The greatest weapons coupled with the fighting skill of the American soldier stand ready on the alert all over the world to defend this country, you the American people against aggression. This is the Big Picture, an official television report to the nation from the United States Army. Now to show you part of the Big Picture, here is Sergeant Stuart Queen. One of the problems which confronts any modern military organization is the problem of maintaining a proper balance of trained specialists among the troops. To train the specialists it needs, your army maintains a number of service schools, both here at home and with United States units overseas. Today we would like to show you a few of these schools in the U.S. zone of Germany, where men of the European command are learning everything from accounting to the care and training of war dogs. This is a Christmas tree fire, or at any rate that's what it's called by the student firemen in the special subject section of the Usurur Engineer School. Their tree is a perforated gas pipe with a valve at the bottom, and the object of this exercise is for the host team to move in close enough to shut off the valve and stop the fire. The site of this interesting exercise in practical firefighting is the Bavarian town of Murnau, since 1947, home of the Usurur Engineer School. The major service schools of the army are, of course, back in the United States. The Usurur schools train only enough personnel to meet requirements for which U.S. trained experts are not available. These student surveyors, for example, are members of units stationed in all parts of Europe and North Africa. Normal changeover of personnel leaves these units continually in need of new technicians. The requirement may be for a heavy equipment mechanic in England, or for a welder in France. In all of the instruction here at the Engineer School, emphasis is placed on having the students actually do what they are learning. Classes are small, with the instructor in a course like the heavy equipment operators, handling only four to eight students at a time. In this way, each student can be given close, individual attention. Before turning a man loose with one of these, you like to be sure he knows what he's doing. To an army man, engineer usually calls forth thoughts of one of the most important and most delicate operations in modern warfare. The use of mines, demolition charges, and booby traps. In any contest to select the world's worst road, this strip in the demolition area of the school would probably win hands down. For eight years, it has served as proving ground to one of the army's most expert wrecking crews. The bulk of the courses at the Murnau School, however, are constructive rather than destructive. An army engineer must not only learn how to blow things up, he must also be able to put them back together again. These men are learning how to handle the tools of the carpenter's trade. Like the surveyor's course and the course for mechanics, this course in carpenter construction has a civilian usefulness as well as a military application. If one of these young men should go on some day to become a carpenter, architect, or construction engineer, he would not be the first to learn his trade or profession in a usurur service school. There are few civilian occupations nowadays which do not have their army counterpart. That includes much of the work going on here in the lovely town of Oberammergau, site of the usururur intelligence and military police school. In just nine years, the Oberammergau school has risen to become the equal of some of the world's finest police academies. Perhaps they don't look much like it in their fatigues, but these men are policemen, military policemen. They're engaged here in mastering the standard formations for riot control. Experts at the military police school give instruction in every phase of police work to students selected from army units and other U.S. agencies throughout Europe and North Africa. Courses are also conducted for students belonging to the armed forces of other NATO powers. This is a course in judo, that remarkable science which for centuries has been used by the small, captured Japanese to cut bigger men down to manageable size. Pistol practice. A high degree of proficiency with this weapon is extremely important. This is a wall search used by policemen the world over because it is the safest way to search a dangerous subject. The suspect is required to place his hands on the wall at a point slightly higher than his waist and to spread them apart as far as possible. With his feet moved out away from the wall, the prisoner thus needs both arms and legs to keep himself from falling. He cannot use them to attack the searcher. These men are learning the most important phase of good police work, the art of striking a balance between safety for the policeman and fairness to a suspect who may be innocent. This accident is a fate, but a legal one, not an attempt to defraud the driver's insurance company. The collision is simulated, part of the student military police course, but it's conducted just like the real thing, including the alibis. Another branch of the Oberammergau school conducts training in intelligence and counterintelligence, training which includes such matters as how to question prisoners of war. And since prisoners of war will not always oblige us by speaking fluent English, the intelligence operatives work also includes intensive foreign language study. One of the byproducts of World War II was the advance it brought about in the field of language studies. New techniques devised to meet army requirements have greatly accelerated the speed with which languages can be taught. A single scrap of information, something learned from a POW or observed by an advanced patrol, can sometimes turn the entire course of a battle. But first, it must be put together with a lot of other information coming in from different sources. Here, in the combat intelligence section, men and women with special aptitudes are learning the art of fitting together that vast jigsaw puzzle which is the story of a modern military operation. A not insignificant aspect of this work is map making and map reading. A military map must be considerably more complex than an ordinary road map. It must convey a great variety of detailed information and all of the details must be exceedingly accurate. Much of the information used by commanders and their intelligence staffs in the construction of their big picture comes to them over the telephone lines and radios of the Signal Corps. In Europe, many of the technicians who handle this vast network of wire and wavelength receive their training at the Euseroar Signal School in Ansbach. Many of the Signal Corps must be able not only to send and receive messages as these students of radio telegraph procedure are here doing, they must also have technical understanding of their equipment which will enable them to locate trouble on their circuits and correct it. In their work, there is no such thing as calling your local repairman. The fuselage of an L-19, a type of plane used by artillery observers, is employed at the school to demonstrate installation of aircraft radio equipment. As the range of artillery weapons has increased over the years, the problem of accurate observation has also increased. This is one of the solutions. As we have already observed, many students in the Euseroar schools belong to the armed forces of our NATO allies. Here, Colonel Fink, commandant of the Signal School, shows Italian Lieutenant Leopold Urbano and Captain Gabrielle Nidion of the French Signal Corps an illuminated model of the installation. A source of special pride to men of the Euseroar Signal School, incidentally, is this post chapel, constructed entirely from materials furnished by the students themselves. The NCO Academy in Munich. In training here are the non-commissioned officers, the sergeants and corporals who are today, as they have always been, the very heart of the army. These men are among the very best the European command can offer. They have to be, or they don't get here. The old-time sergeant was usually a soldier with long seniority who had acquired most of his knowledge in the well-known School of Hard Knocks. These men are younger, but when they finish at Munich, they know their jobs. Discipline at the Academy is strict. Pass inspection here and you'll pass anywhere. The men in this sergeant's unit are liable to discover that when it comes to bunk check, they have suddenly acquired a very tough boss. The schedule here is intensive and rugged, for its purpose is to produce rugged soldiers. Military training alone is not enough. The soldier must have strength and endurance, agility and coordination. In other words, muscle. One of the best methods yet devised for developing muscle is a little exercise known as the Army Doesn't. The non-commissioned officer does far more than simply relay instructions received from his superiors. In a combat situation, the outcome of an engagement, as well as the lives of himself and his men, may depend on the good judgment and tactical skill of a single squad leader or platoon sergeant. A non-comm must first of all be a natural leader of men. But beyond that, he must absorb an ever-increasing amount of theoretical knowledge about the science of war, a science which, like all others, has grown enormously more complex in the modern era. Here is a portion of the course in map orientation. To the untrained individual, a map is often useless. He can get just as lost with it as without it. For example, the map may show you the place you are trying to reach, but before you can get there, he must first find out where you are starting from. Without road signs or highway markers, this is not always easy. To his theoretical knowledge, the non-comm must add much detailed, practical information. Part of his job is becoming familiar with the operation and capabilities of every weapon which may be used by the men under his command. Graduation from this Munich NCO Academy, as from any such institution, is a fulfilling experience, leaving each of its graduates with a feeling that he has earned the right to command. Not far from Munich, in the alpine town of Füßen, is the Army's largest overseas ordnance school. The commandant of the Usurur Ordnance School is assisted by 29 officers and 240 enlisted men who serve as instructors and specialists in the training of some 4,000 men each year. Army and Air Force personnel, together with officers and enlisted men from the NATO countries, study some 21 courses, covering tanks, artillery, tractors, ammunition, wheeled vehicles, and a host of related ordnance subjects. So varied is the work and responsibility of the ordinance today that it is impossible to designate any one of these subjects as typical. Certainly a very important one is the course dealing with the art of handling and storing explosives, taught by means of this scale model of an ammunition supply point. A less glamorous but equally important course teaches the testing and repair of automobile voltage regulators, one of the subjects covered in the five-week Automotive Electricians course. Students learn the fundamentals of automotive electricity in a modern, well-equipped shop under the close supervision of one of the school's many experts. The cutaway model of a jeep showing details of the engine, transmission, differential and brakes demonstrates to students in the Automotive Maintenance course the role each part plays in the overall operation of a vehicle. The engines of many military vehicles today are completely waterproof by means of a system whose effectiveness is dramatically demonstrated by this jeep engine which is capable of running entirely submerged in water. The 98th General Hospital at Newbrook, Germany. In addition to performing the medical services known to army hospitals and other parts of Europe and elsewhere, the 98th also incorporates a specialized course for nurses, the School of Anesthesia. Few areas of human endeavor require so much study or so many refresher courses as does medicine and its related fields. Nurses as well as doctors must continuously acquaint themselves with the newest ever-changing techniques and equipment of their profession. To assist its medical personnel in this task, the Army in Europe maintains this School of Anesthesia at Newbrook as well as a larger medical training school at Degrendorf, Germany. It is a number one requirement of the Army that every service man or woman shall have access to medical treatment of the highest quality.  Under the hospital team concept of the Army Medical Service doctor, nurse, medical aidman and the patient himself are united in a single group whose sole purpose is to make an injured man whole or a sick one well. This is the town of Longreys. Forty miles south of Munich, deep in the Bavarian Alps, Longreys is one of Germany's most attractive cities. A few kilometers outside of this quiet town with its gentle old world charm is also the site of one of the largest, busiest and most popular of the Usurur service schools, the QM School or Quartermaster. It is the Quartermaster Corps which feeds and clothes the soldier. In a service comprising several million men and women, this in itself is a job of staggering proportions. So wide felt is the need for trained personnel in this field that the Usurur Quartermaster School numbers among its students members of practically every branch of the armed services from every part of the European theater. Millions to supply and thousands of different items to be supplied. The equipment for just one soldier represents hundreds of man hours of work. Even so, the Quartermaster School at Longreys, in addition to its regular Quartermaster courses, also finds time to conduct what are known in the Army as adjutant general courses. These are the stenographers, the personnel clerks, the men who make up the payrolls. This is a student group in the midst of one of their administrative laboratories where they begin putting into practice what they have been learning in the classroom. Nobody knows exactly how many documents must be tabulated and filed for each serviceman and his equipment, but it's a lot. As a result, there is probably no office machine from typewriter to calculator which does not have its place in the Army. And of course, each machine requires not only an operator to run it, but also a man who knows what makes it run. Whether at war or at peace, the American Army today is a worldwide organization. The problem of supply is a big one and a continuing one. It is now several hundred years since a famous general remark that an army travels on its stomach. Whatever may be the broad strategic significance of the general's observation, it is certainly true that this subject has always been a matter of great personal concern to soldiers. It is therefore not surprising that fully one-half of the courses at the Usuror quartermaster school deal with some aspect of cooking. An army cook today has a well-earned right to that white hat, which is the traditional badge of the master chef. Cooking for the troops is no longer a simple matter of brewing a few gallons of coffee or frying a mess of flapjacks. The days of hard tack and sourdough are long since passed. Most of us know of the spectacular advances which have occurred in the development of new weapons and new modes of warfare. Less widely appreciated are the equally remarkable developments in that branch of military science, which deals with feeding the man who carries the gun. There was a time when the soldier not only risked his life for his country, but frequently had to do it on an empty stomach. Today we may say without exaggeration that few in the world are as consistently well-fed as the American soldier. Another place where good food is important and appreciated is the dog branch of the Usuror quartermaster school. Here are trained the war dogs. Canny canines recruited from among the very best of European dogdom to serve with the American army's most famous auxiliary. Thoroughbred or just plain dog, candidates are selected for brains and stamina, not family background. Although dogs have been used by armies from the beginning of military history, they first achieved their present honored status during World War II. Today, dogs are used to an increasing extent, not only by military organizations, but also by police departments and as excellent night watchmen for factories, stores and warehouses. The war dog school at Longreys is coeducational. All students, whether human or canine, receive pretty much the same instruction. There are, to be sure, some problems that are peculiar to the forefooted enrollees. But the bulk of their study consists of man and dog learning to work together. Much of the training takes place on an obstacle course not too dissimilar to the regular obstacle course of army basic training. The dog must learn not only what to do and how, he must also learn to do it on command. Each dog has the same master throughout the course. Seventeen weeks are required to complete the dog training course. Instructors at the school are fond of telling their students that the seventeen weeks, which is a relatively long course for a service school, is made necessary by the men, not the dogs. Dogs masters take longer to learn. Dog and master enroll in the school together. Take their exams together. Pass final inspection together. And stay together throughout their army careers. Love of man for dog and dog for man is one of the great romantic themes of human history. Judging by the long waiting list for admission to the Longarees War Dog School, it's a romance that is still going strong. They make a formidable fighting team. Those were some, but not all, of the Ucerus Service Schools. There are others, like the Bansman School at Dachau, the Finance School at Freitberg, the Transportation School at Mannheim, or the Troop Information and Educational School, also located at Dachau. All busy training specialists to serve with our own forces in Europe, or with those of our NATO allies. Now this is Sergeant Stuart Queen. Invite you to join us next week for another look at the Big Picture, the United States Army in action. The Big Picture is a weekly television report to the nation on the activities of the Army at home and overseas, produced by the Signal Corps Pictorial Center, presented by the U.S. Army in cooperation with this station. You can be an important part of the Big Picture. You can proudly serve with the best equipped, the best trained, the best fighting team in the world today, the United States Army.


All right, talking tax here at 5 p.m. on a given Wednesday. I'm Jay Fidel, and that's Roger Epstein. Do you ever see a tax attorney in a flesh?  Raise your hands. Good work. Here's one, Roger Epstein. Hi, Roger. Hi, Jay. How nice to see you. It's always a pleasure to be with you. We framed this show as should the little people be paying the tax. And it actually tracks on a number of discussions you and I have had since what, early 2017, about the tax reform. And I put that in quotes under the Trump administration, because it never really was about relieving the little people. It was always about taxing them, relatively speaking, more than anyone else. Isn't that nice?  Isn't that nice? But where are we now? We have issues in front of Republican Party and Congress around tax in order to pay for infrastructure and other government benefits that are part of Joe Biden's program going forward. And it raises similar questions. Who pays the freight? And what is going on, Roger? And is it bode well or not? Well, I think the bill that Biden has is designed not to tax the lower people, the little people. If it gets passed, the bill is designed to tax anybody over $400,000, which is a pretty high level of income in a year. And that's taxable income. So I think they're trying to do that. One of the things that you asked me to look at for this conversation was a New York Times article that talked about Republicans not only not wanting to raise taxes, but not wanting to give the IRS enough money to collect the $500 billion of tax gap, they call it, which means uncollected taxes. And the vast majority of that is from wealthy people who can get good tax advice and maybe go over the side, over the edge, or even just not being criminal, but just going a little farther than the line. I used to think of Richard Nixon that way. His plan for the law was you go right to the borderline of what's right or wrong under some provision.  And that was kind of the idea of following the law. So I think we're at an unusual phase here where Republicans not only don't want rich people to pay taxes, they don't even want to collect what the rich people owe. And it's really a function of what I used to say. In China, the government controls the business. And in the United States, the business controls the government. And it really, I don't want to get too deep into it, but it gets back to the fact that what was that scandal years ago, the savings and loan scandal, where Keating said, did you give all that money to those congressmen so they would do what you wanted? And of course, that's why I gave them the money.  So it kind of gets to that. But we're in such an incredibly incomprehensible word I can think about, where the vast majority of Republicans are little people who are not so wealthy. And of course, the driving force remains 1% or whatever percent who really don't want to pay taxes, no matter how much money they make. And nobody really wants to pay taxes. But the question is, how do you run the government? And so we've gotten ourselves into this place where incredibly rich manipulate not only the Congress people, but their own constituents. And so how we get out of it, I'm not sure. As I've told you many times, when I first started with the IRS in 1967, the top tax rate had just come down from 90% to 70%. So not that everybody was paying that rate, but they were paying it on income over $1 million a year in today's dollars. And so now, over a million, you're paying 35%, 37.5%. And they're all pissed. Why do I have to pay so much taxes? So we almost get into a question. It's hard to do this in my mind without the philosophy behind it. What's the purpose of government? Are we supposed to have a society where we keep people falling from falling through the cracks and or is government so odious as it seems the Republicans think that we shouldn't give it any money? Let's not feed the beast. Wasn't that the plan some years back? If we don't raise enough money, we can't have all this welfare. We can't have all these provisions because there's enough money for it. So somehow that got sidetracked to, well, let's not collect any money, or taxation is a punishment as opposed to a civic duty. Well, yeah, there's a couple of points you raised that are worthy of unpacking. One is just in order of the way you raised them. One is what happens if people don't want to pay taxes? If Congress doesn't want to, if people don't want to pay taxes and Congress doesn't want to collect taxes, that's pretty serious because the government has no money. People don't pay. The government cannot function. And then you get effectively, you know what it is? It's kind of this thing about anti-government. It's kind of a revolution against government. Let's take government apart. It's just another angle. It's not dissimilar from the insurrection of January 6th. We stop government from functioning by the power of the purse. If they have no money, it won't be a government, and that's what we want. This is ill-advised, of course. But it really comes from the same place. And I agree with you. The second point is I agree with you that there's an ideology involved, and that is we don't want to be our brother's keeper. If somebody down the road is starving, that's his problem. And if he could make a buck and be rich, good for him, if he can't, bad for him, but it's not our problem. And this is, I think, Trump's view of it, and this has been a Republican mantra for a long time, actually, it didn't begin right away. In fact, it goes way back into the 19th century, where it's not my problem. If he wants to be rich, let him be rich. It sounds like Marie Antoinette, you know? Let them eat cake, and the problem about eating cake is that after a while, it's not sustainable, and they rise up with pitchforks. So where does it all go, Roger? If you don't tax and you don't collect tax, then you don't take care of the people who do pay the tax, what happens? Well, you have the kind of society that the Republicans want, trickle down economics, which has trickled down so slowly that 75% of people in Hawaii are living paycheck to paycheck. And it's not much better, or throughout the country, even though I don't have statistics, there's so many people working two jobs. And so this is actually good for business when you think about it, okay? Because if you're hungry, you'll do anything to work. And so if you want laborers, if you want shopkeepers or clerks in your stores, if you want people to be answering phone calls, if you wanna do a lot of kinds of work that don't require sophisticated knowledge or expertise, then you'd like having everybody starving, basically, because they'll take whatever they can get and they'll work two jobs and they have no options. So is it an exacerbated disparity then? The wealth gap? Absolutely, absolutely. Look, when you and I graduated from college, where I paid $200 a year in the same school now as $12,000 a year, the same state college, I was making $10,000 a year and I could buy a house for $15,000, one and a half times my annual pay. If I make $35,000 coming out of college, what can I buy for $50,000, one and a half times my annual salary? What can I buy for $300,000? The price of houses here now is almost a million dollars. And even in the cheap places around the country, it's $200,000 or $300,000, which means if you're making $20,000, $25,000 a year, it's 10 times or more what you're making annually. So yes, the wealth gap has been great, not wanting to sound like a communist, which I certainly hate the concept of top-down communism, but the relative value of labor and capital is out of sync. It's gotten deliberately skewed, I mentioned to you when we started the talk about Louis Powell's memorandum, the former lawyer for the tobacco industry come Supreme Court Justice under Reagan, who wrote a memo in 71 saying the sixties is insane, that these liberals are taking us to communism, we've got to fight back and they took it where he planned. They took it to their own colleges, so we didn't have just liberal professors. They got all the judges enacted, they got all the local politicians enacted. And in 64, they took advantage of the quote Southern strategy. As you know, the solid South was all democratic from the time that the first Republican president, Abraham Lincoln freed the slaves until 1965, when the civil rights laws were passed, and the South against solid Republican, just like that overnight. And even though Lyndon Johnson said, we lost the South for a generation, he was wrong. We lost the South forever, at least the last 60 years, 55 years. So we have a situation where the very wealthy understand that they're in the minority. They want what they want, but they're in the minority, and the way to get there, they have to manipulate some people. And the way they did it was through the race card, and it's been very effective. And they admitted it. They admitted it in the seventies and the eighties. You just have to follow the path and look at some YouTubes and other kinds of material that's right out there. This is, it's not a conspiracy, it's they're American citizens, they can do what they want, but this was their strategy, the strategy work, and we've ended up with this wealth gap that's incomprehensible. And I'm really a deadly to find out that it's an intentional wealth gap. It's an intentional effort to put some people down and put them in this kind of servitude, use that term, experience where they're in a rat race. I'm reminded of a book written by a New York Times reporter was called dollars and cents, I think it was. And she went into the South. She divested herself from all assets. She had nothing in her pocket and she tried to live the life of somebody who was in the put down class in the South. And she got a job at Kmart or Walmart or something like that. No insurance all part time. And they paid her minimum, minimum. And it was impossible, she couldn't. And she looked around her and found that the whole community was like that. They're all living hand to mouth. They had no savings, no prospects, no education, no nothing. And it was remarkable that she found herself in a situation where everyone around her was under the thumb. And this is now almost 20 years ago, she wrote that book. Rosen Swag, I think was her name. Bottom line is, it was intentional. They were able to do it through a number of devices. You could find, I agree with you, you could find writings. You could find professors in some of the Southern schools that actually taught this as a matter of economics. So here we have it and it's being extended now. It hasn't stopped. It hasn't come to rest. It's getting worse, am I right? It is, it is. And I think we're in a civil war, we're in a battle and everything going on now is economics anyway. All the international stuff. It doesn't, they talk about enemies and things but it's really about economics. Nobody realistically thinks we're gonna drop a nuclear bomb on China or they're gonna drop one on us. And it's a whole different world but we're fighting desperately for economics which really, who are our warriors? Is everybody's a global manufacturer. Everybody's a global sales person. So it's wrong and it doesn't make sense, Jay. It doesn't make sense for the reasons you've said and can we change it? My experience has been when things don't make sense they eventually collapse. But we've waited it so heavily ever since Reagan. Reagan really, so you take this Lewis Powell memo and oh, I'm sorry, I gotta think of the name. There's a book that just came out this year that talks completely about this. Explains the whole thing. It's very, very powerful and very clear. And so the idea is the elite, the economic elite deserve what they have. They've worked harder, they've got it. And if they do well, a rising tide lifts all ships. But the problem is they've held on so tightly to the profits competing internationally. So one big jump on this was when the Arabs took over the oil in 74, you had these very wealthy Arab people who were nowhere near as sophisticated and capable as the seans of business in the United States who've been running the world economically for 20 to 30 years since the war. All of a sudden these guys were making more money than them. So they had to ratchet up the senior salaries. And so the guy on the shop floor was making 30 or 40 times less, the CEO was making 30 or 40 times with the guy on the shop floor is making, now the guy on the CEO is making 400 times what the guy on the shop floor is making because they had to play up to that level. And then you had the Japanese takeover of industry and cars and stereos and all this in the late 70s and 80s. And so they had to keep up with that. And so it's like you're at the top of the list and you're still looking up. You're not looking down to see how they're doing, you're looking up to see how you and your contemporaries are doing. And it has to stop or we're gonna go into third world stuff. How much worse could it be than she explained in her book and now it's 20 years later, how much worse do you think it is, Jay? Oh, I think it's a lot worse. And it's getting, it accelerated during the Trump time. By the way, the name of the book is Nicolled and Dime. Nicolled and Dime, if anybody wants to look at that. And it's the same story we're talking about how there are oppressed people all around this country. And what's really ironic is that they're in the red states. These oppressed people who don't know which way is up are suffering more. And so it's hard to accept this. But one thing- Well, let me say, I thought the name of the book. The name of the book is called Evil Geniuses. Uh-huh, good. It's written by a journalist, Evil Geniuses, and outlines all this. And yeah, well, how are we gonna change? Well, not to say that this is the solution, but back again in the 19th century, there was this French concept, there was a French term in Europe. And it's, if you were very wealthy, you felt that you had to help people. The people who you were exploiting, you had to help them and you gave them money. No bless, no bleed. No bless, no bleed. Thank you. Trying to think of that term, that's exactly right. That's gonna be a final exam, Roger. No bless, no bleed. Thank you, hope I pass. So you got very wealthy, and then it was kind of euphemistic because you know that these guys, Vanderbilt and Rockefeller and Andrew Carnegie, they weren't giving a whole lot of money away. When they died, maybe they left it for tax purposes to a foundation. But during their lives, they didn't give a whole lot of money. But the notion that they were selling was, we're helping you, we know we've exploited you, you're gonna get some money from us. And today, as you say, the disparity between the guy on the factory floor and Bill Gates or Jeff Bezos, who spends his money going into space, I find that very ironic. Those guys have so much money, even if they gave billions away for charity, it would be nothing compared to the size of their estates. So what you have is a complete lack of no-bless oblige. It's no-bless oblige in reverse. As we said, I'm keeping mine, and you can struggle. And if you can't be a billionaire like me, it's your problem. And we call that freedom, call that freedom. Everybody has the freedom to do what they want, they want, except we have all the money and we control all the rules. And, but it's all freedom. And, you know, I look back to Franklin Roosevelt in the, at the end of the depression or in the middle, and he was considered a traitor to his class. But his belief in part was if they didn't do something, forget no-bless oblige, if they didn't do something, they're gonna have a revolution because everybody was living in the streets. And it was, you know, much worse than it is today, but we could get there, Jay. Yes, I agree. Every time you turn, more people sleeping in the streets. And why do we need to do that? Why is that okay? Is that the American way of life? When you say government of the people, by the people, for the people, does that mean everybody for himself? I just don't, okay, I gotta get into this philosophical because I'm reading a wonderful book from my dear friend, Elizabeth Satoris, who's an 85 year old evolution biologist who wrote a book called Earth Dance, which says the earth is really alive and everything started with the fire of the earth and then the atmosphere cooled it off and then we had a crust and the crust made rocks and the rocks made minerals and the minerals made one celled animals. And she shows a pattern of how everything goes through unity to chaos, chaos to competition, competition to collaboration and back to unity. And then eventually something throws it back into chaos. But we're in this period now of heavy competition between humans. And the next phase, whether we get there because we have a revolution or it gets so bad that even a people in the South wake up they're being hoodwinked, we've got to change to a recognition that we're all really connected to each other in many meaningful ways, not just no bless oblige, but through quantum physics, we know we're energetically connected to each other. And so if I hurt you, it hurts me. And that's the reality that we now know since Einstein and with Elizabeth's idea, these patterns of how everything evolved in nature, we've just been too competitive, too many thousands of years of murders and wars and killing people and holding down the feminine principles. It seems to me that it's all coming together for a good change. And what that- Well, we're a bad one, Roger. And just as easily it could be a really bad change. The bad one, yes, it could go on, but at some point, as she shows, chaos forces itself to come to, it gets so horrible. If Trump wasn't it, I know it was, but at some point it gets so horrible that you have to react and you're desperate to change things. Okay, but let me say that when you reach that point, you know, the state of the species, if you will, when you reach that point and you recognizes out of the stories of Helm in the Bible, when you reach that point, it may be too late. You can't go back. Some things you can't fix. You know, you didn't realize it was going south. That's not exactly the best expression. You didn't realize it was going south, but it went south. And by the time you realize that you can't do anything and then you're really in the soup. And so going back to your question, what can we do economically in terms of tax policy, in terms of what Joe Biden should be doing and what this is a long one and what Congress should be doing in order to level the field again to get us back to balance. Yeah. Well, I think it's obvious that as a tax lawyer and no matter what the Republicans have said, cutting the tax rate in half and 70% to 35% has had a huge impact on the ability of the government to take care of needs of people and the pollution and all the things that are going on. We really have to do something about that. And there's different ways to do it. You can ratchet it up gradually or you can do something fairly draconian. Put it back to even 50% as a top tax rate or 70%. And had Biden recognized that even people making a couple of $100,000 a year are not living high on the hog. That's why he put it at 400,000. But he only pushed the rate up to what, 39%. So it's gotta go a lot higher than that in my mind. And the second thing is, so number one, you do it at a federal level or what do we do in Hawaii? We have an opportunity in Hawaii like nobody else does in the country. We're a very multicultural society with very few relatively incredibly wealthy working people. We got a lot of retirees. And so we're, could be of a single mind to help everybody have food, clothing and shelter. And so the government knocked down the tax rate. Why don't we kick ours up and take some more money? Why don't we tax the hotels? Here's a, I could make enough enemies for myself for the rest of my life, but really tourism, if you tax the hotel, this is something I've thought about for a long time. If you tax the hotels on their value, then they would either raise rates, which, okay, if people out of state wanna pay that or whatever, or they couldn't raise rates because they're already too high when they used to be quite reasonable relatively. Or you would have to take lower profits. Lower profits would reduce the value of the hotel because the value is a multiple of how much you make. And so the price of things would start coming down. And so is that fair when the price has gone up 10, 20 times more than the price of labor? And so I'm not, I mean, obviously, if you start your own business, if you put your capital into a business, you need to recover. You need to be treated fairly. But like the CEOs, do you make 40 times as much or do you make 400 times as much?  There's another interesting book. Have you ever heard of Donut Economics? Oh, tell me. Donut Economics is a creation of, I think it's about 15 years old now. They're trying it in Europe. Okay. So in the center of the donut, the donut hole is people who have fallen through the crack and don't have enough to live on in your society. The fleshy part of the donut is where you want everybody to be living. And obviously the wealthier people are at the top of, the outside part of the donut or the top of the outer edges of the top and less wealthy people are closer to the hole. But the outside of the donut is when you're screwing up the whole environment.  So that's the control. We don't want to ruin the planet. We don't want to ruin all the systems. And we don't want to let people fall through the hole in the donut. And so taxes is a major part of that, Jay. And it's not, it has never been effective to set values on things, but it's always been acceptable. In fact, we passed an amendment to have an income tax in 1913, over a hundred years ago. So there's nothing improper about it. And in my mind, there's nothing improper about paying more if you've gotten more out of society because you've done better. And here's something that I would love people to understand because so many people on both sides of the spectrum should say we should have just a flat income tax rate. That is so preposterous and so anti-democratic because, okay, I'm making a million dollars a year and you're making 50,000, say 100,000 either. And we pay 15%, right? I pay 150,000 and you pay 7,500 if you're making 50,000.  With my 42,500, I can't even afford to rent a decent house, but you still got 850,000 left and you can't spend more than two or 300,000. And so you've got discretionary income of another four or $500,000.  But on the other hand, we're in the same society. You've benefited enormously more than me and you can't let all these people fall through the donut hole, not if you wanna have a society where people are living decently. And it doesn't help anybody to be in a society. It doesn't make you happy to walk down the street and step over people asking you for money. It doesn't make you happy to see people living in horrible conditions.  And the collective consciousness that Jung talked about is real. We feel it. We're all feeling bad that so many of our fellow citizens are in such a sense. Well, I mean, there's a real practical aspect to that too. Remember Marie Antoinette let them eat cake? She lost her head over that. And so I mean, I think that in the cards, if you have enough people who are beyond the tipping point who have nothing to lose because they're so poor and miserable, they will rise up and the rich guys will be at the wrong end of that. Yeah, and you see in the middle and that's what I was saying about Franklin Roosevelt. He understood that. And he said, we've gotta give some back. We rich people have to give some back to society. Look, if you pollute all the rivers and you leave it on the community to fix it and then everybody gets sick. How can you say, well, I made all this money. I shouldn't have to clean that up. I shouldn't have to pay taxes. And there's so many things that have just gotten not that they're wrong so much as they've just gotten skewed. They've gotten out of alignment. As I said, the relative value of what I can get for my labor doesn't allow me to buy any capital anymore because the prices are so high. And so the only way to get back is to raise the wages and lower the capital value. Well, I wanted to ask you that last question. It's political. How do you fix this? First of all, the article I sent you about the $500 billion, that's low hanging fruit. You wouldn't have to give the Internal Revenue Service very much money. And all of a sudden that would start pouring into the tail because A, because they would go hustle and get it. And B is because people would see they won't be able to get away with not paying it. And that's the key, Jay. That's the key to our system. I worked for the IRS for five years. The key to the system is people believing they'll get caught if they do wrong. And everybody knows you won't because there's not enough personnel around to catch anybody. They only audited 1% 50 years ago. I can't imagine what that number is now. It's probably a tenth of a percent. And certainly the rich people understand that. And so you've got to go after them because they'll take a chance that they're just a little over the line like I was talking about Nixon. Sure. And then that line has a $500 billion. But the other part of that, Roger, and it's another change in our society is that people are more inclined to try to get away with it. Your Richard Nixon example, they get to the line a little bit over the line. To play with the line. And the problem is, we shouldn't be thinking of it that way. We're in this together. We have to find the social compact again. We have to be happy to pay taxes in order to have a good country. Nobody wants that anymore. We've lost that. Wait a minute, doctor. Wait a minute, doctor. I have fallen out of the belief that anybody is gonna do anything really against their own interests. I read somewhere that people worry what people think about them after they have a little, not a confrontation, just meeting.  The other person must think badly of me. And it says, no, 95% of the time we're thinking about ourselves. And so it really doesn't matter.  But we have to, I really believe, Jay, we have to understand not that we're good people Jesus hasn't been able to convince anybody to do it that way for 2,000 years. The way it's gonna happen is through Einstein's exposure, Einstein's understanding that has to come into common knowledge that we are all connected to each other.  Coming back, my bad deeds come back. We're not gonna get it until we see it in our own self-interest, not to hurt you. Our own self-interest, not to throw you into the donut hole. Okay, that takes me to my last question, because we're really out of time here. My last question is, okay, it would be nice if Congress would, you know, appropriate some money to reinvigorate the Internal Revenue Service. That's a big question, whether they'll ever do that. But the other is, you know, you and I were talking about, just as we were talking about the flip side of what Trump did in January of 2017, we were talking about tax reform, real tax reform. That's the key to all of this. If you shake and bake this whole discussion, the key to all of it is tax reform, fair-minded tax reform, reform we should have had years ago. But we have a Congress that's dysfunctional. We can't do this by proclamation. We can't do it by wishful thinking. Even the Internal Revenue Service has to follow whatever the rules are. So query in this country, and we're running out of time, I think, how do we do that? How do we get real tax reform through a statute that's what we need? Yeah, I think Biden's on the right track. You keep pushing. Hopefully, even if it's a slim majority, that will continue on. And when you have a majority, when you can get things passed in both houses, you do it. And whether they got to get rid of the filibuster or what they have to do, go through it to take some months, you know, we'll just filibuster every day. I don't know what you do to, but I'm saying, let's not assume everybody's gonna change to the common sense we believe you and I are speaking. Let's work with our slim majority. Let's keep putting forward bills that make sense that will undo the damage we've done to ourselves over the last 40 or 50 years. And little by little, maybe we'll come back to some balance and then people will begin to see the truth of what's going on is things are better with sensible rules and sensible laws that act on people fairly. Well, I think, Roger, I think I hear your phone ringing and I think it's the White House calling. Hey, White House, oh yeah. That's a line one. Mr. Trump? Mr. Trump? Oh, no, oh, I'm sorry. Oh, no, I got it wrong. Thank you, Roger. We have to continue this discussion. So much more to discuss. Yeah, I know, Jay, it's great to talk to you and I still think we could do it in Hawaii. We don't have the legislature that we would like to have people with open minds and clear thoughts. But we could get there. We could do it in Hawaii. We could start in a lot of ways and we could become the place to model for how to live not only with Aloha, but with a little money in our pockets too. Wouldn't that be nice? Roger Epstein, a fellow who's gonna come back and drill down with me on so many issues that have been raised in this show. Roger Epstein, tax attorney, power excellence. Thank you so much. Thank you, Jay. Aloha.


Theo Progressive Congress' APC Reaver State has claimed the lack of governance in the state as the reason for the defection of 27 members of the state assembly from the People's Democratic Party PDP to the APC. The chairman of the APC Reaver State Caretaker Committee, Tony Okochawa, addressed newsmen in Plotarkot, said some lawmakers in the state confided in him. Okochawa says the move is a good and calculated one which would make his party a majority in the House of Assembly. The APC CTC chairman said it is unacceptable for Governor Fubara to give credence to only four Assembly members over 27. On the floor of the Assembly, and initially it appeared or it seemed like a rumor, yet we saw them flaunt APC flags, but we have been officially communicated of that move. The Assembly members who had defected had confided in me that leadership, governance in Reaver State had to run aground, that there is no governance in Reaver State. Okochawa commanded the lawmakers, saying the cross-cafting would encourage proper checks and balancing in the government. But you and I are witnesses to the fact that it is a complete aberration. Nothing is happening in the state. There is hunger in the land. What you only hear is two persons declaring themselves as speaker of Reaver State of Assembly. Is that the reason why Reaver State voted for them? The answer is no. And so there has to be check and balances. Not that the 27 members have defected to the all-progressive Congress. It's going to be a check on the government because, of course, they have said to me that they would never be in a government that is from this. And so we commend them for this decision that they have taken. Even though maybe I would have thought that they took this decision too late. The lawmakers who defected from the PDP to the APC are those under the faction of them but the speaker of the House, Martin Amowale, a faction loyal to the Ministers of the Federal Capital Territory, FCT.


Hello, Andrea here with dental L. Let's talk about the unmet human needs in the dental hygiene process of care.  How do they apply to the dental office? How do I write them in the chart? What happens if a patient has heavy plaque, heavy charter, gingivitis, they want their teeth whitened? All of those I have to address but which unmet human needs do those go under and what comes first? So that's what I'm going to talk to you guys about today. So let me just share my screen here. So I'm keeping it simple. So I do offer a full course, the Board Exam Prep Academy where the unmet human needs and the dental hygiene process of care is a full module because there's so many things to talk about. But in the purpose of this video, I'm just going to summarize it for you to make it easier to understand, okay? So these are the unmet human needs. Depending on the textbook you read, they might separate these ones a little bit more. So you have 11 and not eight, but don't get hung up on the numbers too much because in most cases, if you're working in a practice, you're going to have this in a template anyway and then you have to fill it in on your own. So these are the unmet human needs. I'm just going to go through them briefly with you. So you have the wholesome facial image, protection from health risks, biologically sound and functional dentition, the skin and mucus membrane integrity of the head and neck, freedom from head and neck pain, freedom from anxiety and stress, responsibility for oral health, conceptualization and problem solving. So let me just give you one example for each one, okay? So the wholesome facial image, this is when the client expresses their concern about their appearance. They might say to you something along the lines of, I've always wanted straighter teeth or I've always wanted wider teeth or I don't like how my teeth stain so much. This is their appearance. Protection from health risks. Some of these examples would be during the medical history, you note they haven't seen a doctor in 10 years. They haven't had a physical in 10 years. They say they're healthy, but how do they know that? They haven't been to the doctor. They might not be taking any medications but maybe they have high blood pressure. They wouldn't know because they haven't been to the doctor or on the other side of things. Let's say you take their blood pressure today because it's their new patient exam at the dental office and it's very high. That's a protection from health risks. Biologically sound and functional dentition and skin and mucus membrane integrity of the head and neck are similar, but how you can separate them is the biologically sound and functional dentition is the hard tissue. So think the teeth, the enamel.  Those are some examples. The skin and mucus membrane integrity of the head and neck is looking at the soft tissues. So looking at do they have gingivitis? Do they have periodontal disease? That isn't necessarily their teeth but it's going to be the soft tissue around the teeth. What if you suspect they have a cold sore on the tongue that isn't going away? It's been three weeks, that would be an issue. The next one, the head and neck pain. So this would be kind of what it states. Do they have a toothache? Do they have cold sensitive teeth and they're in pain? Maybe they have a lymph node on their neck that when you're doing the extra oral exam, it's quite puffy and quite sore to the touch. That's where that would fall under. And then anxiety and stress. This is a big one. I probably deal with it every day. Where clients admit to you, I haven't seen the dentist or the dental hygienist in 10 years because I'm terrified. I got yelled at when I was a kid for not brushing and I haven't been back since, just an example. So are they anxious to see the dental hygienist for a cleaning? Are they nervous that they're going to get yelled at because they don't brush properly or they think they don't brush properly? The next one for oral health. This is there and everybody's responsibility. If they admit to you, well, I just come once a year just because I know I probably should get my teeth clean but I don't really care to. I know you're telling me I should have my teeth cleaned every three months because I'm a heavy smoker, but I don't care. I'm just gonna do it once a year. This is an issue. They have responsibility for their oral health. And then the last one, conceptualization and problem solving is, do they understand? So you're telling them to have their teeth cleaned every three months because they're a heavy smoker. They get heavy plaque, heavy tartar, but they're like, I just wanna come once a year. What's the big deal? Well, you're going to educate them to help them understand, well, what is the big deal? It's not their fault if they don't know what they don't know. You have to educate them. Maybe somebody's told them in the past, it's no big deal. You can have your teeth cleaned whenever if the teeth aren't falling out, who cares? Well, it is a big deal, but they might not know that or perhaps as children, their parents took them to the dentist every five years because they just simply didn't have the money. So they didn't realize the importance. It's our job as dental professionals to educate. So you guys, does that make sense? So this is how you would input it into the client's chart. You would look at all of these problems, decide what the problem is, and then what the solution is. So just as an example on how to write this up. Let's say the patient tells you they really don't like their stained teeth. They want white teeth. So that's a problem that you're going to fix. So you would say their unmet human need would be wholesome facial image due to them telling you they want whiter teeth, okay? How are you going to plan that out? How are you going to implement that? Planning would be the next appointment. You are going to book for them a one hour teeth whitening session. And then you're going to talk to them about how the teeth whitening is going to work. How did their teeth stain in the first place? How to prevent that? And any post-op care? Are their teeth going to be cold sensitive? Are you going to recommend a new toothpaste? All of that is just for one issue. They don't like their stained teeth, but you're going to fix that for them. So you guys, I hope that helps. That was just a basic summary of our unmet human needs. How you need to think about everything when it comes to the patient to make you the best dental professional possible. Let me know you guys, if you have any questions, thank you for watching and I'll see you in the next one.


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Good morning all of you yesterday we were looking at one of the fundamental solutions to natural convective boundary layer flow past a vertical flat plate and this was initially attempted by Polhausen again and the theory behind this similarity solution is a continuation of the Blasius solution we assume that the similarity variable is of the same function as in the Blasius solution only difference here will be that the different dependence of boundary layer thickness instead of being on Reynolds number we suitably modify it to be a function of Grashof number okay accordingly Polhausen chose the similarity variable something like this and then we proceed in the same lines as we derived the Blasius equations starting from the stream function definition and then substituting this to find the u velocity v velocity and also the gradients of all the velocity components and then finally when we substitute into the momentum equation we end up with the following similarity equation okay similarly if you do the similar transformation from the energy equation you get the following similarity equation for the temperature ? okay so here we have defined ? to be the non-dimensional temperature based on T – T 8 by T wall – T 8 okay so these are some of the fundamental components to deriving a similarity equation and they are pretty much common so if you do this a couple of times you will become familiar for the third time the only cache is how do we find the right similarity variable to transform this solution so that is the most important point and once you find it either by trial and error or by intelligent guess okay so you will be able to most likely convert the PDE into a similarity ordinary differential equation so now you should understand that these two equations are coupled in the sense that you have this term ? which is sitting in the momentum equation and therefore unlike the external force convection case you cannot solve this separated so you have to do this simultaneously when you use the shooting method and we will see that in a short time but before that I asked you to check whether you get these similarity equations I hope some of you could try it so are you able to get the same equations anybody who tried so far no anyway so I think I request you to please check because these are all very critical part of the similarity equations okay do not because substitution if you do it a couple of times you will understand know how the derivatives are computed and things like that so now let us write down the boundary condition see unless we write the boundary conditions we cannot complete the you know we cannot say for sure that this is a similarity equation okay so the boundary conditions also should be independent of X and Y so there are cases in mixed convection where you can get a similarity equation but the boundary conditions does not show a self similar set of boundary condition so in that case what happens is you cannot solve those equations anyway even though they are converted okay so so we have to first also ensure that your boundary conditions satisfy the requirement for similar equation so what are the boundary conditions here so if you take the case of the vertical plate pretty much similar conditions as in the case of external forced convection at we have the coordinate here X and Y so therefore to solve this we need to therefore define three conditions for F and two conditions for ? right so and therefore at when we said do this transformation from ? which is a function of XY to ? so we apply also the transformation for the similarity variable ? so therefore at Y equal to 0 since we have the no slip boundary condition okay so we can also say that at using our similarity variable ? equal to 0 right Y equal to 0 ? equal to 0 what will be the condition for DF by D ? 0 so we have based on the fact that U equal to 0 we can say DF by D ? equal to 0 and what about you can we say something else from V velocity when V equal to 0 so DF by D ? at ? equal to 0 V equal to 0 so therefore F equal to 0 okay so we need one more condition where can we apply at ? going to so why going to infinity okay what will be the condition let us look at the condition with respect to why going to infinity what do you think will be the condition U equal to 0 okay can we also say DU by DY equal to 0 if you draw the velocity profile here if your natural convection case the gravity acting downward okay so this is 0 outside and also at the plate so we can say both U equal to 0 and also derivative of this equal to 0 so therefore if you put the condition U equal to 0 what happens DF by D ? equal to 0 again and if you put the condition DU by DY equal to 0 D square F by D ? square equal to 0 okay so now we should also remember that the condition at X equal to 0 is also part of ? going to Z infinity correct so therefore at X going to 0 ? going to infinity what is the condition U should be equal to 0 okay so the X going to 0 condition is satisfied by this condition as well right so these are the conditions now similarly let us write it down for the thermal boundary so at for the energy equation at Y equal to 0 what is the temperature this is the wall temperature which is constant and therefore correspondingly at ? equal to 0 ? will be one and at Y going to infinity okay corresponding to ? going to infinity ? will be going to 0 so this is pretty much the same as the original Poisson's boundary conditions only that the case of momentum you have now DF by D ? equal to 0 whereas what is the condition in the Blashe's equation going to 1 U by U infinity equal to DF by D ? okay so now we should understand actually this entire component okay is your what U reference correct so this is the starting point we assume U by U reference is actually a function of ? okay which is nothing but DF by D ? so this 2 times crash of number to the power half ? by X should be equal to U reference you can please check that okay so we are our U reference definition is 4 times G ? T wall minus T infinity into X okay so you can replace this with crash of number so G ? into T wall minus T infinity is what how do you rewrite this in terms of crash of number ? of number into ? square by X Q okay so therefore you have 2 times so this is local crash of number you take this this is new and this is X square if you take this is new by X right so this is nothing but your U reference here so in the Blashe's case this was your U infinity at the Blashe's case since here you do not have any U infinity you introduce a reference velocity and this is the reference so in the original Blashe's case therefore ? going to infinity DF by D ? was 1 so U by U infinity U is equal to U infinity so therefore DF by D ? was 1 but here we cannot say U approaches U reference okay it is U is 0 so therefore DF by D ? is therefore 0 here so this is the difference also in the boundary condition now you if you therefore look at the boundary conditions all of them show that this is a this are similar equation with the similar boundary conditions so you can say that all of them do not involve any X or Y components in that okay so therefore we have we can say for sure that we have found a self similar solution to this problem and the next step is to go ahead and solve it so we will once again use the shooting method that you are so familiar by now you have been using it for so many different problems both in external convection as well as in internal convection okay so you know the equations can you please convert them into ODEs ODEs of first order we have a third order ODEs please try to reduce this into three first order ODEs and similarly the energy equation so what do you start with DF by is equal to is equal to G this is your first first order ODE and then therefore next DG by is equal to H this is your second first order ODE and then finally you put it into the master ODE okay so what will be D square F by D ? cube DH by D ? okay plus three times F x H – 2 times D G x whole square plus ? equal to 0 so this is your third first order ODE similarly your energy equation we can say D ? by D ? so what do you use generally D ? by D ? is equal to let us say something like Y okay this is your first first order ODE next you have DY by D ? plus 3 PRF x Y is equal to 0 this is how you have converted so now just you can take the vertical plate discretize this in the ? coordinate system okay so break this into finite domain with discrete number of points going from ? equal to 0 all the way to infinity will be some large value okay it could be 10 15 whatever so you have points i equal to 1 all the way to i equal to n right so therefore you will be marching in space so these are all first order ODEs you can use a simple Euler backward differencing and then you can just simply march in space forward so once you know the solution at the previous location you can use that to calculate solution at the next location and keep going forward till you reach i equal to n okay now therefore in order to march in space you need to know the boundary conditions for F G and H right at i equal to 1 that is at ? equal to 0 then only you can stray march in a straight forward manner okay let us see how do we convert this into equivalent boundary conditions okay as far as F is concerned so at ? equal to 0 we have F equal to 0 is known okay so therefore the first equation can be solved straight away what about DF by D ? DF by D ? is also known right so this second equation also can be solved now coming to the third equation we need a boundary condition for D ? F by D ? square at ? equal to 0 which we do not know okay so we do not know therefore the boundary condition for D ? F by D ? square which is nothing but H okay at ? equal to 0 is unknown but what we know is DF by D ? at ? going to infinity that is we know the boundary condition for G which is equal to 0 okay this is like your blashes solution again so there you have DF by D ? equal to 1 okay same way here also if you look at for ? so you know that ? at ? equal to 0 is equal to 1 okay but you do not know what is D ? by D ? at ? equal to 0 so this is your why this is not known but what you know is ? at ? going to infinity which is equal to 0 so therefore we have to now introduce the shooting method so you have to shoot a guess here in this case for H which is D ? F by D ? square okay and simultaneously now you have to understand in this case these two have to be solved within the same loop okay both with respect to iteration and within the same space loop okay so it has to be it has to be all both of them have to be solved together okay first you solve the three equations three first order OD is as guessing some value of ? for example okay and then you put that into this and then solve for ? okay and now this has to be iterated again and again till you reach a final solution okay so you have the iteration loop outside and inside you have the space loop within which you have to solve these two simultaneously so when you when you solve this the problem is yeah you do not know again the boundary condition for H here and also for why here so then therefore you have to shoot a guess for in this case H and also in this case why and then use Newton Raphson to make more accurate estimate of these boundary conditions provided you satisfy the condition that G at ? going to infinity is equal to 0 okay similarly here ? at ? going to infinity equal to 0 so once you satisfy these conditions that means you have reached a final converged solution okay so till that point you have to keep guessing the values of both H as well as ? and then solve these two equations simultaneously so that means at each point you should be putting the corresponding value of ? and then you get the solution and then that value of F is put in the equation for ? and solved okay so once you do this finally you will have the equations solved for different values of Prandtl number so now you will have therefore unique solution for also velocity as a function of Prandtl number because Prandtl number is the one which decides the value of you know the temperature profile and that temperature profile will go into this and decide the velocity solution so now Prandtl number will govern both the temperature as well as the momentum profiles so I will just give you how the gradients look the gradient of velocity as well as temperature at the wall because these are the important quantities to calculate the skin friction coefficient and the Nusselt number so and then we will go ahead and see how the profiles of velocity and temperature look so Prandtl number we have F double prime of 0 and then ? of 0 so finally this is what you guess and after you reach a converged solution this will be your final values so if you vary the Prandtl number so for four different Prandtl numbers if you find the solution by shooting method you will end up with 0.9862 and 0.6760 0.41 so now you therefore see that the gradient of velocity is also a strong function of Prandtl number unlike the external force convection so that value was simply 0.332 okay so here you have a function of Prandtl number okay because it is coupled with the energy equation so the corresponding values of temperature gradient sorry this will be ? dash right so you have the corresponding values here you can just compare for your understanding so approximately this is close to Prandtl number one so you have 0.6760 as the value of F double prime what was the corresponding value for the external force convection flat plate 0.332 okay and what was the corresponding value of d ? by d ? for Prandtl number equal to 1 that is all same 0.332 okay so these values are now slightly higher than that but does not mean now the final Nusselt number is going to be larger than the force convection we will see that now we will convert that into an expression for Nusselt number okay so can you all do that so once you know the temperature gradient at the wall now you should write down what is the expression for Nusselt number yes so in this case it should be negative right so let us say minus of ? dash that is correct so what is d ? by dy 1 by x into ? of number by 4 raise to the power 1 by 4 okay therefore if you define a local Nusselt number as Hx by K we simply have minus d ? by d ? equal to 0 into ? of number by 4 by 4 okay so this is your expression in the case of force convection what did you have d minus d ? by d ? d ? equal to 0 into Reynolds number raise to the power 1 by 2 okay so you have this factor now by 4 because we have defined this in the similarity variable so accordingly this will get scaled okay so if you do not use the factor of 4 the value of the temperature gradient will also be different it will be lower it will be 4 times 4 to the power 1 by 4 times lower so then therefore you do not have this factor so now that you have put this constant so this will be 4 to the power 1 by 4 times larger than the normal case okay so everything gets proportionally scaled okay so the question is now we have a functional dependence of Prandtl number so we cannot directly say some value of d ? by d ? there we have to fit a curve now as a function of Prandtl number so this was done actually by Ostrac so initially when Paul Austin solved he could not solve for so many Prandtl numbers because he did not have access to numerical techniques so therefore he stopped with the equation and maybe found just one solution but it was later Ostrac who extended it to so many Prandtl numbers Prandtl number much lesser than 1 to much greater than 1 and then he fit a curve to this d ? by d ? as a function of Prandtl number so according to that it comes out to be minus d ? by d ? ? equal to 0 according to Ostrac is 0.676 okay so this was by Ostrac you can do a quick check for Prandtl number equal to 0.7 whether you recover the value shown here if you have a calculator you can quickly check that so therefore with this curve fit we can write down the final expression for Nusselt number this is your exact solution okay so now that unlike the case of you know classical Paul Austin equation where you have 0.332 times RE power half Prandtl number to the power one third so now you have a more complex dependence on Prandtl number and instead of Reynolds number you have Grashof number okay so this is how the Nusselt number varies now what we will do is also plot the solution for ? and the velocities okay so once you solve these ODE by shooting method whatever is described here you should be able to also plot df by d ? which is nothing but u by u ref and ? so first I will show the variation of ? which all of you are mostly familiar so with this is 1 0 so ? going from 0 to a large value so at ? equal to 0 T equal to T wall right so this will be equal to 1 and then for large values of ? it will decay to 0 and what will happen to the temperature gradient with increasing Prandtl number it increases okay so this will also shift downward right this indicates higher slope at the wall so for increasing Prandtl numbers your temperature profile will be varying like this similarly if you plot your u by u ref which is nothing but df by d ? as a function of ? okay so this also shows a functionality with Prandtl number so you find that something like this so it reaches a value of depending on what you take as your u ref okay so suppose somewhere here it is your u ref it reaches 1 here okay and if the peak is not your u ref that will exceed 1 okay and similarly with Prandtl number what happens what happens to the slope of the velocity at the wall it decreases with increasing Prandtl number the slope decreases so therefore how should the curve shift with increasing Prandtl number downward right so this is your increasing Prandtl okay so for a given value of d ? so your du will be smaller for this compared to the other one okay so this is how your similarity solutions look now you should remember that the similarity solutions for natural convection both velocity and temperature are functions of Prandtl number okay so we have to be careful about it so next thing what I am interested is if you want to calculate an average heat transfer coefficient just like we did for the you know the classical Polovson solution sometimes when you solve heat transfer problems you are not interested in the local heat transfer coefficient but average values okay so let us try to therefore start from this point here okay try to calculate an average heat transfer coefficient which we will call as h bar which is nothing but 1 by L integral 0 to L H of X DX and then define a Nusselt number based on the average heat transfer coefficient and based on the total length of the plate H L by K so can you do this and tell me what will be the average Nusselt number so if you complete this exercise so you will find out that you will have 4 by 3 into Grashof number now this Grashof number will be defined based on the plate length okay after you evaluate the integral you will convert all your X into L okay so the Grashof number will be defined based on the plate length and therefore you will get the expression that the average Nusselt number will be 4 by 3 times the Nusselt number local Nusselt number when your X is replaced with L okay so this is another useful relation that you can use when you are doing calculations for heat transfer rate and so on to where you define your heat transfer coefficient based on the entire plate lengths so what was the corresponding relation for the external force convection twice of N U at X equal to L right so here we have 4 by 3 we have any questions so far I hope the procedure is clear because we have now done enough similarity solutions so it is just you have to go through the mathematical procedure and substitution and you will get it there now what we will do next is move on quickly to the case of constant wall heat flux boundary condition okay so this is the extension to what Paulhausen did so he started with the constant wall temperature case and later on Ostra completed the solution for different Prandtl number ranges now the extension to this is to find the solution for constant wall flux boundary condition so this was attempted by two people's paro and great so now similar to the flat plate case where we had constant heat flux boundary condition now we have to find another similarity variable we use the same similarity variable more or less there but the way we have defined our non-dimensional temperature ? okay so the constant wall temperature case we use this definition and in the constant heat flux case since T wall – T infinity is not a constant we have to replace this in terms of heat flux which is known which is fixed so similar to the flat plate case so what we can do is assume this is your T wall this is your T infinity and therefore we can relate some kind of scaling to convert this temperature difference into heat flux using the Fourier conduction equation so what we can say is that your Q double prime is equal to – K say DT by DX therefore this can be written as T wall – T infinity the order of magnitude of this will be Q double prime into X by K we are just looking at the order of magnitude so therefore we will write ? here as T – T infinity by instead of T wall – T infinity we have Q double dash now we are coordinate this is actually Y and this is your X so therefore we have to be careful we will be using Y here okay by K so this is how we try to transform temperature dimensional temperature T to a non-dimensional temperature ? okay just doing order of magnitude analysis now we have to also find the right definition of Grashof number okay so your conventional definition of Grashof number is also based on temperature differences now how do we convert again this temperature difference into what is known to us in terms of heat flux again we will use a similar scaling okay so we can simply write therefore T wall – T infinity as something like Q double prime X by K so X and Y they are just the order of magnitude of X and Y are comparable now okay so we will just interchange them so that we can define a Grashof number we will use Grashof number star now to differentiate this from the conventional Grashof number now this will be based on your heat flux so therefore this will become Q double prime and then what will be X power 4 by ? square K so this will be the modified Grashof number this is called the modified Grashof number for constant wall heat flux boundary condition so you understand so we know what is the wall heat flux if you so we are replacing Y with X now we cannot use in the Grashof number Y into X power 3 you understand so we are just doing some scaling where we say the order of magnitude of X and Y are kind of similar and therefore we are converting that also into X why do you want to complicate the definition of Grashof number the Grashof number is only based on one local coordinates why should we use Y times X how do you then come compute your is it a two dimensional variable okay so Grashof number is just a local coordinate which is attached to the plate length okay so we cannot therefore define a two dimensional Grashof number here it is like defining a two dimensional Reynolds number okay so therefore this is a definition okay there is nothing wrong in defining a Grashof number the way you want it provided it is dimensionally consistent okay so this might not be an exact transformation of your conventional Grashof number but you say get a non-dimensional group okay so that is all you have to be worried about we should not think about complicating it further and all you need to do is once you know your heat flux put it into this and therefore now you have a local Grashof number varying as a function of X so this will be the starting point for defining the similarity variable right so and once again now when you look at the similarity variable what was the similarity variable in the constant wall temperature case so we have ? equal to Y by X your normal Grashof number by 4 raise to the power 1 by 4 now if you simply replace this normal Grashof number with Grashof number star what happens to the similarity variable it becomes Y yes so that means you will not find the correct similarity variable because there will not be any function of X now your Grashof number star is X power 4 so X power 4 1 by 4 is XXX cancels so you will have a similarity variable which is only a function of Y which is not possible correct so therefore now accordingly you have to modify the definition of similarity variable for this case so how sparrow and Greg did it was just changing the 4 to 5 okay so now the functional dependence of ? on X and Y are retained is that clear okay if you use the default similarity variable you cannot find a similarity variable for this therefore you have to modify it a little bit okay they I mean if this is the right modification you should be able to find a similarity equation so that we will check how we convert this into a similarity equation so but basically this is the starting point you be redefined the definition of similarity variable in the constant heat flux case because we have now defined a new modified Grashof number okay so please keep this point in mind and then in the next class we will continue from here now the rest of the rest are details so once you identified the similarity variable then finding velocities substitution they are all the standard procedures and then maybe you can do this as an exercise and check what kind of similarity equation that you get okay so then we will meet in the next class