Typically, when Shohei Otani is on an MLB DFS slate, we know exactly what to do, and that is to use Shohei Otani as a pitcher. Tonight, I'm not quite sure I can get there due to a combination of a couple of factors, and it kind of throws a wrench into our Otani and logout approach, and I feel like we actually do want to turn elsewhere for today. So it's disorienting, it's not fun to not be on Shohei Otani, but I do think all things considered, that is the right way to play things for tonight. We're gonna break down why that's the case with Otani, where I'm looking instead of Otani for tonight and getting you ready for Wednesday night in MLB DFS. Welcome on into the solo shot. That's right here on the FanDuel Podcast Network and NumberFire.com. My name is Jim Saunas. I am a senior writer and analyst for NumberFire. You're gonna break down Wednesday's seven-game main slate with locks set for 6.40 p.m. Eastern for today. Couple weather notes here. The first one is in Philadelphia for the Phillies and the Braves. There's a chance of rain there. Looks like as of now they should be okay, but I'd check back on the timing and intensity of that rain later on to be sure. A Yankee Stadium for the Mariners and the Yankees. Winds are in from right at 10 miles per hour. With the way the stadium is composed, don't think that should be a huge issue, but would slightly downgrade bats. There's similar thing in Cleveland for the Guardians and the A's. Wind may matter a bit more there, so slightly large downgrade to bats for the Guardians and the A's as a result of the wind being in from right for that game. We're gonna dive in and get you ready for tonight's slate here in just one second. But first, a reminder to make sure you're subscribed to the NumberFire Daily Fantasy podcast feed. Wherever you get your podcasts, our breakdown of PGA DFS for the Travelers Championship went up yesterday with myself and Brandon Gadilla breaking down the field for this year's designated events. Can find that wherever you get your podcasts. Also check it out. Check out the solo shot over on the Fandal YouTube page. And as of now, you can get both the solo shot and covering the spread. Each episode over on the Fandal TV Plus app. Fandal TV Plus is available on Amazon Fire TVs, Apple TV and on Roku as well. So if you've got those devices, you can get run it back up in Adams. All your favorite Fandal TV shows and the solo shot and covering the spread all in the same place just by logging in to your Fandal account. So if you want to download Fandal TV Plus again, check it out over on Amazon Fire, Apple TV, Roku and get all episodes of the solo shot and covering the spread there as they are posted later on. Already today is very exciting development. The podcast still available in usual spots but now available on Fandal TV Plus as well. Baseball season is in full swing and there is no better place to get in on the action than Fandal America's number one sports book because right now new customers get a no sweat first bet up to $1,000. That's up to $1,000 back in bonus bets if your first bet doesn't win. So don't miss your chance to snag a no sweat first bet up to $1,000 when you join Fandal today. Fandal official partner of Major League Baseball. Major League Baseball trademarks used with permission must be 21 plus and president select states first online and real money wager only $10 deposit required. Refund issued is non-withdrawable bonus bets that expire seven days after receipt. Restricts and supplies see full terms at fandual.com slash sports book. Fandual is offering online sports wagering in Kansas under an agreement with Kansas Star Casino LLC. Gambling problem call 1-800-GAMBLER or visit fandual.com slash RG in Arizona. 1-800-NEXT-STEP protects next step to 533-4-2 in Connecticut 1-888-789-77777 or visit ccpg.org slash chat in Indiana 1-800-9 with it in Wyoming and Kansas 1-800-522-4700 or in Kansas KS GamblingHealth.com. Louisiana is 1-877-770-STOP in Massachusetts gamblinghelplinema.org or call<PHONE_NUMBER> for 24 seven support in Maryland MD gamblinghealth.org in New York 1-877-8 Hope and Why and in West Virginia go to 1-800-GAMBLER.net Pitching preview for this main slate for tonight Shohei Otani comes in with a salary of $10,700 on Fandual followed by Luis Castillo 10-6 Sonny Gray checks into 93 with Michael Kopeck at 95 Aaron Nola is 93 Hugh Darvish 91 with Martin Perez AJ Smith-Shover as the other guys at $8,000 or higher. Now we'll talk through Shohei Otani later on and things to watch and outline why I'm lower on him for tonight. As for the rest of the slate, Aaron Judge still is not back for the Yankees. And until he is, that's gonna make the Yankees a plus matchup for opposing batters. And that means tonight, we can go at Luis Castillo and feel pretty good about doing so. The Yankees active roster has a 92 WRC plus against righties that's actually tied for the worst mark on the entire slate. They don't draw a lot of walks which leads to shorter playing appearances which helps pitchers go deeper in games. And Castillo hasn't been perfect recently. He's had some hiccups but broadly he's been very good. Across nine starts for Castillo with his velocity stabilized, he has a 3.53 skill interactive ERA with a 29% strikeout rates. He is still letting up too much hard contact which could give him in trouble Yankee Stadium but even with the hard contact being in there across that nine start sample, his ERA is still 3.42 which is totally acceptable. Castillo has hit double digit strikeouts twice in that time. He had nine in another. He is one of the guys in the slate who can actually get you double digit strikeouts which he actually did do on the road once. One of those 10 strikeout games was on the road. Now not projected that high for tonight. I've got Castillo at 7.1 here which is not a massive number but it does rank second across the slate for tonight. So that's enough for me to give Castillo a go here. Feel pretty good about him just in general feel pretty good of using batters against the Yankees or using pitchers against the Yankees until we get Aaron Judge back in the mix there. Number two behind Castillo is going to be Aaron Nola and Nola is in a tough match but tougher matchup than what Castillo has for tonight because Nola is facing the Braves but he is at least a home and I think that means we can use Nola tonight at $9,300. Nola really did struggle to open this year and it's something we discussed in the show kind of thought that might happen because he was a guy who had a very long pace last year with the pitch clock thought he might have a tough time adjusting. We did see that with Nola initially and he hasn't fully ridden the ship yet because his ERA this year is 4.66 still but the peripherals from Nola are getting much better. Over his past 10 starts, Nola is throwing more sinkers and the sinker for him is not a strikeout pitch but it has still led to increased effectiveness overall. Across those 10 starts Nola has a 27% strikeout rate. His skill interactive ERA is 3.55 and he's led up a decent hard hit rate. It's not good but it's decent. It's not terrible I guess is the way I'd phrase that. The results for Nola in that span are fine with his ERA at 4.34 but he's had huge single game ups that which we'll want here for DFS. Nola 12 strikeouts in one game, 10 in another and both those games were at home which is where he is at for tonight. We did see Nola against the Braes once in the stretch. That game was in Atlanta and they did get to him. Five earned runs allowed, three home runs but also seven strikeouts for Nola. So he can get strikeouts in this matchup. That matchup happened almost a month ago so there's enough time between them to not worry about familiarity. So it is risky. He could let up five runs again tonight. That could definitely happen. The Braes are a very good team but it comes with upside and to me that's a fair trade off and one I'm okay making because I won a gun for upside at all times in DFS. I'm gonna rank Nola second at pitcher for tonight at $93 behind just Luis Castillo. So to me the studs are ranked Castillo one, Nola two as the top two studs on the main slate. We'll talk about Shohio Tani later on. As far as the value play goes you might not need to go far down tonight because the stacking options I like the most are not gonna come with high salary. But I actually don't mind one of the value plays here. That guy is Garrett Whitlock. His salary is $6600 which is way, way too low and I think you should be at least a consideration even though we're not gonna need the salary savings for tonight. Whitlock is facing the twins and that offense has very good pieces especially with Byron Buxton being back but they strike out a ton. The twin strikeout rate against righties is 28.5%. That is the highest on the slate by 3 percentage points. Whitlock has made four starts coming off the IL and throwing fewer sinkers, more changeups in those starts and it's worked out pretty well so far because in that four start sample his skill interactivity rate of 3.59, batted ball data for Whitlock is good too. The striking rate is 24% so not massive but also not low and it does get a boost here against a very high strikeout team. I have Whitlock projected for 6.1 strikeouts which is very high for a guy with his salary and again I'm not sure if you'll need it. Most of the higher salary batters on this slate are in tougher matchups but Whitlock is pretty nice. I do wish we got him on a slate where I needed the savings more but I still think he's at least worth considering here. So to me the slate is Castillo and Nola as the focal points. Gotani kind of hanging out there potentially being consideration maybe you go to Michael Kopeck too but and then Whitlock is the value again if you decide to need it I don't think you will but just in case he's at least worth bringing up for today. Let's dive now into the stacks and discuss why we may not need those salary savings because the top stack to me is going to the Mariners they're facing Johnny Brito. Brito coming back up for the Yankees and we saw him struggle in his first dart and first didn't the rotation didn't have great results in AAA either which allows us to stack the Mariners for tonight at Yankee Stadium. Brito made 10 appearances with the Yankees before being sent down and eight of those came after he shifted toward using more sinkers. So I think that's the most relevant sample and in those eight outings Brito had a 5.42 skill interactive ERA with a 16% strikeout rate. The bat of all data still was not that great there despite using more sinkers. So you would hope that would come with the territory did not there and the results for Brito matched the peripherals which is why he was sent down made four starts in AAA and the first two went okay but the second two were pretty big steps back from that. Overall in those four starts Brito had a 4.93X flip now he comes back up and he facing the Mariners tonight the Mariners have a 100 WRC plus against righties. So they're about average they're not the world's best offense but they're also not an actively bad offense and they get a big park factor upgrade and going to New York for tonight. So I think this all does give us a green light to stack the Mariners here and feel pretty okay about them. So the Mariners to me the number one stack on the slate. The park factor upgrade as I discussed is bigger for lefties than for righties given that Seattle's not terrible for righties but does give a boost to Jared Kalnick. Kalnick has struggled in the month of June only one home run this entire month but that's pushed his salary back down to 31 the results again not great but even in this month of June he still has a comparable hard hit rate to what he had before his barrel rate is actually the same as well and had a barrel last night. He's just striking out too much but facing Brito lower strikeout guy maybe that allows Kalnick to flash those bad at ball skills more often. So to me not super concerned about Kalnick's rough issues recently mentioned on covering the spread that I like him as a home run bet for tonight at plus 450. I think that Kalnick is a rock solid option the guy I feel good about for today and just in general the Mariners a fun team for me to stack for tonight. Number two stack we're gonna go back to stacking against Martín Perez. I tried this last week and it did not go well. He held the Blue Jays to two runs across six innings but not the best slate for stacking. So I think I'm gonna go back and give it a crack again which means stacking the Chicago White Sox against Perez for tonight. So the White Sox is the number two stack for me behind the Mariners. Perez to his credit did pitch really well in that Blue Jays game. He allowed just five hard hit balls on 18 balls in play and that's what he was doing back in the day when Perez had success he was suppressing hard contact. But the start before this one against the Jays Perez really got knocked around. He led up seven earned runs in three and one third innings led up six earned runs, two starts before that and both those starts came on the road. He's on the road again tonight. Perez in a very small sample this year has much worse numbers on the road than at home which could be fluky because home road splits might not be stable over the course of an entire year much less a couple of months. But either way doesn't hurt. Maybe it means I made a mistake in stacking against him at home last night but he's on the road now. So he's facing an offense whose WRC plus against lefties is back up to 111. So I think it makes a lot of sense to be on the White Sox for tonight. One guy would want to exclude if he winds up playing from those stacks is Tim Anderson. I think Anderson had been struggling all year and it was kind of odd because he's been such a good batter for such a long time but now missing some time in the shoulder injury and shoulder injuries can linger they can set power even when you're playing through them. So I think honestly it's kind of a relief that he's been setting out because hey, you hope he gets better because Tim Anderson is really fun and you want to see him healthy being to Anderson and you want him to rest up and get better but also it means that temptation is not there for DFS for stacking. So even if Anderson does wind up playing I really don't want to be there given that we know that now this injury related. So to me Anderson despite being a guy who benefits from a matchup with a lefty despite being a guy I've loved for a very long time I think even if he winds up being in there I don't really want to go there. And again, probably not gonna need the salary savings either with Anderson whose salary has shot down. So Luis Robert, Roy Jimenez, Andrew Vaughn, Jake Berger, all those guys bigger focal points for me when stacking the White Sox and Anderson if he does wind up playing for tonight. For our third stack let's talk to you about the Angels facing Michael Grove who not officially but sounds like he'll be coming back up to start for the Dodgers. He's had some big issues when he's gotten chances in the big leagues and a pretty tough matchup with the Angels. So Angels to me do make sense as my third stack behind the White Sox and the Mariners. Grove has made seven appearances in the majors. ZRA there is 8.10. His expected ERA is 5.32. So not as bad as the results would say but also definitely still stackable. The plate discipline numbers for Grove are fine. So like he's not losing there. It's from the batted ball data. Grove is letting up a 41% hard hit rates and getting ground balls just 36% of the time. So a lot of line drives, a lot of fly balls, a lot of them are well struck. That's how you get into pretty big issues and lead to an 8.10 ERA. And that's an issue that Grove had in the majors last year in a small sample as well. When we look at the time in the minors for Grove it hasn't really cured that. So I don't think that the time he spent down in AAA really fixed him. He's made three appearances coming back up and he's let up seven barrels in those three games. So didn't get fixed that first trip down, got sent down this time and didn't make any starts down in AAA. The Angels have a 120 WRC plus against right easily, 218 ISO and a lot of fly balls. So it's a pretty bad matchup for Grove. A guy who's struggling with hard contact to face a team that can do what the Angels can do. So to me, I think the Angels grade that really well for stacking. As always the bummer here when stacking the Angels when Otani is pitching is we can't use Otani in stacks but it does seem like Mike Trout is maybe better. Maybe I know the results are bad still in June but in the month of June, 59% hard hit rate. So even though the results have not been there the power has not been there he's still making really hard contact and eventually you'd think that would turn into good results. Again, it is not yet but maybe it will as the sample expands. Sally for Trout is still not low, $3,900. So we're not buying low here but I am more comfortable with Trout when after digging into the badder ball data than I was before that. So to me, I think you'll turn it around and that would make him a good play at 39 but it's been a large sample where the power has not been there. Not a low salary but I still think Trout very much worth buying into for tonight. Let's go now to things to watch and didn't wanna talk about Otani quickly as a pitcher. There are a couple of reasons why I'm lower on him for tonight and the first one is he's facing the Dodgers that's just a very tough matchup. So that part's obvious. The second part is Otani just struggling recently his skill interactive ERA is 4.01 since he started throwing fewer sliders. I'm expecting to be back on Otani here pretty soon but I am okay taking a breather from him when he's in such a tough matchup with the Dodgers and things have not been super, super smooth for him recently. Sunny Gray has been in a pretty massive funk recently bigger than Otani's. He struggled against the Tigers last time out and got yanked after just four innings. So that was pretty rough. He's facing the Red Sox for tonight and the temperatures at Target Field are very, very warm. They're the warmest in the slate by 14 degrees. So good park for hitting. I think the Red Sox could be a fun contrarian stack here. Gray does not let up many fly balls. So keep that in mind for sure but good park for hitting for tonight. Red Sox offense isn't bad. There are a lot of paths to failure but I think the Red Sox given they won't be popular are at least an enticing contrarian stack for tonight. Finally, I don't hate the idea of stacking the Phillies. They're facing AJ Smith-Shover who has gotten good results so far but he hasn't been overpowering, I wouldn't say. Let's up a ton of fly balls. So if you're looking for home runs, I think the Phillies are kind of decent in that regard. I would rank them below the others but could be a good spot for some dingers, especially given the amount of fly balls AJ Smith-Shover has allowed. Let's finish up here the Dinger calls for today. The boring one, I will go Mike Trout. Again, the hard contact has been there. The results have not. I think eventually it should get there. And again, Michael Grove letting up a lot of hard contact, a lot of fly balls. I think that bodes well for Trout. So we'll go Mike Trout as a boring home run call for today. For the fun one, I'm not sure if this counts. This might be cheating, given how good he was to start this year but Jared Kalnick won home run the month of June. I'm gonna count that as being a fun home run call. You can yell at me if you want and that's fair. I understand that but I think it's Dinger odds that Fandals Sports Book pretty good at plus 450. So we'll go with Mike Trout and Jared Kalnick as the official home run calls for today. I'd also mentioned Nick Castellanos is heating up and if someone does something terrible today, Castellanos guaranteeing Homer, the bad of all data finally coming around. So the bonus home run calls Nick Castellanos at 33. It seems like he is starting to pick things back up from a bad of all perspective once again. That is all that we have here for today on the solo shot as mentioned, do not forget to check out our PGA DFS podcast breaking down the Travelers Championship that is available over on the Number Fire Daily Fantasy podcast feed wherever you get your podcasts. Also again, check out the Fandal TV Plus app where you can get run it back up in Adams and of course the solo shot and now covering the spread all in the same place and just a great place to get all of your Fandal TV content at once. If you've got any questions for me, I am on Twitter at Jim Sonnis, J-I-M-S-A-N-N-E-S. You can also follow the Fandal Podcast Network at Fandal Podcasts. I wanna thank you all for tuning in for today. Good luck to you with your MLB DFS lineups for tonight. We'll talk to you once again tomorrow to break down Thursday's slate. This has been the solo shot right here on the Fandal Podcast Network.


Well, welcome back everyone. We're going to jump right on in here. So Carlos mentioned in his presentation right before the break about all the comments about the role of product marketing and PMM. So I just want to have a quick show of hands. Who in this audience has heard at least some mention of the role of the product manager at Airbnb and the demise of the role of product manager. Quick show of hands if you've heard that at all. All right. For those of you who haven't heard it. I do recommend there was a popular podcast Lenny's podcast that came out this past weekend. It's worth a listen to if you actually listen to the dialogue. I think it's more about the coming together of product management and product marketing and less about the demise of the product manager, but the demise of product management gets many more clicks in social media. And this whole kind of commentary originated back at the Figma conference a few months ago. And that was actually the origin of this panel. Because that dialogue has started all sorts of chatter and banter about like, where are the lines? How does product marketing and product management partner effectively together? So what we did was we brought together a cross functional panel here.  You've got a few marketers on the stage here. So we're going to share our perspectives about the role of product management and product marketing and sometimes how those roles collide. But before we jump into the meat, we want to do a quick round of introductions. So if each of you could just quickly introduce yourself and share a bit about how these product managers in the audience can use your products. Let's start with you, Ritu. Welcome, everyone. I hope you're having fun so far. My name is Ritu Kapoor and I'm the CMO of Product Board. I live in the Bay Area with my two kids, 11 and 16. The 11 year old still loves me. Before I got to Product Board, I was CMO at a company called Lobb, which is in the direct mail automation space. And before that, I was VP of product marketing at Automation Anywhere, which is in the RPA space. Actually, before that, I was in the RPA space. Actually, before that, I was in engineering and product roles, but I'm going to be dating myself here if I tell you how many. And when I first was introduced to Product Board about a year ago, I remember thinking I would spend countless hours banging head against wall as both a product marketer and a product manager, just trying to figure out what customers want to see from the product. And in fact, I would have really saved those hours. So at this point, I believe we have 6,000 customers who work across both commercial and enterprise, both mid-market and enterprise. And the three things that really, that I will take out from what they tell us and the value that Product Board provides them is really, A, it's a system of work for the product manager. Purpose built for their needs. It's not for the project manager. It's not for the engineer. It's really a way for them to do their daily jobs in the right way without friction, whether that's writing features packs, whether that's prioritizing features, creating roadmaps, aligning with their teams, things that they need to do on a daily basis. Just make it simple. The second thing I hear from them is being a central source or finding Product Board to be their central repository for all customer feedback, all stakeholder feedback. And being able to take all of those different pieces of feedback would be hundreds and thousands. And getting the insights and using those insights to be able to do their jobs well. And I'm glad that both of you use it as well. I'd love to be able to talk to you a little bit later about Product Board. And the third thing I hear, and for me, this is the most important, is alignment with your go-to-market colleagues. Often it's a silo, product works. In one part of the room, go-to-market works in the other side of the house. So how do you basically make sure that the entire company is aligned on one product vision? People know what you're building. People know how you're building. Your salespeople are able to present the most up-to-date roadmaps to their customers without having to pull product managers in the room. And just even looking at revenue targets for each feature, all of that together, I think for us, Product Board really becomes that system of work, that central repository, that go-to-market alignment that product managers are looking for. So anyways, I'm a big fan. Thanks, Ritu. So my name is Karan Mubai. I'm Senior Director of Product and User Testing. I've been in product management or in product roles for about over 20 years now. I spend a number of years at SAP, at Business Objects and a variety of companies both here in the Valley and based in Vancouver, Canada. So for fellow Canadians, welcome to beautiful San Francisco. At User Testing, we lead a movement to bring human insight and empathy into your product experiences. And one of the things that I'm excited about is we enable product teams and everything from user research, designers, product managers and our colleagues in product marketing to really get at the why behind what's happening with your product. So we're inundated with a lot of data in our day to day lives. We have a lot of great tools that bring us a lot of behavioral data and we really help to dig in further underneath that and really get at the why of what's happening, interactions with the users, discussions with the users of your products and your experiences. I'm really excited. I'm the token product manager on this panel of marketers but obviously filled with a room of colleagues here. So thank you for bringing us on. Hey folks, this is Arshal. I'm a principal product marketing manager at Amplitude and I have an engineering management background. I've worked in both startups and enterprise companies across a range of roles from product management, solutions consulting and now product marketing. Amplitude is a digital analytics platform that you as a product manager can use in order to build better products. And so you can use Amplitude to look at user behavior and journeys, understand metrics like conversion, retention, monetization of your users in your products and then take that to derive insights and decide what actions you can take on your users and those actions could be deploying A.B. tests and experiments. They could also be deploying marketing campaigns and Amplitude will be there along the way to power and enable all of those. So I'm excited to be here on this panel and looking forward to the discussion. Thank you so much for those introductions. So let's jump into the first question. So product marketers and product managers, they worked very closely together. Some companies product marketing reports into product management, sometimes reports into the CMO, the marketing organization. But putting that aside, there sometimes is some overlap. I'd love for you each to kind of share like give me one specific example of the situation where there's been some overlap between the product management function and the product marketing function and what was the negative consequence of that overlap? And let's start with the product manager on the stage. Let him go first. Yeah, so this has definitely been an experience that I've, you know, from company to company, you go to and one of the things I recommend to every product manager, you join a new company, there's always an established product practice, whether it's product marketing, product management. And within that, there's the roles that have been doing the functions in and around product management or product marketing for a fair bit of time. And you come into it, you don't know exactly who's doing what. And where the friction or the issues tend to happen is, you know, you haven't really established those norms or understood the practices that are there within the company. So a lot of times pricing and packaging comes on. I think that's very common. And, you know, I think others can probably touch on that. Anytime you bring up pricing, you lose up about an hour in every meeting discussing that. But the issue that I had at a previous company, when loss analysis between sales, marketing, product management, we always were discussing like, who should actually be running this? Why is it important? Obviously, there's a lot of insight in understanding why you want a particular deal or why a customer may have chosen a different solution. And then, so there was this constant discussion and friction around who should be leading that, why it's important for us to having that. And ultimately at the end of the day, it's just you want that function to be happening. You need the outputs of that to really help drive your decision-making. So I don't get too hung up on the ownership rather than making sure that we are doing the different things that we need to across the teams and that we are getting the output and the data that we want. But before we move on, what happens when it's not clear? What are some of the negative issues when you don't know who's owning the competitive intelligence? You don't know who's winning. Ultimately, it either falls on the floor because you're not dealing with that friction within the company and so people sometimes naturally don't want to have friction with their colleagues, whether that's in a new environment or an existing one. And so you're either not doing it well or it's being done across the board and so you end up having an issue where you're running the same program in multiple areas. That's not really efficient and are you really sharing the data or doing that effectively?  But I think the one that I tend to see a lot is you're not dealing with it head-on and really addressing the underlying problem, which is you need to effectively collaborate in order for this to work well. That's great. I'll be you, Darsall. Yeah, pricing and packaging for sure. So a while ago, I was at a startup where we were going from a one product to a multi-product company and the product manager for the new product we were launching had strong opinions on how we would go to market, specifically selling it and packaging it as an individual skew or its own product. And as we spoke with our executive buyers at all of our customer accounts, we started to learn that they don't actually see those products selling individually or buying them individually. They see value when they buy the first, the core product and then use the additional one with it. And so as you can imagine, as a result of that, we had to have a number of alignment and stakeholder conversations to try and think about a new pricing and packaging strategy where we sell it as a platform as opposed to individual skews and then to answer your question, the result of that is delays and really just time that could have been spent building additional capabilities or launching something new is spent debating these factors inside. And I want to agree with what Quran said that there's an element of deduplication of effort. So when you are duplicating efforts, as a product marketer, I'm telling the product manager, here's what should be or what should not be on your roadmap that's counterproductive to them and conversely, what's counterproductive to product marketing is if there's roadblocks to rolling out faster when it comes to pricing and packaging. And so where overlap exists, it's really duplication of efforts can be counterproductive and leading the time delays but where overlap includes alignment and going to market, I think that can be a stronger facet for the company as opposed to not having that at all. All right. Ritu, how about yourself? Yeah, I mean, pricing and packaging for sure and the other thing I'll bring up is competitive strategies. So I think the audience show of hands if you've ever filled out those massive Excel sheets for the Gartner Magic Quadrants and the waves with your product management colleagues or product marketing colleagues, it takes weeks because and it really showcases the differences in how both teams look at competitive strategies, stops down, bottoms up and just trying to get alignment is the first three weeks of that Gartner survey. The negative consequences of having this misalignment or having this overlap in job duties is not acting on the insights you have. Product marketing goes and brings their own product marketing management is looking at their own versions of these insights and you're sitting on them instead of acting on them and what suffers is the market, the go-to-market teams, the users that are waiting for you to act on the feedback and act on the insights that you've gotten. So the market suffers in the end. And just to build on what the panel has said from my own experience, one of the negative consequences is morale, right? And there's a challenge when there's a duplication of efforts towards something you think you're about ready to launch, then all of a sudden there's a disagreement for the people actually doing the work, the more hands-on folks that has a significant implication both to the product marketers as well as the product managers because that lack of connection at the top can really impact their day jobs, which leads us to... So those are some of the negative consequences. What have you seen in your careers work positively? How have you seen product marketing and product management effectively work together and collaborate together? Let's start with you, Raju. So I think the most effective working relationship is when you start with exact alignment. Your product leader and your marketing team leader are joined at the hip. They have regular syncs. They have conversations around resources, around prioritization, even right down to the everyday activities. And when it starts with that, then those projects and then those, I think working relationships are just a lot better. And when done right, that team is that's responsible for both acquisition, retention, activation, expansion. That customer journey is phenomenal. When those two work together and there's alignment from the top, you have kick-ass products. You really do. Let me go. I couldn't agree more with what you said. In fact, just going back to your last point, a lot of times when it's the actual practitioners, they know that this function is there. And a lot of times they're sitting there struggling and trying to work through that dysfunction. So I love the follow-up, which is how do you sort of get past that? How do you effectively collaborate? I think I referenced that you need that alignment when you're going into a new org or you're in an established org of who is doing what function and couldn't agree with Ritu more because these were the priorities that we're working on. How are your respective collective teams that are going and tackling this, sometimes in the same org, sometimes in different orgs, going to do that effectively and do that collaboratively. I think one of the things that I've shared with my teams or I've tried to do myself is start early on. You're working on your planning, bring your product marketers very early into that planning so that you're aligning on the releases. You're aligning on what you're messaging and your themes are around those releases. You can get a sense of where you're going directionally so that we can talk about the pricing and packaging much earlier rather than later.  So I think really early effective communication between the two functions is really critical and really focus on what are the white spaces where you know you need to go and do more. We all use different frameworks out there that tell us what we should be focused on as product managers or product marketers. And there is overlap in those as we discussed a minute ago. And if you can, there are areas that you're just, as an organization, you're not focused on and you're not doing. And if you can take those, one of my biggest pieces of advice to any product person, no matter the role, is go and find those white spaces where your organization isn't doing the things that they should be doing and go and try to focus those and learn on those and bring your colleagues into those learnings as you're going about doing it. And I think collectively you'll rise the effectiveness of your organization. I love that approach of the white spaces. I just want to build on that for a moment because I hate this answer that it depends, it varies, but the reality is every company is a little different. And that line between product marketing and product management really does vary from company to company. So when you go in and you identify where those white spaces are, then you can assign for lack of a better term and say like, hey, this is a function that could go to product management or it could go to product marketing. Who's going to do it? It's not happening right now. Someone should do it. Who's the best student to do it? And then who has the bandwidth? I do want to transition to some questions from the audience. Some of you guys submitted questions via LinkedIn. So I really, really appreciate that. So I'm going to do the best job I can at articulating them. One question that came up from multiple people was early on in the product development lifecycle, really early on, what role does product marketing actually play? The underlying theme, these were all questions from product managers saying like, hey, I've got my product marketer early on in the product lifecycle, but I don't know what they should be doing. So I'd love your perspective. Let's start with you, Richard. So I think I come from the startup world, so I'll take that view on it. A lot of times, both product marketing and product management are going out and validating the founder's vision to be quite honest. Product marketing is going out and validating the ICP, building upon what the founder's vision was on who they wanted to sell to, validating the needs, looking at market trends and trying to determine what would this MVP look like. That product management then takes some bills and product management at that point early on owns the customer feedback loop. And then once you do have an MVP, I've seen product marketing takeover and try and package the benefits and try and figure out how you then take that message and then feed that back into the market. But I just really found a lead in companies that I've been in and been validating the founder's vision. Yeah. I think, Darshil, you'll have a unique perspective on this being the product marketer on the panel. Yeah, so how many people remember the first ad of the iPod out here? It was not 5GB in your pocket. It was 1,000 songs in your pocket. And so, you know, as you're working with your product marketer early on, they can help you look at your ideal customer profile, buyer personas, use cases. If you're expanding or planning to ultimately scale across multiple verticals or even expanding into local markets like APAC or EMEA, how can your product go to market in those regions? They will have expertise there or will no partners there that you can work with to get insights early on. And ultimately, as a product manager, you know, you don't want to build something and hope that people buy it or it just sells. You want to build something that is aimed at solving customer problems. And so your product marketer can help you with thinking through those and crafting your product to look like a solution set. So as you start thinking about your sprints and your roadmap, you're less hung up on individual features within that roadmap and more thinking, hey, how is this going to help us with our early alpha and our MVP? Are we going to be able to solve those main problems if so we're ready to go into GA? If not, we're just not. And it's less about feature versus feature and more about solution at that point. Some of your answers naturally dovetail to the next question that we got from some of the people via LinkedIn. And the question was, who owns customer insights? Right? Frequently, the product marketing team wants to be the voice of the customer, voice of the market. But then the product managers are also very involved in listening input as part of the beta programs and ongoing, right? So I think that you're very natural to speak on that based on where you work to start. I've loved your thoughts. So where's the line? Great question. I mean, I think as a company, we think that everybody should be focused on customer insights and customer feedback. So I don't think that there's a right answer. I think you're right. Voice of customer programs exist. They live in product marketing or marketing teams. But we all know that as product managers, if we're not talking to customers, we're also not doing our job. So I think it's really dependent on the type of customer feedback that you're trying to do. If you're doing discovery or early on, just trying to get an understanding of where you might take your product or your particular experience, you're going to have your product or research teams really focused on that. Whereas if you're thinking about messaging, feedback, win-loss analysis, some of that may be later on and really closely aligned with the product marketing team. So I don't think that there is a bright line in terms of this team owns customer insights or feedback. If you talk to our customer success teams in our organization, they also feel that they have a very important stake in gathering or discussing that with customers. So I think it's really the type of feedback that you're trying to gather, really drives who might be leading it, who might be bringing those insights to the rest of the organization or using different tools to capture it and get those insights broadly distributed within the org. Darcy, do you want to give a shout? Yeah, so when it comes to feedback, I think the company's only be successful if everybody is customer-centric. I don't think any one team should necessarily own it. But that being said, when it comes to product feedback, so feature requests, bugs, product-specific enhancements, that should be more directed towards the product team and the product marketing team can own executive buyer feedback. So how is this product helping us drive value? They should own customer advocacy, so helping generate customer success stories that you as a product manager can use to take a social proof and sell more of your product. And really, at AppleDude, we have a strong process where customer success and sales teams are closely involved anytime there's interactions with any members or any types of customer feedback that we're collecting. Like many of these things, I do think it's a team effort, and I think this customer feedback is one of those things. Many times, I've seen that specifically in like a beta program, the product manager and the product marketer attach at the hip, and that during the beta program, the product marketer might own the customer feedback, but the product manager is right there with them listening to all the feedback, but making sure it happens is sometimes relies on the product marketer. But again, it does vary from company to company. Richard, do you have anything to add on this question? I'm going to do a shameless plug for product board here. Two sets absolutely help when you have a centralized repository, whichever one that will be, and have customer feedback in there. You don't have to keep going back to the customer. You're not constantly knocking on the CSM's door to try and get all of this feedback, and whether it's whichever team goes out and gets it and is able to log it in a central repository, people can go back, the other team can go back and take a look. And you know constantly, it's not who gets it, it's how it's being used, and I think that's the difference. Any team can go out and get the feedback but more teams need to use it. So just using your product board example, are there specific use cases that product marketer is used product board for? Like what specific use cases? Absolutely, so when you look at a roadmap and you have all of these capabilities and feature sets in the roadmap, most of them should be customer-defined. So if you look at all the feedback that came with a particular feature set from product board, that absolutely changes the game for a product marketer and the product manager built the feature set. The product marketer now doesn't have to go out and ask a million questions about that feature set because he's already seen the feedback on why it was built and what customers were asking. So messaging and positioning is the game changer. Got it, absolutely. So we're running a little short on time but one quick question. So there's this kind of evolution and Carlos spoke about it in his last presentation like that. A lot of product leaders are effectively becoming GMs of the business, right? I would just love each of your perspectives as like, where do you see the roles of product marketing and product management evolving over the upcoming years? What changes do you see happening? Let's start with you since you're at the far end. You know, I think for product marketing specifically and if you guys have heard of this growth marketing term, I see that role in the growth marketer and the product marketer become one person. Just AI is giving us so many data sets, so much data to be able to look at. PLG is taken off. I think just having that sort of data, you need a growth marketer's head and you need a product marketer's heart. So I do see that become one person and focus specifically not so much on acquisition but on activation. And I see product managers really focus on, you know, more empathetic product managers, really focus on retention and expansion. I've seen these roles evolve in the 20 years pretty constantly and depending on the org. Even within an org, they've evolved over the years. My role at SAP started as a product manager. It became a solution manager, which I would say was much more akin to a product marketer before I went back to, you know, quote-unquote product management. So I think there is a, you know, this idea that these roles might come together. There's so much breath to cover in terms of effectively doing the roles in the job of product that I think there's going to be distinct roles within all organizations to continue. Now, maybe in a B2B organizations, it's a little bit more bright line and distinct in a B2C organization. As you referenced, Brian Chesky in Airbnb has brought product management and product marketing closer together and established a more program management function. So I think this is a constant evolution. I think Ritu's accurate and that there's so much data, this idea of growth marketing and product marketing really coming together is maybe a somewhat evolved role of product marketing. We see that increasingly being pretty critical in terms of activating your customers. Yeah, I tend to agree with growth marketing and product marketing. I'd even add that, you know, at the practitioner level, as you start thinking about all the jobs that need to be done, you know, organizations will keep changing titles and who's going to do them. But I don't see one individual owning everything from product road mapping, sprint planning, working with design and engineering counterparts, and also running campaigns, thinking about positioning, messaging and everything that that entails. And so these roles are going to continue to intertwine and there's going to be more interoperability between the two, but I don't think they're going to completely merge into one and going to be done by just one individual, but at the practitioner level. And as a product manager, that being said, I'd recommend to this audience, start thinking about and working closely with your product marketing counterparts. Because the more you think about your buyer persona and the value and use cases they're trying to solve, the stronger your product is going to be. And also you're going to go to market and have a better alignment and launch with your marketing team. I'm going to build on some of the things that each of the panelists had just mentioned. We two did a good job at calling out growth. That was something that we didn't mention to this, but that is like the third leg of this duel between product, product marketing and growth. They're all participating in these various PLG and self-serve aspects. So they'll continue to be tight collaboration. I share I've been in this industry for more than 20 years and when I started, product marketing reported in a product. It was effectively a product role with a specialized skill. Over time, sometimes it more frequently reported into marketing, which is great. Regardless of the reporting structure, there has to be very, very, very tight collaboration and that's only going to continue.  I think that may be some specific use cases. That may be true, but the reality is that there's going to be a need for specialized functions, especially for the people doing the work. At the top level, there's just going to need to be increasingly more collaboration and alignment. But for the doers or practitioners, there's going to be just plenty of work to do. And with that, I want to thank the panelists for being here. I want to thank all of you for joining. And if you want to learn more about any of the companies that they work at, they all have boosts out in the back. So let's give the panelists a quick hand.


From Benway State comes a report that the state governor Samuel Othom joined other dignitaries at the Nigerian Air Force Aerodrome, MacCurdy, to flag off the resumption of commercial flights to MacCurdy to state capital. Governor Othom said the resumption of commercial flights to and from MacCurdy by air peace is a mega milestone in the long quest to facilitate air links between Benway and the rest of the world. The state government had earlier gotten approval to allow air peace to resume commercial flight operations to MacCurdy or from MacCurdy to Lagos at the Nigerian Air Force airport in MacCurdy. The state was also given approval for the construction of Civil Aviation Airport in Kura in MacCurdy by the Federal Minister of Aviation and Nigerian Civil Aviation Authority, MCAA. The Nigerian Civil Aviation Authority has granted approval for air peace to operate into this place. I want to also use this opportunity to appreciate this excellency for meeting up all the recommendations that we've made. I thank the excellency for the extra effort he put into this flight happening today and we promise the the states, we promise the travelers of Benway State that we will not fail you. We had an extensive engagement with all the key players in the aviation industry. As a state we have invested heavily to help meet Nigerian Civil Aviation Authority rigorous requirements for the resumption of commercial aviation services here. Facilitating geodetic surveil of the airport to ensure the airport is included in the ICAO maps so that the pilots can rely on instruments to fly to MacCurdy.


Today, we will continue with our discussions of ground water. We have already seen the Darcy's law which relates the hydraulic gradient and the velocity with the constant of proportionality, which is known as the permeability. And we have also seen how when we pump a well the water level or the piezometric level goes down. So, let us see what happens when we pump a well. So, this is the ground level and let us say we have a confined aquifer being pumped through a well. As we have seen the piezometric surface will go down as we start pumping and the difference is known as the draw down typically denoted by s. So, this s as we have seen is proportional to q because we have assumed that the flow is laminar. This is generally true, but when we are pumping from a well typically the velocity is very large near the well and therefore, near the well the flow will be turbulent. Similarly, near the well because of the casings when the flow passes through the casing there will be additional head loss. We combine these and call them the well loss and we write the total draw down at the well as summation of the laminar loss, turbulent loss and the casing loss. So, this will be total draw down at the well and if we draw the same figure again. This is the initial piezometric level before the pumping is started and then a final piezometric level after the steady state has been reached and this is the draw down at the well. So, if we say that there is only laminar flow then there will be head loss or a draw down because of the laminar flow. This is because of turbulent flow near the well and this is the loss due to casing well casing. As we have seen the laminar loss generally is proportional to the discharge. So, swl will be proportional to q. The turbulent loss is normally q to the power something and typically we can take it as q square. So, we can write swt is proportional to q square. The casing loss has also been seen to be proportional to q square. So, both of them swt as well as swc both of them are proportional to q square. These are known as the well losses and since both of them are proportional to q square we can write that the well loss is proportional to q square or we can write as w, some constant into q plus another constant into q square, where this c 2 q square represents the well loss. And we want the well loss to be as small as possible, so that the well is considered more productive. To find out these constants c 1 and c 2, we can pump the well at different rates and note down the draw down at the well. And we can write this also as which indicates that if we plot sw over q versus q, we would get a straight line and the intercept will give us c 1, the slope will give us c 2. So, if we pump the well at different rates note down sw for different q values, we can compute sw over q and plot it against q and get the values of c 1 and c 2. We want c 2 to be small, so that the losses are minimum. If well losses are large, for example, if c 2 is large, large c 2 will indicate in efficient well. And if we plot sw versus q, you would get a straight line with the coefficient c 1 and the slope as c 2. So, this method gives us a way of finding c 1, c 2 and we see that if c 2 is large, the well is inefficient. So, we want to have a small c 2 for the well. If the c 2 is very large, then the well may be inefficient and we may have to look for replacements. The other concept which is related to the well loss is known as the specific capacity and specific capacity is defined as the discharge per unit drawdown. So, naturally we want large discharge and small drawdown. So, specific capacity of well should be high, so that it is efficient. If we look at the equations, we have already seen that we can express the drawdown as q over 2 pi t log of r over r w, where r is the radius of influence, r w is the radius of the well, t is the transmissivity. So, we can see that a specific capacity is proportional to the transmissivity from this equation. If the flow is transient, then we have the equation using the Thais equation and the Cooper Jacob approximation and including the well loss. If you look at the previous equation, there was no well loss term included here. So, we have assumed ideal conditions here without any well loss, steady state conditions, but if the flow is transient and there is well loss, then we have to include this c 2 q term also and this is using the Jacob approximation for well function. So, on the transient conditions, the specific capacity which is q over s w will be given by this equation and we can see that a specific capacity decreases with increase in q and t, because the increase in q, this term will increase, will increase in t, this term will increase and therefore, specific capacity will decrease. So, any well, if we pump at a higher rate, specific capacity will be smaller, if we pump it for a larger time, specific capacity will decrease. Now, let us look at some of the conditions which occur in the field. For example, till now we have discussed most of the things assuming the aquifer to be homogeneous. That means, there is no variation of conductivity with distance, but most of the times when we see natural porous medium, they will be layering. For example, deposition of if this is the bedrock, then there may be a layer of material here. Depending on how the porous medium is formed, there would be layers of different materials which will have different conductivities. So, for example, this may be a thickness b 1 and conductivity k 1. Similarly, there will be another layer which may be of thickness b 2 and conductivity k 2 and so on. So, under these conditions, we want to look at how to obtain an effective conductivity for this area. For example, we can assume or we can replace this by an equivalent porous medium. Let us say that there is an impermeable layer here also. Then, what we would like to do is, we would like to replace this porous medium by an equivalent homogeneous porous medium of height b. So, to find out this k equivalent it depends on whether the flow is taking place along the layers or perpendicular to the layers. For example, there may be some recharge from the top, then the flow will be perpendicular to the layers and if there is natural groundwater flow horizontal direction, it will be along the layers. Under both these conditions, the equivalent conductivity are different. For example, in this case, the discharge q 1, q 2, q n, they would be added up to get the total discharge, but the head loss from one point to the other point would be same for all the layers. In the case of flow being perpendicular to the layers, the discharge is same through all the layers q, but the head loss in each layer will be different and has to be added to get the total head loss. So, doing these computations, we can obtain the equivalent conductivity for this case. For example, in this case, the equivalent conductivity can be given by the arithmetic mean and then the harmonic mean. So, these two can be used to obtain the equivalent conductivity and then we can treat the porous medium as homogeneous with that equivalent conductivity and the thickness b, which is b is nothing but sigma b i and i will go from 1 to n, where n is the number of layers. So, after looking at these flow situations, where the flow may be steady, unsteady, we may be having a one dimensional flow or radial flow towards the well, we may have layering and non-homogeneous conductivity. So, we have looked at all these flow situations. Now, we will take some examples to explain some of these concepts. So, we will take the example of a confined aquifer and unsteady flow through the confined aquifer. The data, which is assumed is that there is this charge of 2 meter cube per minute. So, we have a confined aquifer being pumped at this rate q. The transmissivity of the aquifer is given as 1 meter square per minute. Storativity as 0.001. Now, there is an observation well, which is 50 meters from the pumping well and the water level in this observation well is being monitored. So, r is 50 meters. Using this data, we want to find out how the water level in this piezometer. So, initially there is some water level. So, the piezometer will show the same water level. When we start pumping with time, this water level will be going down. So, we want to see how this water level goes down and that we can do using the Theis method. For example, suppose we want to find out what will be the draw down at let us say 1 minute after the pumping starts. So, if we take t equal to 1 minute, we know that the equation for the draw down is the draw down q over 4 pi t times the w u well function and u is r square s over 4 t. So, in this case, suppose we take r equal to 50 meter that is what we want. So, r square s will be 2500, s is 10 to the power minus 4, 4 t is 1 and r square then t is also 1 minute. Now, we could have used second also, but typically in the draw down conditions, minutes are preferred. So, we will use the minutes here and for discharge meter cube for transmissivity meter square, but the time units we will be using as minutes. So, if you do this, u which is a dimensionless quantity will come out to be 0.0625 and corresponding to this u, we can look at the well function tables or there are some formula which give us the well function for any given value of u and using that we can see that w u is equal to 2.26. So, putting the value of w u here and the value of q s 2 t as 1, we can get s equal to 0.36 meter which is what is shown here. So, what we can do is we can draw down. So, for 1 minute we have 0.36 meter of draw down. Similarly, you can see that at the end of the measurement which is 240 minutes or 4 hours there is a 1.22 meter draw down in the observation well which is 50 meters away from the pumping well. This data is shown in the plot here. So, we have the time here in minutes and s is in meters. So, this shows the time was a draw down curve at the observation well which is 50 meters away from the pumping well. And we can see that initially the draw down is increasing very fast, but then as time progresses the rate of increase becomes slow. It will not reach a steady state because the Thais equation assumes that the aquifer is infinite. So, slowly the radius of influence will increase and there is no limit to it the increase of the radius of influence. Therefore, this will not achieve a steady state it will continue to increase, but at a very slow rate. So, this data which we have computed based on the Thais curve most of the times what we will not have is t and s. We will not be knowing the values of t and s, but what we will have in the field is the time versus draw down data or the time versus draw down curve which is this curve. So, the second question which comes to the mind is if this curve is given to us given s versus t curve how to find t and s. So, this is an inverse problem or a parameter estimation problem in which from a given draw down data we want to estimate the transmissivity and the storage coefficient. One of the methods which we have seen is known as a Jacob's method or Cooper Jacob method in which we say that for very large value of time. So, large t the well function can be approximated by the first two terms and then what we do is we fit on a log plot we fit a straight line through the data corresponding to large time and extend that straight line up to the 0 point the draw down equal to 0 point and we call this t 0. In this case we see that t 0 comes out to be about 0.11. The other thing which we need in Jacob's method is what is a draw down per unit log cycle of time. So, we can look at 10 and 100 we can take any log cycle, but let us take this and denote this by delta s. Delta s it turns out to be is about 0.36 meters. So, that is the difference between this point and this point which is one cycle of log here. We could have taken 1 and 10 also and get the same value here or here. So, using the data on delta s and t 0 the Cooper Jacob method has the equations 4 pi delta s and s. So, as we have seen q is 2 delta s is 0.36 and this gives us a transmissivity of 1.02 meter square per minute which is very close to the transmissivity 1 meter square per minute which we had assumed to generate this data. So, this method works quite well for estimating the value of t. Similarly, once the t is known we can put that t here t 0 is obtained as 0.11 minute and r is 50. So, s will come out to be 1.01 again very close to the value 1 into 10 to the power minus 4 which we had taken to generate the data. So, the Jacob method works very well for cases for cases where we have a straight line portion available to us or where the measurements have been carried for large time. If we do not have this large time data available suppose we had only this data available to us then we would not be able to fit a line here or even if we fit the line it will not be the correct straight line. So, Jacob's method will not work if the data is or the experiment is not carried out for a long time and data is not available for very large time. So, this straight line portion has to be available in order for Jacob's method to be applicable. Therefore, what we do mostly is use the Thais curve fitting method or the type curve matching method in which we prepare a generic plot. So, this is a generic plot, generic curve or the type curve which plots 1 over u versus w u. Now, 1 over u as we have seen 1 over u is equivalent to t and w u as we have also seen is equivalent to s. So, on a log log scale if we plot 1 over u versus w u it should be similar to the behavior of the drawdown curve. So, this should be similar to s versus t. So, the idea of Thais curve matching as we have discussed is try to match this curve, the type curve with the actual data. The actual data which we have plotted on log log scale. So, this is the same data which we had earlier, but earlier we had plotted on simple scale now we plotted on log log scale. So, this is s in again in meters t is in minutes and now this curve should match with this curve. As you can see both curves it will not match as we put it as it is. So, we have to shift the axis in order to make a match and that is what is done here. This is the drawdown curve the symbols and the line shows the type curve. So, we shift the drawdown curve or the type curve the axis should be parallel. We shift it in such a way that all the drawdown curve data matches with the type curve and by this shifting when we get the perfect match then we note the ordinates which match for example, for some w u we find out corresponding s and for some value of 1 over u we find corresponding t. And then we use these values to estimate the transmissivity and the storage coefficient. So, the if we match it suppose we take 1 by u as 10. The corresponding t star which is the point which corresponds to 1 over u equal to 10 is about 0.6. Similarly, we can match w u equal to 1 and 1. So, w star equal to 1 and corresponding value of s comes out to be 0.16 from this figure. So, this is s star this is t star this is 1 over u star and this is w star. So, using these 4 values of the starred variables we can use the thies curve matching equations to obtain the transmissivity. So, the equations which are given t equal to q over 4 pi w star over s star and s equal to 4 pi t star u star over r square. So, w star here is 1 s star is 0.16 putting these values we get t equal to 0.995 again this value is very small very close to 1 and s comes out to be 9.6. So, this is also very close to 1004 minus 4 which we had obtained or which we had used to generate this data. So, type curve matching method involves some subjectivity in this case you can see that the fit is very good here that data points all lie exactly on the type curve because the data which we have generated is synthetic there are no errors. In general the data would not lie exactly on the line it may have some values like this. So, we have to adjust what is the best fit once we get the best fit w star s star u star and t star can be obtained and they will give us the value of the transmissivity and the storage coefficient using this method. Now, let us look at the first slide which we had showed us time versus draw down for values of q equal to 2 t equal to 1 s equal to 0.001 and r equal to 50. Now, we can see what will be the effect of changing t and s. So, we can generate a new data set which includes t value which is one-tenth and s value which is 10 times. So, the value which we use for t and s now are t equal to 0.1 and s equal to 0.001. So, using these values we can regenerate the data using the thys curve and you can see that this figure shows time versus draw down. Earlier for a time of 1 minute we had a draw down of 0.36, but here you can see that there is almost no draw down till 1 minute, but at the end we had a draw down of about 1.22 meter here we have a draw down about 4.93 meters. So, changing t and s will affect the rate of draw down or the shape of the draw down curve and if we plot the draw down curve it looks like this. So, we can see that earlier one had a shape like this, this one has a shape which is much more steep. So, again we can use the thys curve matching technique to match this observed draw down curve with the type curve and of course, in this case the shifting will be different than the previous case where the curve was like this. So, here you can see again that the data now plots in this portion again a very good match is being observed. Now, we can again obtain the same for example, this is 1 over u equal to 1 and it corresponds to t of t star of 7. Similarly, w also we can take as 1 and it will correspond to s star of. So, using this data we can again obtain t in this case t is obtained as 0.094 meter square per minute compared to the value which we have used as 0.1 and s is obtained as 1.05 minus 3 compared to the 1 into 10 to the power minus 3 which we had used to generate this data. So, different values of t and s can be obtained using the type curve matching only thing is that the axis will have to be shifted literally different for different kind of data and the match it depends on our judgment a little bit where to match this. Similarly, since it is graphical method the reading of t star and s star would also be a little approximate for example, the value here and the value here there may be some approximation involved in reading these values which may cause some deviation of the values. For example, this shows about 6 percent error this shows about 5 percent error, but for most groundwater practical cases 5 percent 6 percent error is tolerable. So, this method can be used these days there are lot of other methods which are proposed for example, we can use computational methods to try different values of s and t and generate the low down data try to match it with the observed low down data and then try to minimize the error by choosing optimum values of s and t. So, computational methods are becoming more popular these days, but graphical methods are still very good for a first approximate guess. Now, let us look at another example for example, this data we had generated for r equal to 50 meters or the first slide showed data which had t equal to 1 s equal to 0.001, but again at r equal to 50 meters. Now, what happens if we have two different wells. So, suppose we have the confined aquifer being pumped and then we take the observations in two different observation wells one may be let us say r equal to 50 meters the other may be let us say 100 meters. So, naturally the 50 meter well will show a larger draw down 100 meter well will show a smaller draw down. So, this curve shows t again in minutes and s in meters the draw down corresponds to 100 meter well and 50 meter well. We can see from this figure that these open circles which represents the 50 meter draw down they are higher than 100 meter. So, the draw down at the 50 meter well would be higher than that at 100 meter well and these two are shown here. Now, since these draw down curves are different we can estimate the t and s values either separately for both of them or there is another method which uses combined data and if you look at the definition of u then we can see that this r square over t term occurs in the definition of u. So, instead of plotting t versus s if we plot t over r square versus s then both of these curves may come at the same location.  We can see also that at the end of 4 hours which is 240 minutes the draw down in the well at 100 meter is about 1 meter and the draw down in the well at 50 meters is about 1.2 meters. So, the combined curve shows the same thing the data for t over r square for 100 meter well stops here which is 1 meter draw down the data for the 50 meter curve goes up to 1.2 meter draw down. So, t over r square what we are doing is kind of non dimensionalizing the time with respect to the distance. So, t over r square versus s curve t again s is meters t over r square here is minute per meter square. So, the curves the two curves which are quite different here. So, these two are quite different here, but may be make it non dimensional respect to r square then we get the same curve and now we can use this single curve for curve matching or the type curve fitting and we can see that the data fits again very well. So, here these again open circles these are the 50 meter well the filled circle there represent the 100 meter well this is the type curve and this match again shows a very good matching between the data and the type curve. The procedure is exactly the same. So, let us say that we take 1 over u star equal to 1 which is this line and it gives us a t by r square equal to 2.4 10 to minus 5 which is corresponding to this point the scales are shown on this line. So, I have taken it here similarly I will write this as also star t over r square star similarly for w star we can take n 1 which is this and it corresponds to s star of 0.16. So, this is 0.1 this is 1. So, this point is 0.16 and using these now we have t 0.995 and s. Again these two are very close to the values which we had used to generate the curve for t over r square versus s. This was used as 1 again this was used as 1 into 10 to power minus 4. So, this has 2 percent error this has 0.5 percent error which is quite good. The only thing which needs to be mentioned here is that s is given as 4 pi t star u star over r square. So, now instead of t star we will have t star over r square directly substituted from this value. So, using the thious curve we can estimate the value of s and t for any combined aquifer. Most of the times we will have data for one well or sometimes more than one well and we can combine them using the t over r square to get all the data on a single curve and then match with the type curve. Cooper Jacobs method can be used if the data is available for a longer time or as the dimensionless parameter u should be a small. So, if it is not available then we will have to look for other methods. For example, the graphical method of curve matching or numerical methods of parameter estimation. There are some other advanced methods also for example, slope matching or derivative matching methods, but we will not discuss them here. So, this method tells us how to estimate the quiver parameters if we have data available for a well. Sometimes data from wells may not be available or there may not be a pumping well. Sometimes we may have just a few observation wells in an aquifer. So, we can look at a technique to estimate the gradient and then knowing the conductivity how to estimate the ground water velocity or if we know the ground water velocity we can estimate the hydraulic conductivity. So, suppose we have the ground level impermeable bed and then there is this water table which is at certain gradient. So, that the flow occurs because of this gradient. If we have observation wells here we can note down what is the ground level here and what is the ground water table at this point. So, this will give us an idea about what is the ground water level at this point. Typically what we will have is elevation at the ground level this data is easily available and what we will have the other measurement will be depth to ground water. If we have another well here and we also have the same data available here ground level as well as depth water table this will give us some idea about the gradient here. If we know that the flow is in this direction, but a number of times it is not possible. For example, if we look at the top view there may be some area here where there are wells here here and here and we do not have any idea about what is the direction of flow of the ground water. For example, it may be flowing like this it may be flowing like this or it may be flowing like this. Some idea about this movement may be obtained by noting down the ground water elevation here. So, if this is higher elevation and these are lower then we know that the flow will be towards this side, but exact direction of flow will not be known. So, for this case if we have three different observation wells and we have the measurement of ground water elevation and depth of ground water at the three wells. We can estimate roughly what is the direction of flow and if we know the conductivity hydraulic conductivity k. We can also find out or estimate what is the velocity of ground water movement or if we somehow measure the ground water velocity then we can estimate the hydraulic conductivity. So, in this case what we do is let us say that we have one well here, another well here, another well here and let us say we have measured at the wells A, B and C the ground water elevation by measurement of the ground level and the depth of water. So, let us say that at A ground level is let us call it 105 meters and depth to ground water let us call it 4.6 meters. So, if we have these two data available to us we know that the ground water elevation ground water level at A would be nothing but the difference of these two and it will be 100.4 meter. So, at A we have ground water elevation which is of 100.4 meter and similarly, let us say at B we have all the data available at C also and let us say that at B we have an elevation of 101 meter this is all ground water elevation. So, these are all ground water levels and at C let us say that the elevation is 100 meters. So, if we look at these three elevations 101 here, 100 here, 101.4 here we know that ground water flow will be from the higher head to the lower head, but it may be in this direction it may be in this direction it may be in this direction. So, in order to find out or estimate roughly what is the direction we can do a linear interpolation for example, this is from 100 to 101. So, we can estimate where on this line would be 100.4. So, if we divide this into five parts then this would roughly be 100.4 and that means the line joining A with this point will roughly be a line where the ground water elevation is 100.4 and then we can draw lines parallel to this from all the points they will represent ground water elevation of 100, 100.2, 100.4, 100.6, 100.8. So, knowing these ground water contours we can say that the ground water flow direction would be perpendicular to these and we can make a rough estimate of the gradient by measuring this length and saying that the head loss delta H is 0.2 meter in a length of L. So, delta H over L will be 0.2 over L. Knowing the conductivity we can say the velocity will be k i and knowing the conductivity and knowing the i we can estimate what will be the velocity of ground water or if somehow we have obtained the velocity of the ground water if we know this we can estimate what is the hydraulic conductivity. So, this will give us an estimate of the conductivity if we do not have a pumping well and we have some three observation wells which measure the ground water elevation. So, in the ground water chapter we have looked at various flow situations we have looked at the Darcy's law which relates the conductivity gradient and the velocity. We have also seen what happens when flow occurs between two parallel bodies of water one dimensional flow or sometimes we have a pumping well which will cause radial flow. We have looked at confined aquifers and uncomfined aquifers in which the behavior of or the distribution of the head is very different from each other. In the confined aquifer it is the piezometric head with changes, but the area of flow remains constant. In the unconfined aquifer the area of flow also depends on the head in the aquifer and therefore, it becomes more complicated. We have looked at unsteady state flow towards a well in confined aquifers and we have looked at a steady state flow in both confined and unconfined aquifers. We have seen some methods which are used to predict the drawdown for known aquifer properties and pumping conditions and we have also looked at the inverse problem in which we estimate the aquifer parameters from the measure data of drawdown versus distance or time and for a given pumping rate. So, for any aquifer we can design an experiment with different pumping rates to find out the aquifer properties. Similarly, we have looked at the well loss, how to estimate the specific capacity of a well, how to estimate the C 1 and C 2 constants in the well loss term and how to obtain or how to estimate whether the well is efficient or not and when it should be replaced.