the levels were already below the AMA guide. The water the county drinks, provided by Detroit Water and Sewage, NOCWA and SOCWA contains 0.43-0.55 ppm fluoride, in the center of in the range I would have picked. Fluoride concentrations are higher in towns that use well water, about  0.65-0.85 ppm. I do not know if this is because the well water comes from the ground with these fluoride concentrations or if the towns add more, aiming at the Department of Health target. In either case, I don’t find these levels alarming. If you live in one of these towns, or outside of Oakland county, check your fluoride levels. If they seem high, write to your water commissioner or add a filter to your tap. You can also switch from fluoride toothpaste to non-fluoride, or baking soda. In any case, remember to brush. That does make a difference, and it’s completely non-toxic.

Robert Buxbaum, January 9, 2017. Another toxic additive is chlorine. I discuss chlorine addition a bit in this essay. As a side issue, a main mechanism of sewer pipe decay is related to tooth decay. The roofs of sewer pipes grow acid-producing, cavity causing bacteria that live off of the foul sewer gas. In time these bacteria destroy concrete sewer pipes. The remedies for this erosion is to clean sewer pipes regularly, after having them checked by a professional, about once per year. As with death, one should repair cavities early. Here too, it seems high fluoride cement resists cavities better.

A British tradition of inefficiency and silliness

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While many British industries are forward thinking and reasonably efficient, i find Britons take particular pride in traditional craftsmanship. That is, while the Swiss seem to take no particular pride in their coo-coo clocks, the British positively glory in their handmade products: hand-woven, tweed jackets, expensive suits, expensive whiskey, and hand-cut diamonds. To me, an American-trained engineer, “traditional craftsmanship,” of this sort is another way of saying silly and in-efficient. Not having a better explanation, I associate these behaviors with the decline of English power in the 20th century. England went from financial and military preëminence in 1900 to second-tier status a century later. It’s an amazing change that I credit to tradition-bound inefficiency — and socialism.

Queen Elizabeth and Edward VII give the Nazi solute.

Queen Elizabeth and Edward VII give the Nazi solute.

Britain is one of only two major industrial nations to have a monarch and the only one where the monarch is an actual ambassador. The British Monarchy is not all bad, but it’s certainly inefficient. Britain benefits from the major royals, the Queen and crown prince in terms of tourism and good will. In this she’s rather like our Mickey Mouse or Disneyland. The problem for England has to do with the other royals, We don’t spend anything on Mickey’s second cousins or grandchildren. And we don’t elevate Micky’s relatives to military or political prominence. England’s royal leaders gave it horrors like the charge of the light brigade in the Crimean war (and the Crimean war itself), Natzi-ism doing WWII, the Grand Panjandrum in WWII, and the attack on Bunker Hill. There is a silliness to its imperialism via a Busby-hatted military. Britain’s powdered-wigged jurors are equally silly.

Per hour worker productivity in the industrial world.

Per hour worker productivity in the industrial world.

As the chart shows, England has the second lowest per-hour productivity of the industrial world. Japan, the other industrial giant with a monarch, has the lowest. They do far better per worker-year because they work an ungodly number of hours per year. French and German workers produce 20+% more per hour: enough that they can take off a month each year and still do as well. Much of the productivity advantage of France, Germany, and the US derive from manufacturing and management flexibility. US Management does not favor as narrow a gene pool. Our workers are allowed real input into equipment and product decisions, and are given a real chance to move up. The result is new products, efficient manufacture, and less class-struggle.

The upside of British manufacturing tradition is the historical cachet of English products. Americans and Germans have been willing to pay more for the historical patina of British whiskey, suits, and cars. Products benefit from historical connection. British suits remind one of the king, or of James Bond; British cars maintain a certain style, avoiding fads of the era: fins on cars, or cup-holders, and electric accessories. A lack of change produces a lack of flaws too, perhaps the main things keeping Britain from declining faster. A lack of flaws is particularly worthwhile in some industries, like banking and diamonds, products that have provided an increasing share of Britain’s foreign exchange. The down-side is a non-competitive military, a horrible food industry, and an economy that depends, increasingly on oil.

Britain has a low birthrate too, due in part to low social mobility, I suspect. Social mobility looked like it would get worse when Britain joined the European Union. An influx of foreign workers entered taking key jobs including those that with historical cachet. The Brits reacted by voting to leave the EC, a vote that seems to have taken the upper class by surprise, With Brexit, we can hope to see many years more of manufacturing by the traditional and silly.

Robert Buxbaum, December 31, 2016. I’ve also written about art, good and bad, about the US aesthetic of strength, about the French tradition of innovation, And about European vs US education.

How do you drain a swamp, literally

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The Trump campaign has been claiming it wants to “drain the swamp,” that is to dispossess Washington’s inbred army of academic consultants, lobbyists, and reporter-spin doctors, but the motto got me to think, how would you drain a swamp literally? First some technical definitions. Technically speaking, a swamp is a type of wetland distinct from a marsh in that it has no significant flow. The water just, sort-of sits there. A swamp is also unlike a fen or a bog in that swamp water contains enough oxygen to support life: frogs, mosquitos, alligators,., while a fen or bog does not. Common speech ignores these distinctions, and so will I.report__jaguars_running_back_denard_robi_0_5329357_ver1-0_640_360

If you want to drain a large swamp, such as The Great Dismal Swamp that covered the south-east US, or the smaller, but still large, Hubbard Swamp that covered south-eastern Oakland county, MI, the classic way is to dig a system of open channel ditches that serve as artificial rivers. These ditches are called drains, and I suppose the phrase, “drain the swamp comes” from them. As late as the 1956 drain code, the width of these ditch-drains was specified in units of rods. A rod is 16.5 feet, or 1/4 of a chain, that is 1/4 the length of the 66′ surveyor’s chains used in the 1700’s to 1800’s. Go here for the why these odd engineering units exist and persist. Typically, 1/4 rod wide ditches are still used for roadside drainage, but to drain a swamp, the still-used, 1956 code calls for a minimum of a 1 rod width at the top and a minimum of 1/4 rod, 4 feet, at the bottom. The sides are to slope no more than 1:1. This geometry is needed. experience shows, to slow the flow, avoid soil erosion and help keep the sides from caving in. It is not unusual to add one or more weirs to control and slow the flow. These weirs also help you measure the flow.

The main drain for Royal Oak and Warren townships, about 50 square miles, is the Red Run drain. For its underground length, it is 66 foot wide, a full chain, and 25 feet deep (1.5 rods). When it emerges from under ground at Dequindre rd, it expands to a 2 chain wide, open ditch. The Red Run ditch has no weirs resulting in regular erosion and a regular need for dredging; I suspect the walls are too steep too. Our county needs more and more drainage as more and more housing and asphalt is put in. Asphalt reduces rain absorption and makes for flash floods following any rain of more than 1″. The red run should be improved, and more drains are needed, or Oakland county will become a flood-prone, asphalt swamp.

Classic ditch drain, Bloomfiled MI. Notice the culverts used to convey water from the ditch under the road.

Small ditch drain, Bloomfield, MI. The ditches connect to others and to the rivers via the culvert pipes in the left and center of the picture. A cheap solution to flooding.

Ditch drains are among the cheapest ways to drain a swamp. Standard sizes cost only about $10/lineal foot, but they are pretty ugly in my opinion, they fill up with garbage, and they tend to be unsafe. Jaguars running back Denard Robinson was lucky to have survived running into one in his car (above) earlier this year. Ditches can become mosquito breeding grounds, too and many communities have opted for a more expensive option: buried, concrete or metal culverts. These are safer for the motorist, but reduce ground absorption and flow. In many places, we’ve buried whole rivers. We’ve no obvious swamps but instead we get regular basement and road flooding, as the culverts still have combined storm and sanitary (toilet) sewage, and as more and more storm water is sent through the same old culverts.

Given my choice I would separate the sewers, add weirs to some of our ditch drains, weirs, daylight some of the hidden rivers, and put in French drains and bioswales, where appropriate. These are safer and better looking than ditches but they tend to cost about $100 per lineal foot, about 10x more than ditch drains. This is still 70x cheaper than the $7000/ft, combined sewage tunnel cisterns that our current Oakland water commissioner has been putting in. His tunnel cisterns cost about $13/gallon of water retention, and continue to cause traffic blockage.

Bald cypress swamp

Bald cypress in a bog-swamp with tree knees in foreground.

Another solution is trees, perhaps the cheapest solution to drain a small swamp or retention pond, A full-grown tree will transpire hundreds of gallons per day into the air, and they require no conduit connecting the groundwater to a river. Trees look nice and can complement French drains and bioswales where there is drainage to river. You want a species that is water tolerant, low maintenance, and has exceptional transpiration. Options include the river birch, the red maple, and my favorite, the bald cypress (picture). Bald cypress trees can live over 1000 years and can grow over 150 feet tall — generally straight up. When grown in low-oxygen, bog water, they develop knees — bits of root-wood that extend above the water. These aid oxygen absorption and improve tree-stability. Cypress trees were used extensively to drain the swamps of Israel, and hollowed-out cypress logs were the first pipes used to carry Detroit drinking water. Some of these pipes remain; they are remarkably rot-resistant.

Robert E Buxbaum, December 2, 2016. I ran for water commissioner of Oakland county, MI 2016, and lost. I’m an engineer. While teaching at Michigan State, I got an appreciation for what you could do with trees, grasses, and drains.

The straight flush and strong shower

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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.

Most flushable wipes aren’t flushable.

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I’m a chemical engineer running for Oakland county water resources commissioner, and as the main job of the office is sewage, and as I’ve already written on the chemistry, I thought I might write about an aspect of the engineering. Specifically about toilet paper. Toilet paper is a remarkable product: it’s paper, compact and low in cost; strong enough to clean you, smooth on your bum, and beyond that, it will disintegrate in turbulent water so it doesn’t clog pipes. The trick to TP’s dry strength and wet-weakness, is that the paper pulp, wood cellulose, is pounded very thin, yet cast fluffy. For extra softness, the paper is typically coated with aloe or similar. Sorry to say, the same recipe does not work for wet-wipes, paper towels or kleenex (facial tissues); all of these products must have wet-strength, and this can cause problems with sewer clogs.

Patent 117355 for perforated toilet paper claimed it as an improved wrapping paper.

Patent 117,355 for perforated toilet paper on a roll. It’s claimed as an improved wrapping paper.

Before there was toilet paper, the world was a much sadder, and smellier place. Much of the world used sticks, stones, leaves, or corn cobs, and none of these did a particularly thorough job. Besides, none of these is particularly smooth, or particularly disposable, nor did it fall apart — not that most folks had indoor plumbing. Some rich Romans had plumbing, and these cleaned themselves with a small sponge on the end of a stick. They dipped the sponge end in water for each use. It was disgusting, but didn’t clog the pipes. I’ve seen this in use on a trip to Turkey 25 years ago — not in actual use, but the stick and sponge was there in a smelly bucket next to the hole in the ground that served as the commode.

The first reasonably modern toilet was invented in 1775 by Alexander Cummings, and by 1852 the first public flush toilets were available. The design looked pretty much like it looks today and the cost was 1¢. You got a towel and a shoe-shine too for that penny, but there was no toilet paper as such. Presumably one used a Roman sponge or some ordinary, standard paper. A popular wipe, back in the day was the Sears-Roebuck catalog. It came free to most homes and included a convenient hole in the corner allowing one to hang it in and outhouse or near the commode. It was rough on the bum, and didn’t fall apart. My guess is that it clogged the pipes too, for those who used it with flush toilets. The first toilet-specific paper wasn’t invented till 1859. Joseph Gayetty, an American, patented a product from pulverized hemp, a relatively soft fiber, softened further with aloe. This paper was softer than standard, and had less tendency to clog pipes.

Toilet paper has to be soft

Toilet paper is either touted to be soft or strong; Modern Charmin touts wet strength, while Cottonelle touts completeness of wipe: ‘go commando.”

The next great innovation was to make toilet paper as a perforated product on a roll. These novelties appear as US Patent #117,355 awarded to Seth Wheeler of Albany, NY 25 July 1871 (Wheeler also invented the classic roll toilet paper dispenser). Much of the sales pitch was that a cleaner bum would prevent the spread of cholera, typhoid, and other plagues and that is a legitimate claim. As the  market expanded, advertising followed. Some early brands touted their softness, others their strength. Facial tissues, e.g. Kleenex, were sold specifically as a soft TP-like product that does not fall apart when wet. Sorry to say, this tends to go along with clogged toilets; do not flush more than one kleenex down at a flush. Kleenex is made with the same short fibers and aloe as toilet paper, but it contains binders (glue) to give it wet-strength. My guess is that Charmin is made the same way and that it isn’t great on your plumbing.

Paper towels and most baby wipes are worse to flush than Kleenex. They are made with lots of binder and they really don’t fall apart in water. Paper towels should never be flushed, and neither should most baby wipes, even brands that claim to be ‘flushable.” When flushed, these items tend to soak up fat and become fat bergs – the bane of sewer workers everywhere. There is a class action law suit against flushable wipe companies, and New York City is pursuing legislation to prevent them from claiming to be flushable. Still, as with everything, there are better and worse moist-wipe options. “Cottonelle” brand by Kleenex, and Scott flushable wipes are the best currently. In a day or less they will dissolve in water. These products are made with binders like kleenex, but the binder glue is a type that dissolves in any significant amount of water. As a result, these brands fall apart eventually. For now, these are the only flushable brands I’d recommend flushing, and even then I suggest you only flush one at a time. In tests by Consumer Reports, other brands, e.g. Charmin and Equate flushable wipes do not dissolve. These manufacturers either have not quite figured out how to make dissolvable binders, or they can’t get around Kleenex’s patents.

Robert Buxbaum. October 10, 2016. If you live in Oakland County, MI, vote for me for water commissioner. Here’s my web-site with other useful essays. I should mention Thomas Crapper, too. He invented the push-button flush and made some innovations in the water cistern, and he manufactured high-end commodes for Parliament and the royal family, but he’s irrelevant to the story here.

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.

More French engineering, the Blitzkrieg motorcycle.

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There’s something fascinating that I find in French engineering. I wrote a previous essay about French cars, bridges, and the Eiffel tower. Here’s a picture or two more. Things I wanted to include but didn’t. First here’s a Blitzkrieg Vespa motorcycle; the French built some 800 of these from 1947 to 1962 and used them in Vietnam and Algeria. What’s remarkable is how bizarrely light and unprotected it is. It’s a design aesthetic that follows no one, and that American engineers would not follow.

French Blitzkrieg Vespa used in Vietnam

French Blitzkrieg Vespa used in Vietnam; cannon range is 4.5 miles.

The key engineering insight that allows this vehicle to make sense is that recoil-less rifles are really recoil-less if you design them right. Thus, one can (in theory) mount them on something really light, like a Vespa. Another key (French) insight is that a larger vehicle may make the soldier more vulnerable rather than less by slowing him down and by requiring more gasoline and commissariat services.

Americans do understand the idea of light and mobile, but an American engineers idea of this is a jeep or an armored truck; not a Vespa. From my US engineering perspective, the French went way overboard here. The French copy no one, and no one copies the French, as they say. Still, these things must have worked reasonably well or they would not have made 800 of them over 15 years. A Vespa is certainly cheaper than a Jeep, and easier to transport to the battle zone….

Robert Buxbaum, February 18, 2016. The Italians have a somewhat similar design aesthetic to the French: they like light and cheap, but also like maneuverable and favor new technology. See my blog about a favorite Fiat engine.

The chemistry of sewage treatment

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The first thing to know about sewage is that it’s mostly water and only about 250 ppm solids. That is, if you boiled down a pot of sewage, only about 1/40 of 1% of it would remain as solids at the bottom of the pot. There would be some dried poop, some bits of lint and soap, the remains of potato peelings… Mostly, the sewage is water, and mostly it would have boiled away. The second thing to know, is that the solids, the bio-solids, are a lot like soil but better: more valuable, brown gold if used right. While our county mostly burns and landfills the solids remnant of our treated sewage, the wiser choice would be to convert it to fertilizer. Here is a comparison between the composition of soil and bio-solids.

The composition of soil and the composition of bio-solid waste. biosolids are like soil, just better.

The composition of soil and the composition of bio-solid waste. biosolids are like soil, just better.

Most of Oakland’s sewage goes to Detroit where they mostly dry and burn it, and land fill the rest. These processes are expensive and engineering- problematic. It takes a lot of energy to dry these solids to the point where they burn (they’re like really wet wood), and even then they don’t burn nicely. As shown above, the biosolids contain lots of sulfur and that makes combustion smelly. They also contain nitrate, and that makes combustion dangerous. It’s sort of like burning natural gun powder.

The preferred solution is partial combustion (oxidation) at room temperature by bacteria followed by conversion to fertilizer. In Detroit we do this first stage of treatment, the slow partial combustion by bacteria. Consider glucose, a typical carbohydrate,

-HCOH- + O2 –> CO2 + H2O.    ∆G°= -114.6 kcal/mol.

The value of ∆G°, is relevant as a determinate of whether the reaction will proceed. A negative value of ∆G°, as above, indicates that the reaction can progress substantially to completion at standard conditions of 25°C and 1 atm pressure. In a sewage plant, many different carbohydrates are treated by many different bacteria (amoebae, paramnesia, and lactobacilli), and the temperature is slightly cooler than room, about 10-15°C, but this value of ∆G° suggests that near total biological oxidation is possible.

The Detroit plant, like most others, do this biological oxidation treatment using either large stirred tanks, of million gallon volume or so, or in flow reactors with a large fraction of cellular-material returning as recycle. Recycle is needed also in the stirred tank process because of the low solid content. The reaction is approximately first order in oxygen, carbohydrate, and bacteria. Thus a 50% cell recycle more or less doubles the speed of the reaction. Air is typically bubbled through the reactor to provide the oxygen, but in Detroit, pure oxygen is used. About half the organic carbon is oxidized and the remainder is sent to a settling pond. The decant (top) water is sent for “polishing” and dumped in the river, while the goop (the bottom) is currently dried for burning or carted off for landfill. The Holly, MI sewage plant uses a heterogeneous reactors for the oxidation: a trickle bed followed by a rotating disk contractor. These have higher bio-content and thus lower area demands and separation costs, but there is a somewhat higher capital cost.

A major component of bio-solids is nitrogen. Much of this in enters the form of urea, NH2-CO-NH2. In an oxidizing environment, bacteria turns the urea and other nitrogen compounds into nitrate. Consider the reaction the presence of washing soda, Na2CO3. The urea is turned into nitrate, a product suitable for gun powder manufacture. The value of ∆G° is negative, and the reaction is highly favorable.

NH2-CO-NH2 + Na2CO3 + 4 O2 –> 2 Na(NO3) + 2 CO2 + 2 H2O.     ∆G° = -177.5 kcal/mol

The mixture of nitrates and dry bio-solids is highly flammable, and there was recently a fire in the Detroit biosolids dryer. If we wished to make fertilizer, we’d probably want to replace the drier with a further stage of bio-treatment. In Wisconsin, and on a smaller scale in Oakland MI, biosolids are treated by higher temperature (thermophilic) bacteria in the absence of air, that is anaerobically. Anaerobic digestion produces hydrogen and methane, and produces highly useful forms of organic carbon.

2 (-HCOH-) –> CO2 + CH4        ∆G° = -33.7 Kcal/mol

3 (-HCOH-) + H2O –> -CH2COOH + CO2 +  2 1/2 H2        ∆G° = -21.9 kcal/mol

In a well-designed plant, the methane is recovered to provide heat to the plant, and sometimes to generate power. In Wisconsin, enough methane is produced to cook the fertilizer to sterilization. The product is called “Milorganite” as much of it comes from Milwaukee and much of the nitrate is bound to organics.

Egg-shaped, anaerobic biosolid digestors.

Egg-shaped, anaerobic biosolid digestors, Singapore.

The hydrogen could be recovered too, but typically reacts further within the anaerobic digester. Typically it will reduce the iron oxide in the biosolids from the brown, ferric form, Fe2O3, to black FeO.  In a reducing atmosphere,

Fe2O3 + H2 –> 2 FeO + H2O.

Fe2O3 is the reason leaves turn brown in the fall and is the reason that most poop is brown. FeO is the reason that composted soil is typically black. You’ll notice that swamps are filled with black goo, that’s because of a lack of oxygen at the bottom. Sulphate and phosphorous can be bound to ferrous iron and this is good for fertilizer. Generally you want the reduction reactions to go no further.

Weir dam on the river dour. Used to manage floods, increase residence time, and oxygenate the flow.

Weir dam on the river Dour in Scotland. Dams of this type increase residence time, and oxygenate the flow. They’re good for fish, pollution, and flooding.

When allowed to continue, the hydrogen produced by anaerobic digestion begins to reduce sulfate to H2S.

NaSO4 + 4.5 H2 –>  NaOH + 3H2O + H2S.

I’m running for Oakland county, MI water commissioner, and one of my aims is to stop wasting our biosolids. Oakland produces nearly 1000,000 pounds of dry biosolids per day. This is either a blessing or a curse depending on how we use it.

Another issue, Oakland county dumps unpasteurized, smelly black goo into Lake St. Clair every other week, whenever it rains more than one inch. I’d like to stop this by separating the storm and “sanitary” sewage. There is a capital cost, but it can save money because we’d no longer have to pay to treat our rainwater at the Detroit sewage plant. To clean the storm runoff, I’d use mini wetlands and weir dams to increase residence time and provide oxygen. Done right, it would look beautiful and would avoid the flash floods. It should also bring natural fish back to the Clinton River.

Robert Buxbaum, May 24 – Sept. 15, 2016 Thermodynamics plays a big role in my posts. You can show that, when the global ∆G is negative, there is an increase in the entropy of the universe.

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.