Before we get into the video today, I just want to give a quick shout out to one of our sponsors, Gnostic TV. Gnostic TV is ancient wisdom reimagined. This is a Netflix for those who are spiritually curious and want a place to go where there is no censorship. I personally am doing a whole series on Gnostic TV called The Esoteric Explorer, where I am providing exclusive content to Gnostic. Gnostic TV is a host to all sorts of different content creators, many of whom are your old favorites. If you would like to check out Gnostic TV, there is a link down in the description box below. Hello, everybody. Welcome back to Esoteric Atlanta. This is just hopefully going to be a quick little video. As you guys know or maybe you know, currently right now, today is April the 10th, 2024. So we have in the United States right now, we've got the Chad Daybell trial that is starting apparently on Wednesday, April 10th. Today they are doing their opening statements. They selected the jury on Monday, and then I believe they had Tuesday off, which makes a lot of sense. If you're not familiar with this case, this is the case of basically there were two defendants, Lori Vallow Daybell and Chad Daybell. And they ended up unaliving. Well, Lori Vallow has already been found guilty. So we can say yes for sure, but for Chad in the United States, everybody is presumed innocent until proven guilty. It's the state, it's the prosecutor's job. They bear the burden of proof to prove that Chad Daybell did in fact participate in the unaliving of Tylee Ryan, J.J. Vallow and Tammy Daybell, Chad's first wife. In my opinion, he is extremely guilty. This is a capital punishment case. So we've got the stakes are really high. Lori Vallow's case was not capital punishment due to, I think, a technicality. And so the stakes are really high. The case is being tried over in Idaho. Now I'm super fascinated in this case because this case, in my opinion, really stems from a huge, huge delusional and magical thinking. And as you guys know, as I stated last week and with Shanti on Shanti Show, which I'm going to put the links to that because we're going to talk about this live at 12 p.m. Eastern time. I think this is a really important case for anybody who's in the disclosure community or the truth or community to look at because I see a lot of commonality with Lori Vallow, Chad Daybell, their delusions and a lot of the delusions that are on telegram today. And delusions are well and great. And, you know, a lot of people create this alternate reality in their mind as long as you're not hurting anybody, whatever, no harm, no foul. But in a lot of cases, it goes overboard and people lose their lives. And in this case, two children were among the victims. Now there are four victims. I just want to go ahead and get this out of the way because, you know, I have a lot of people from other countries watching once again in the American judicial system. We have federal court, but we also have state courts. So if somebody, wherever you commit a crime, that's the county and the state that you will be charged with the crime in. So yes, we do have at this point that we are aware of four victims. We have Tammy Daybell, Chad Daybell's first wife. We have Tyler Ryan and JJ Vallow. They were all unalived in the same county. So the case that we have in Idaho with Chad Daybell is involving these three victims. Lori Vallow has already been found guilty of these three victims. And I've seen a lot of these news YouTube stations or people from other countries are getting really, really mad because the news reporter isn't talking about Charles Vallow, the fourth victim. Y'all, there's a reason for that. In the court case that's happening right now, Charles Vallow is not a victim in this court case because he was unalived in Arizona. Again, the United States, I understand like in Europe, the countries are really small. So things are done very differently. But like Australia, like Canada, we're big Russia, we're big countries like United States has continental United States has four time zones. That's not even including Alaska or Hawaii, which are not considered continental United States, but still under, they're still American, right? Yeah, those and we've got multiple, like six or seven different time zones. If we're a huge country, huge. So the only people that can still the jury are people that are from the county where the crime was committed. I mean, there are a lot of different laws around this. And so Chad, excuse me, Charles Vallow was unalived in Arizona. Now, Lori Vallow has been charged in his unaliving, but she has not gone to trial yet. So she is due to stand trial for his unaliving. But at this point again, the United States, everybody is innocent until proven guilty. But Lori has been found guilty for Tylee JJ and Tammy now Chad is facing those charges. I don't think that Chad will be charged for for Charles. He was anywhere near the situation. We'll see what unfolds after. But nonetheless, what Chad DeBell is facing now is a capital punishment case. So his life is literally on the line and the jury was selected on Monday. Now, from what I understand, the judge in this case in Idaho, Idaho, it is a quicker flight for me to fly to London, England than it is for me to fly to Idaho. That's how far Idaho is from me, even though I'm in the same country. In Idaho, it's behind me in time. What the judge in this case has because it's such a high profile case, the jury needs to remain anonymous. So the judge has allowed, I believe, I believe the judge has allowed cameras in the courtroom, but the jury cannot be filmed. This is for the jury's safety. So I think there are 18 jurors selected, 12 are actual jurors, and I think six are what they call alternates. In case something happens to one of the 12. Now the six alternates, if all 12 make it to the end of the case, the six alternates will not be deliberating, but they will have to be present for all of the trial and take notes just like the jury in case one of the jurors something happens, they're compromised, gets sick, whatever. So with the jurors, my heart goes out to the jurors because this is such a high profile case. Anytime you serve on a jury, and I love jury duty, I love it, but anytime you serve on a jury, you have to stay away from everything. You can't talk to anybody, you can't talk. Even in the case that I served in LA, I couldn't even talk to my fellow jury men and women until we deliberated. So you can't even talk to the people you're on the jury with. And with a case like this, you have to stay. Now the times I've served jury duty, it hasn't been big cases. There's been no media coverage, so I was pretty safe. But with a big case like this, the jury cannot watch any media coverage. They cannot talk to anybody about the case. When they go home at night, they can't talk to their spouses, their friends. They have to be very, very much keep everything to themselves until deliberation. If by chance, they slip up and they watch a YouTube channel or they watch the media, they have to report it to the judge and they have to be dismissed from the jury. Now a lot of people are like, how do you keep people from doing that? Actually in my experience, most Americans take this very seriously. In my experience and the jury that I have served on, most American people understand that they cannot be influenced by any outside sources, that they have to get all their information from the courtroom. Now, because again this case is such a big deal, from what I understand, all of the jurors have to meet at a certain location before court at a certain time, get into a van together where a bailiff, and a bailiff is basically just like a court cop, and they probably are going to have a couple of them, will drive them to the courthouse so they can be escorted into the court together. Now for me, I don't think this has anything to do with any news reporters trying to talk to them or any people trying to talk to them. I think this is where they're safe deep. The reason why I say this is most news reporters who cover true crime very much know the law and they know that they cannot approach the jury. They cannot approach people who are, basically the jury is the people that are going to decide the fate of this man, right? They know that and I think most, most reporters, like I was listening to a reporter say today on his YouTube channel that if he were to even go into a convenience store on a break and see one of the jurors in there, he'd turn around and leave because he doesn't want to compromise that juror in any way shape or form. And also for some of these reporters who work for big media companies, I personally would be afraid of being held in contempt of court because I think the judge probably looks at these reporters, especially the ones that have been doing it for a very long time. They know the rules. They know they're not supposed to approach the jury during the case. So after the case is over, all's fair. And so I think a lot of the reporters could potentially be held in contempt of court if they try to approach the jury. But again, the reason why I think they're being escorted by the bailout, this is just strictly my opinion, is because of safety. Because this is such a tumultuous case. We're talking about two children, right? And so I think they just, I know, I believe that it was when Laurie Valos case was going on, she herself had to go to court every day with a bulletproof vest on. You know, like, this is serious. People's emotions are high.  My opinion that they gave Tuesday off for the jurors, they have a day off in order to go sort out their affairs at home to make sure that they had this, this trial could last anywhere from 8 to 10 weeks. So they had to make sure they had help for their children, that they had everything worked out because they were going to be in the courtroom. And when you're in the courtroom, you don't have your cell phones. The cell phones typically are confiscated, especially for the juror, the jury. So they have to make sure everything's set up at home. Now as far as sequestering, I would be curious to see if they make it the whole case without being sequestered. And what is sequestering? So sequestering means that they force the jury, they take the jury and they put them in a hotel together. So they are watched so they can't, you know, make sure they're not watching any news stations. I do know that from what I heard from another reporter that if they do find Chad Debell guilty and they have to go now deliberate the punishment. So again, capital punishment is on the table.  Life imprisonment or capital punishment. And I believe that that's the case that they find him guilty that they will be sequestered while they talk because it's such a serious, serious punishment, right? That's from what I understand. Now but with that being said, we are on Aquarius Rising Africa today. I think it's very kind of serendipitous that this case, this court case started while we were going over the… We started with Ruby, Frankie and Jodie Hildebrandt and we were like, let's just talk about Lori Vallow too. And then I had no idea Chad's Debell's case was going to be starting during this time. But we are going to, as we kind of talk about this case, Shanti and I are actually going to start to break down Mormonism. And I want to make this very, very, very, very clear. I think Christianity is not good. I think a lot of religions are not good.  I'm not talking about you. I do understand that people are grandfathered into their faiths. But what I want to look at is some of the delusions. And this again is why I also think it's very important people study the law of one. So they understand negative polarity and positive polarity. And we talk about Joseph Smith, the founder of Mormonism. We are going to be talking about what the Cassiopeans have to say about him and it's not good. It is not good. So when you are working... So there's the Book of Mormon. So I don't even think Shanti was aware of this. So we have the Bible and then the Mormons also have a second book. Well, they have the doctrine and all these other things too. But let's just talk right now about the Book of Mormon. Now, in my opinion, I've read the Book of Mormon. I read the Book of Mormon just for shits and giggles. I just want to know what it said. Wasn't I ever going to become a Mormon?  I think it is. There's a lot of reasons, academic reasons why the way Joseph Smith translated the Book of Mormon. It just so happened to be translated into the same King James English as the King James Bible. Which if these were gold plates from however many centuries ago, it would not be in King James English. Common sense, right? But basically the Book of Mormon talks about this Jewish family, Lehi, who gets this revelation from God to basically lead Jerusalem before it falls to the Babylonians and get on a boat and, lo and behold, they find America. And that these are the ancestors of the Native Americans. And so he has these sons. He has Nephi. Anyway, it just breaks off into laminates. Jesus after he comes, he resurrects and then comes over to America and tells everybody in America, hey, I'm the son of God. And I was just killed over. Anyway, and then all of a sudden, boom, here comes the colonist. It's very racist. The Book of Mormon, they talk about white skin being white and delights them. We'll get into all of that with Shaunty. But I wanted to kind of talk about something. I'm actually getting this from the LDS website in the very beginning of the Book of Mormon. We're hit with a story of Nephi, one of the main characters, the youngest son of Lehi. Nephi is like the godliest of sons, right? And he has to go and get some plates from one of the authority figures of the area before they can even get on a boat and go to America. They're still in like the Jerusalem area. And God tells Nephi to basically unalive this man, Laban, this man, decapitate him in order to take these plates. Like God tells him to unalive somebody. Now, again, I think the Book of Mormon is pure fiction, pure fiction. I always thought it was pure fiction from the moment I read it. I was like, this ain't nothing but fantasy. You know, this is not legit. But if you're taking this story as accurate as something that's literally part of your doctrine. If we look at things like the Law of One, I'm going to pull up the LDS website here, you guys. We'll look at things like the Law of One. The light, the only time it is ever acceptable to unalive a human being or an animal, according to the positive side of God, is if your life is being threatened and that's your self-defense, or the person or the animal is in misery, needs to be put out of its misery. If there's an entity telling you to unalive someone, especially because the person he unalives, Laban is drunk, like passed out drunk, it's not threatening Nephi. So if you've got a voice telling you to unalive someone, it ain't God. It ain't God. And the Cassiopeans have a lot to say with that. They talk about, if I remember correctly, which we'll get to that when we talk more about Joseph Smith, that little narcissistic psychopath in my opinion. We'll talk about his influence from the Reptilians that the Cassiopeans speak about. So this is directly from the Book of Mormon. First Nephi, which is the first book of the Book of Mormon 3. So it's like, boom, right smack in the beginning of the Book of Mormon, you're hit with this story, alright? So what appears to be a breaking of a commandment is actually an example of God's great mercy. This is gaslighting. This is word salad. This is actually narcissistic abuse. This is a prime example of confusing people. So we know there's a commandment not to unalive. Do not unalive someone. They're going to actually, but this is God's mercy because this dude, Nephi, chopped the head off of someone who was drunk and passed out. For some people, especially those new to the Book of Mormon, and most challenging or unsettling story is Nephi slaying of Laban. Couldn't Nephi have just taken Laban's clothes, reached the plates, and then left with Zoram? Nephi chose to include the story. And the many times I have studied and taught this account, I pondered why Nephi included it. Surely he understood how hard this would be for others to understand. Couldn't he have skipped the difficult detail about unaliving Laban and just said that by the power of God, he and his brothers were eventually able to get the plates from him? The point is he did not. Nephi felt impressed by the spirit to write detailed accounts of how he obtained the brass plates. It's important to know that when Nephi began this record, he wrote with hindsight. He had more than 30 years to ponder the encounter with Laban, and its importance became even more significant to him. He saw clearly what the Lord had done for him and his family. And why? In 1 Nephi 1, with a perfect perspective of where he was leading his readers, Nephi explained a major theme of what he was about to write. But behold, I Nephi will show unto you the tender mercies of the Lord are over all those whom he hath chosen because of their faith to make them mighty, even unto the power of deliverance. Well, here we go too. This is also a good sign of a negative polarity. All those whom he hath chosen. That's elitism. That's a pecking order. That's a huge red flag. So this whole story from the beginning of the Book of Mormon, we have red flags for a negative satanic polarized religion. Ultimately, the particular deliverance I am focusing on was not merely the plates or Nephi's life, nor was it the deliverance of the Nephi nation alone. Instead, the outcome was something much greater. It was intended to assist in the deliverance of all mankind. Anyway, I'm going to include a link to this down in the description box below. But we're going to talk a lot about this. I don't want to go too deep into it because we're going to get to it with Shanti. But the reason why I bring this up now, with speaking about Chad Daybell and Lori Ballo, who were practicing Mormons, we're talking about a faith where there is such thing as blood atonement, where there is such thing as almost like an honor killing, right? And we see that right at the beginning of the Book of Mormon. And we know that Chad Daybell, allegedly, we don't know that because he's innocent until proven guilty, but we can definitely say for Lori Ballo because she was found guilty, that they raided people as being dark or light souls. And the ones that were too far gone dark, they called zombies. And they felt like they had the right, the God-given right to unalive these people, two of whom happened to be Lori's juvenile children. And we see in some of the talks that Lori references this story.  Now, again, I know most Mormons are never going to hurt anybody like I get that. This is an extreme case, but we have to take it back to the beginning because their delusions come directly from Mormonism. And a lot of their delusions, a lot of the people out there who are in the disclosure community, in the truth or community are following a lot of the same delusions. In fact, one thing that Chad used, allegedly used to determine if someone was good or bad, or to determine who somebody was in a past life because they also believed in past life reincarnation, which is something that is not taught from my understanding in mainstream Mormonism. My pendulum is stuck to one of my bracelets here, guys. Here we go. One thing he would use is a pendulum. How many people on Telegram are using pendulums to ask if somebody is good or bad? Again, that's abusing. That is abusing tools of divination. A pendulum is only supposed to be used for you. That's it. And it's supposed to be used for basic questions that you have no emotional attachments to. Like, do I need more vitamin C in my diet? Should I go to the grocery store on Tuesday or Wednesday? When's a good day for me to do laundry? That's what this is for because it's not reading anybody else's energy but yours. It's reading your energy.  If you cannot use pendulums in the way that they're supposed to be used, which is strictly for you, then you should have your pendulum taken away from you. If you are following anybody that uses a pendulum in order to tell you the value of another human being soul, then you are following a delusional narcissist. A pendulum cannot tell you the value of somebody else's soul. A pendulum cannot tell you whether somebody is a dark soul or not. If you don't like somebody, put a boundary up but you don't get to rate them as dark or light and if you are doing that, have fun in hell because that's a negative polarity. If you're following somebody who does that, you might want to rethink who you're following. Look at the Chad Daybell and Lori Vallow Daybell case. Does it remind you of people on telegram? Yes, it does and hope to God that none of these telegram groups that are doing the exact same thing and the disclosure and truth or community that Lori and Chad are doing, I hope to God it does not lead to unaliving people. Alright, so that is why it's super important that we speak about this case. I'm still horrified every time I see the pictures of Tylee and JJ. It just breaks my heart.  Her children are beautiful and I cannot believe that she put a man over the safety of her own children. That is not ironically enough. That is not something a spirit of the light like she thinks she's this ultra spirit of a goddess which we'll talk about that. Gods and goddesses, plural or big and Mormonism, they all think they're going to get their own planet one day. Yep, we'll talk about that with Shanti and again, I have many friends who are Mormon and if you're, I'm just talking about the manipulation of the LDS church and the powers that be starting with Joseph Smith. We're going to talk about Joseph Smith because what a scumbag he was. He was not a prophet. Listen, if you're in any religion, Christianity included that has prophets, you're in a negatively polarized religion, negatively polarized. Only on the negative side are there special people who can talk to God. On the positive side, we're all prophets. We all talk to God. So anyway, please make sure you join us on a, excuse me, Solutions with Shanti, the second channel. Solutions with Shanti at 12 p.m. Eastern time today on Wednesday as in every Wednesday. We're going to finish talking about the actual case, like what happened, the timeline that we know of with Lori Vallow and Chad Debelle and then as we progress through the trial, every week we'll have updates on what is going on in the trial. Hopefully, Chad Debelle will be found guilty. I'm assuming he will be because there's just overwhelming evidence. But they have, the prosecution has said that there will be new evidence with the Chad trial. So it'll be interesting to see what comes up. I do know that Lori's, one of Lori's brothers, a guy named Adam Cox and her uncle, Lori's uncle, who supports the jury, supports the punishment. They know that their sister and their niece did horrific things. They have a podcast called, I think it's called Tiley, or J.J. and Tiley Silver Lining, Silver Lining, Silver Lining, J.J. I'll put a link to it down in the description box below. And they, if you want to know more about this case, again, Hidden True Crime is doing a lot. They have a lot, I just really enjoyed. They really dedicated a lot of work to getting to know the players in this case and talking about the cult following around this case, Julie Rowe, all these people that are involved in this delusional, psychotic world, prepper world, which again rings a bell with the Truth or Disclosure community, doesn't it guys? So we're going to go into way more detail over with Shanti, but I wanted to give you guys a heads up. So please join us at noon. If you can't join us at noon, you can always go back and watch the replay. But if you join us at noon, you can join with us on the live and add your opinion and your thoughts on this case. We'd love to talk to more Mormons about this or anybody who knows the family. Rest in peace to Tammy Daybell. Rest in peace, J.J. Vallow. Rest in peace, Tylee Ryan. And rest in peace, Charles Vallow. These were four lives that were gone way too soon. All because of a damn pendulum and a religion in my opinion that was founded on pure delusion. Alright you guys, we'll see you over on Solutions with Shanti.


Welcome to this lecture number 14 on unsteady radial flow in confined and unconfined aquifers. Here in this lecture, in the previous lecture we discussed on unsteady flow into the wells and in this lecture we will be moving on to unconfined as well as unconfined aquifers and of course, the flow is radial and it is unsteady. And here in this previous lecture, so there was this unsteady flow equation which was solved by two methods that is two graphical methods. One is the time drawdown method as well as the unsteady radial flow in confined aquifers. So, in the previous lecture we had this, we discussed the solution of Thay's equation by two graphical methods namely one by type curves and two by Cooper Jacob approximation. And in this lecture we will discuss another method for the solution of the Thay's equation which is used in the unsteady radial flow in confined aquifers and that method is the another method for solution of Thay's equation by this developed by Chow. So, which is this method, that is why this method is known as the Chow's method, Chow's method of solution. So, here what is done is, so in a pumping test, so the a curve is plotted and a semi-logarithmic plot, the observation data is plotted on a semi-log plot that means the drawdown axis is linear this one scale and the time axis is on logarithmic scale. And here, so this is on the plotted curve, so arbitrary points are chosen and their coordinates that is the time coordinate t as well as the drawdown s, so they are determined just like say here. So, this is the, this is drawdown s and then this is log of time t and here, so this is a tangent to the curve at a chosen point and determine the drawdown difference delta s in feet per log cycle of time. So, here actually say that is say suppose this is the, say these are the points suppose we are getting, so what should be done is, so this is the log t axis and here say this is maybe this is 1, this is 0, this is 1, this is 2, 3 and 4 and so on. So, here say 2 points are chosen on this plot such that the difference in log t is equal to 1 and so that the corresponding difference in this say for example, these are the 2 points here. So, this is, so this difference is 1 where and this is, so this difference is delta s that is the change in drawdown per that is 1 scale difference of the log value of time and here, so this f u is a parameter which is a function of this well function u, well function parameter. So, this is equal to s the drawdown divided by delta s, so drawdown divided by delta s, this is delta s and then the original value of this is s here. So, this is the value s the drawdown the typical value s and then, so this is delta s. So, this s by delta s is denoted as f u, then what is done is the corresponding values of w u and u are obtained from the figure. So, this figure is, so here we have this f u which is s by delta s and then here we have this w u that is the well function. So, here the corresponding values of w u and u are obtained from this figure. So, here this in this, so this f u, so this is also on logarithmic scale, so this is log scale and w is also on log scale. So, this is a log log plot of f u versus w u and here, so this curve will have a shape of like this. So, initially the slope will be flat and eventually the slope increases. So, this will be the type of the curve and so these along this the curve, so the values of the well function u are plotted are denoted and here typically, so this is say this f u axis may start with 10 to the power minus 1 and then this is 1, this is 0.1 and then this is 1 and then so this is 10 and similarly here this is, so this is 10 to the power minus 2 and then this is 10 to the power minus 1 and then this is 10 to the power 0 or this is 1 and then so here this is 10 and then so on. So, basically both these scales are, this is a log log plot and here typically the values of u, so they start with say here at the top it may start with say point this u is equal to point triple 0 1 that is 10 to the power minus 4 and so here we will get this is 10 to the u is equal to here, u is equal to 0.001 and somewhere here we will get u is equal to 0.01 and here this is u is equal to 0.1 and then here where the slope changes, so rough when this u is 1 and here this all the way it is close to this one, so this u is equal to say 3. So, typically this is how the value of the well function u changes and then so using this, so here what is done is, so using this equation that is f u is equal to s by delta s, so this one, so this f u is equal to s by delta s, so let us denote this equation as 1 and then so here the corresponding values of w u and u are obtained from the figure that is this figure. So, this is the relationship between f u and w u, so this is the Chou's relationship between f u, w u and u the well function u, so this u is the well function and so here what is done is the formation constants that is the transmissivity, the aquifer formation constant with transmissivity t is obtained by, so the equation that is the typical drawdown is equal to q divided by 4 pi t and into this w u, so here this w u is known, s is known, q is known and so therefore, t can be determined, so that is t the transmissivity t is equal to q divided by 4 pi s into w u and so this is the first this one and then next the the storativity, the storativity s is obtained by the equation s is obtained by, so this is a storativity s obtained by the equation that is r square by t is equal to 4 t by s that is the well function equation, so we know that well function is equal to r square s divided by 4 t into t, so by this expression we get that is, so this is the well function equation, from this the storativity s is equal to that is u into 4 pi and u into 4 transmissivity t into time since pumping divided by r square, so like this using this Chou's relationship between this f u and w u, so we can determine the formation constants of the aquifer and so now we will move on to the unsteady radial flow in unconfined aquifers, so this Chou's method is a third method by which we can solve the Thay's equation and now we will move on to unsteady radial flow in unconfined aquifers. So far we have seen the confined aquifer wherein it is under pressure and wherein the things are somewhat more straight forward I should say as compared to the unconfined condition and here in this case, so this there will be it represents 3 types of behaviors say suppose we plot the drawdown s versus time t on log scale, so this is log of s the drawdown and then the log of t the time since the pumping, so here, so it indicates 3 different kinds of nature, so the first one is this segment 1 wherein the slope is quite steep, so this here we can denote, so this as the segment 1 wherein the slope is you can say it is relatively steep, then so this is what happens is, so the as time increases the as time further increases the drawdown will just marginally increase and so this one here we can denote this as segment 2 or stage 2, segment 1 having a relatively steep slope, then segment 2 having a relatively flat slope, then again in the third this one, so this is here you can say, so this is segment 3, so here what happens is, so the gravity drainage and obviously in this unconfined aquifers, so the drainage is by gravity and this gravity drainage is not immediate and obviously that is why it constitutes an unsteady flow condition and so the water flow towards well in unconfined aquifers is characterized by this slow drainage of interstices, so basically and water flow or rather ground water flow towards a well is towards a well in an unconfined aquifer shows a slow drainage through the interstices or the pores that is why initially what happens is when the pumping starts, so then so this drawdown increases and this is drawdown increases relatively steeply in this first segment and then once so this it has increased, so then what happens is, so the here, so the that is the cone of depression, so here there will be compaction of the aquifer as well as expansion of the water as pressure is reduced from pumping, so initially there is compaction of aquifer, compaction of water as pressure is as there is a reduction in pressure due to pumping, so this the first segment that is, so the first segment having the steep slope or steep drawdown, so here what happens is, so this will continue for a very short while and here so the drawdown reacts similar to a unconfined aquifer, so that means, so here this is the gravity here in this region it more or less behaves like a confined or artesian aquifer or pressure aquifer and afterwards what happens is, so this gravity drainage starts, so this is basically here you can say this is segment 1, here you can say this is analogous 2, so here this segment 1 is analogous 2 say confined aquifer or artesian aquifer or pressure aquifer, confined flow, next here the segment 2, so here so this is slow gravity flow in the segment 2 and here so this is because of the expansion of the cone of depression, so in the in segment 2 there is expansion of the cone of depression, here you can say there is a gradual expansion of the cone of depression and hence slow gravity drainage and so this continues and next is in the third segment in segment 3, so the time drawdown curve almost resembles non-equilibrium type curves that is unsteady ground water flow curves, so and therefore, so there are three distinct segments, segment 1 having analogous to confined flow, segment 2 having slow gravity flow and then in segment 3, so there is this is unsteady flow again which is may be again somewhat like segment 1 and then again the slow flattens like that, so here so therefore, in such case, so this the relationship between the drawdown and the discharge was drawdown S and discharge Q was developed for a fully penetrating well in an unconfined aquifer by Newman in 1975 as S is equal to the drawdown S is equal to Q divided by 4 pi T the discharge divided by 4 pi into transmissivity and here so this is a so well function of three parameters that is UA, UY, eta and here where this UA, so each of them represent one segment UA is equal to R square into storativity divided by TT, so in case of the unsteady flow in a confined aquifer it was the well function U is equal to R square S by 4 TT whereas, in this case, so this UA is R square S divided by simply T the transmissivity multiplied by the time since the beginning of pumping and here so this is so this is this W of UA, UY and so this is the note this is denoted as the unconfined well function UA is given by R square S by 4 TT and then UY is given by R square SY divided by TT and this is applicable for higher T values higher values of time. So, it represents segment 3 and this eta, so eta is given by R square KZ divided by B square KR, so here this KZ is the vertical hydraulic conductivity and KR is the horizontal hydraulic conductivity and obviously R is the radius and then B is the that is the unconfined aquifer thickness. So, using these 3 parameters that is this the unconfined well function is more complicated as compared to the well function in case of a confined aquifer wherein there is only one parameter that is well function parameter that is U is equal to 4 square that is R square S by 4 TT whereas, in this case it is a function of 3 parameters that is UA, UY as well as eta and here the theoretical curves for this UA and UY as well as eta are given by this Newman's curves. So, the Newman's curves for unconfined well function that is W UA, UY, eta, so here in this Newman's curves we have along the vertical axis of course, here also this is a log-log plot and so here we have, so this is W UA, UY and eta and here it starts with say 0.01 then 0.1, this is 1, 10, 100, so this is the unconfined well function which is plotted along the that is the vertical axis and then here we have that is 1 by UY along the horizontal axis. So, it starts with say 10 to the power minus 5 then 10 to the power minus 4, 10 to the power minus 3, 10 to the power minus 2, 10 to the power minus 1 then this is 1 then it further extends. So, this is 10, then this is 10 square or 100 and then this is 10 cube or 1000 and here what happens is, so somewhere between this 10 to the power minus 1 and 1, so here this is the curve it goes up to, so this is 1 and then similarly somewhere between 10 to the power minus 5 and 10 to the power minus 4 and so this curve goes up to say little over 10. Here, so these are the, so this is the, here actually let me, so this is the phase curve for 1 by UA and this is the phase curve for 1 by UY and in between we have, let me use the different color, this one that is, so this is 7, so this is 2, this is 2 and so here this is 0.2, next here this is 0.001, so this is 0.2 then this is 0.001, so these are all the, so this is the eta values, so this is eta is equal to 7, eta is equal to 2, eta is equal to 0.2 and then this eta, so this is eta is equal to 0.01, so this is how the theoretical curves for the, you can say this is the Newman's theoretical curves for unconfined well function. So, like this, here we will get the, it is more complicated as compared to the unconfined flow, radial flow in a confined, I am sorry, unsteady radial flow in a confined aquifer wherein, so it is, there is, it is only there is a well function parameter that is U is equal to r square s divided by 4t into t whereas, in this case, so there are 3 parameters, one is Ua which is given by r square s by tt representing the first segment, Uy which is equal to r square sy divided by tt which is applicable for the higher values of t representing the third segment and then eta, so which is a ratio of r square by b square that is the distance from the well axis, the radial distance from the well axis, square of that divided by the square of the unconfined aquifer thickness of course, that is a, itself is a variable and multiplied by the ratio of the vertical hydraulic conductivity and the horizontal hydraulic conductivity. So, like this in this, the unsteady radial flow in an unconfined aquifer is, even though it is the unconfined aquifer is the one which is much, which is the first aquifer as we encounter when we go from the ground surface, but here, so because it is at the top and then so there it is more, it is subjected to more fluctuations because of the natural as well as natural ground water recharge and it is the reason and many times, if it is a, this one in some cases where the, even the operation may also play a predominant role at if the, if there is a tropical desert kind of situations like Oasis or anything. So, therefore, so it represents more intensive, so unlike the unsteady radial flow in confined aquifers, so this unsteady flow in unconfined aquifers represents more this one. So, now with this, we will go to, we will just, I will briefly, that is start with, that is leaky aquifers, so that is the unsteady flow and here, so this leaky aquifers, so they may have either a bottom confining layer which may be leaky or they may have a top confining layer which may be leaky or even both the top layer as well as bottom layer may be leaky and of course, one, if the bottom layer is having more perforations or in that case, so what happens is there will be, the aquifer will be losing water whereas, on the other hand, if the top confining layer is more leaky as compared to the bottom confining layer, so then in that case, the, this leaky aquifer may gain in terms of ground water, so therefore, so it represents an entirely different this one and here, so this is the, the Walton presented the theoretical curves for leaky aquifer, so this is, so this leaky aquifer may have say with single leaky confining or rather confining, say semi confining layer, say leaky that means semi confining layer with double semi confining layers, so double means this confining layer may be at the top or as well as at the bottom, so in this case, the theoretical curves were developed by Walton in nineteen, so theoretical curves for leaky aquifer, so this is the Walton's theoretical curves for leaky aquifer, so they were developed in the year 1960 and here, so similar to the well function for the unconfined aquifer, here we have a well function for the leaky aquifer and that is denoted by W U, R by B and here, we have this is 1 by U and of course, both are on this one and here, this access the W U, R by B, so that is, this is denoted as leaky well function, so this is the, so in case of confined aquifer, it is W U, there is a well function that is W U, whereas in case of unconfined aquifer, we have unconfined well function, so that is W U A U Y, eta whereas in this case, the leaky aquifer, so this is somewhere in between a confined aquifer and an unconfined aquifer, so here, there are two parameters, the first parameter is U and the second parameter is R by B and so this is the leaky well function that is W U, R by B and it is the theoretical Walton's theoretical so it is here, the W U access will start at say 0.01 and then, this is 0.1, so this is 1 and then, 10 and then, similarly here, the 1 by U access will start at 0.1, 1, 10, 100, 1000 and 10000 or say 10 to the power 4 and here, so this Thais curve is the one which starts somewhere in between that is 0.1, that is 0.1 and 1 and so it starts here, so this is the Thais curve, so here, this is R by B is equal to 0.05 and this is the Thais curve and here, from the same point, so this is R by B is equal to 2.5 and in between, so there are different of this one, so this is R by B is equal to 1 and here, this is R by B is equal to 0.1, so like that, so this in this case, the drawdown which is a function of R and T is given by Q divided by 4 pi T into the leaky well function that is W of U, R by B and again, so here, this U is the same as the confined well function parameter that is R square S divided by 4 T T and this and R by B is equal to R into under square root K dash divided by K B B dash and this U is the same as the one and here, this is here, this B dash is the equator thickness, so this is the K dash is the hydraulic conductivity of aquitard, aquitard or leaky aquifer, so that is leaky aquifer and B dash is the thickness of aquitard that means leaky aquifer and K and B are the for the regular aquifer. We will stop here and we will continue in the next lecture and we will move on to the further topics in this well hydraulics. Thank you.