Hey, difficult day obviously for you know the players and the coaches and the NFL and our fans and anybody that's you know even knows the NFL. So obviously we want to you know on behalf of the Titans organization our players and everybody involved send our deepest sympathies and our concerns and our prayers to Damar who you know by all accounts is fighting his tail off in Cincinnati you know to his family who watched that unfold you know in front of their eyes you know to Damar's football family and Buffalo and and Pittsburgh you know those teammates and you know we have one of those guys who shot Weaver was a teammate of his so you know doing everything we can just to continue to support him and sending out you know obviously our thoughts to everybody involved and it just commends Zach and Sean for their leadership that they showed last night for the example that they showed really in all of the players on both sides Buffalo and Cincinnati the way that they supported each other was was amazing to see you know and I just you know we all watch these games differently you know fans watch them at home or a bar or you know coaches in this league watch them you know as they're working in the in the games on the background so you know we were all affected you know differently but you know we just send our condolences and and really just the respect that we have for everybody involved and wish nothing but the best for Damar Mike with that has there been any discussions about whether or not to play this weekend considering he's still in critical condition no no no discussions that would be a league thing you know we're doing our best to prepare for the amazing opportunity that we have and for our football team you mentioned the the human element as coaches I'm presuming maybe in the building last night did it was it a moment that you turn you watch how struck were you by that I mean you've been a player you've seen players taken off teammates taken off how difficult was it maybe to see that start happening and did you could you was it must see TV at that moment well I think the one thing that that resonates now is you know when you're a parent and your kids play sports with all respect to the other players you don't really watch them you don't watch the game you stare at your son or your daughter who's an offensive lineman or a third baseman and you don't know if it was a ball or a strike and you don't know if it was a run player pass play you just kind of kind of watch your son or daughter and that's kind of how you watch sports as a as a parent so I guess that's what I thought is you know that he has a grand grandparents or parents you know that that watch that and they didn't know how T Higgins got the ball they just saw make a tackle they watched them you know progress through the play so I guess that's where where I went and then you know just watched everything unfold with the coaching staffs and you know the players how they supported each other you know we shared you know some some great conversations you know had an opportunity to you know you know discusses how everybody's feeling I think guys are you know they understand you know the the the severity you know of this they understand the game and then what we love you know sometimes things that you love the most and that can give you the most can also take the most away but you know there's some really really cool comments that our players shared with each other and with me and everybody else so I think that they are doing their best to support former teammates who are in Buffalo but also understand that you know we have a we have a great opportunity to continue to do what we love to do and one of our leaders said you know and this is someone that knew tomorrow knows tomorrow is that they're grateful they reminded it they're grateful that they get to do this and I thought that that was really special to hear some of those guys talk well I don't think that those discussions ever really stop I mean I think we all you know have to at least appreciate you know what we do where we do it and who we get to do it you know with you know and just understand the you know the things that go along with with playing football and being a teammate and everything else and so you know that those conversations with injuries may come up or you know in this case something you know much much worse so I don't I don't want it to like necessarily have to go anywhere I wanted to be you know part of you know the conversation if that's where the players feel like you know they wanted to go or you know how we all deal with things and we're gonna feel each person's gonna feel you know maybe a little differently shifting gears for Josh to take over a huddle in such short order the leadership qualities that come and some of the things tend to rely on with the quarterback developing over time how difficult is it to ask a guy and to and what can you expect out of a guy in short order as compared to what you get out of a guy that puts a whole offseason into it well I mean you know I mean quarterbacks have been quarterbacks since they probably grabbed a footballer then they six years old and they started throwing a football and you know they kind of have characteristics and qualities and you know half the battle is acting like one you know is acting like a quarterback and I think Josh is gonna be very well prepared and understand that we'll have to go in on a you know great environment on Saturday night and we'll start that preparation today but he understands that and he's played quarterback and he's played in front of big big crowds and he's played in big games just as far as adjusting to that role as a leader here that you know in this locker room so quickly well I think probably you know from the get though I think he was probably just trying to focus on knowing what to do and the terminology and then you know I think we went to the Cowboys game and there's some guys he probably didn't even know know their first name I think that's that'll probably change by the time Saturday comes about getting some of your guys back how much use does it give you know when you got a game plan now that includes Simmons, Autry, Fulton, Booker and the rest that you get back. Henry, that's a big one. I think that that's just something that everybody felt after the game you know I think that that our players felt it you know I felt like they you know they played extremely hard they prepared extremely hard you know just you know came up a little short obviously the other night and guys were back I think they're energized in this you know it's such a difficult thing you know when you want to try to send a message of you know we talked yesterday about being excited and embracing the opportunity and then life happens you know last night and but we still I think we still need to get there and we still will be there and I think we'll you know go out and and start our preparation today on the field. Playing mistake free or close to it. You want guys to be cleaner but how much do you need them not to like over overthink that? Yeah, we don't want to sit there and paralyze ourselves with being perfect. You know I think we have to try to be precise and not worry about being perfect. Nobody's gonna be perfect out there on the football field. There's a lot of things that you know keep you a bit you know from ever being perfect. We don't we don't want that we want them to understand the concept of the play the details they're associated with it you know the technique and fundamentals to do their job and you know communicate with urgency and you know a lot of those things you can make up your makeup for mistakes with you know some other things with with effort and finish and communication you know and playing you know as a team and letting somebody else you know help you if you make a mistake the guy next to you hopefully can can fix it. Have a different plan for Ingram or do guys just have to execute better against them? Well, I mean we probably need to be tighter on them and be able to you know keep our leverage tackle you know but he you know I mean that's not like they're gonna not target him you know he's he's had 36 targets in the last four games had the one two days ago so you know he was you know been a really good productive player here down a stretch for him.  Well, I don't think that anything that we've done prior to this is going to really matter in all three phases the only thing that's going to matter is what we do on on Saturday night and if we score great we're going to need to go down and score again and we'll need more than seven to win and if we don't score we'll have to you know come off and and make some adjustments and keep swinging and so you know it'd be great to score you know the first possession of the game you know but it'd also be great to you know stay really consistent and take advantage of the opportunities and play complementary football and take care of the football. No observation for long this week Mike? Not as of today no. Autrey the first time you guys played the Jags coincidentally not so coincidentally you didn't have any sacks on on Trevor how much can he help the pass for us? Well yeah I mean the sacks are one thing you should you know we have to focus on how we can disrupt the quarterback yeah to you know our ability to disrupt them and affect them that wasn't good either you know not only were the sacks weren't there but you know so we'll have to try to you know find different ways and make sure that you know he doesn't have a hundred and twenty rating and you know because that would be that'd be tough to overcome. Is there anybody other than Long who could be in line for that last activation? I think we addressed this the other day I don't think that there is no I don't think at this time. How's the patched up offensive line done over the last couple of games have you seen improvements? I mean there were some good things there were some times where Thursday Josh had some time to to progress through and then other times where you know needs to be better and again that's gonna be another good front this week it's all about the Jacksonville Jaguars and how we you know can block you know Allen and Key Walker Harris inside and everything that they do and and Hamilton the pressures they bring to safety pressures or you know Blitz and a backer so that that's what it's gonna be about and hopefully we'll we'll be able to start that preparation here today. Does having a six-year guy like like Dobbs as the quarterback does that allow you to kind of open things up a little bit more call the game differently as opposed to a rookie like Malik? Matt I think you're going with a game plan and you see kind of how you know how it's working and what he feels comfortable with against some of the stuff that they're doing and I don't know if that's you know the game plan is gonna be the same for for both quarterbacks. Do you feel with the way that he's able to progress through like does that keep the offense on schedule a little bit more? Running good plays and executing good plays keeps us on schedule not having unforced errors penalties that that I think are avoidable you know some penalties are what they are you know but some of them are avoidable that that's what helps stay on schedule and you know starts with the substitution starts with the operation the cadence all those things that we're gonna have to be great with on the road. I think he's you know he's got a calming presence you know I mean I think he's you know he's got a nice confident calmness to him seemed like he came over on the sidelines communicated well with the players communicated well with with Todd and Pat and Malik you know about what he saw you know I saw him communicate with the receivers afterwards and an intelligent player it's been really you know it's been nice having him around and working with him and getting on him I've really always admired him from a far you know his career and you know what he's done. Intensify this feeling like a road playoff game? Yes yeah this would be you wrote I mean I think this is a playoff it's certainly a playoff game for us so that's how we'll treat it and you know make sure that we're doing all those things that you know they give you a chance to win and make sure that we're we're working all the cadences and working the silent and the crowd noise and substitution all those things that are gonna be critical for us on offense and special teams.


Hey, this is Brett, and this 2021 Chevy Silverado 2500 Crew Cab Short Box LTZ is stock number 13426Z. I am here at Summit Automotive in Fond du Lac, Wisconsin, your new and used heavy-duty truck headquarters this 2021 Chevy Silverado 2500 has the 6.6 liter Duramax diesel engine. This paired up with the Allison 10-speed automatic transmission puts out 445 horsepower. This truck has been fully safety and inspected by our service shop has a fresh oil and filter change all the fluids have been checked and topped off and it is 100% ready to go. I'm going to go all the way around in this video inside underneath started up and take a look under the hood in hopes of giving you the most accurate representation of the truck possible. Both sky blue metallic is a color and I shoot all my videos in 4K so if you have HD capabilities turn them on now because it is your best way to check out the quality condition options and of course cleanliness of the truck before seeing it in person. Down the driver's side box is in excellent shape didn't see any dents or dings the cab and doors are all in fantastic condition as well as is the front fender and as always if you like the video you can subscribe to my YouTube channel which is youtube.com slash summit auto click the bell notifications and you'll get updates on the videos I do each and every day here at Summit Automotive. Very very nice down that side this one comes with the 20 inch polished aluminum rims and they look kind of painted right now because they're a little cold but you can see they're in nice shape. Then it comes with Goodyear Wrangler trail runner AT tires these are LT 275 65 R20s and they have just about all the tread left on them frame and under body is in excellent shape and once again the front fender is really nice condition. Comes with the LED headlamps the LED running lights as well as the LED fog lamps front bumper parking sensors and no dents or dings on that front bumper looks really good. You get the chrome trimmed grille and it has the true cobble induction hood I'll show you how that works at the end of the video and I didn't see any dents or dings on that hood passenger side front fender excellent condition as well and the passenger side rim is in really nice shape too. North sky blue metallic sky a lot of metal flake to it little bit of purple and black looks really good and as you go down this side of this 2021 Chevy Silverado 2500 take note of how clean that body is how reflective and mirror like that paint is. I take these HD videos so if you are far away or even if you're close by and you just cannot make the trip down but you're still interested in purchasing the vehicle you can see the truck hear the truck and of confidence in the vehicle that you're looking at before you even get here so when you do get here there's absolutely no surprises and you can make a smart and informed buying decision from wherever you're at. If this video helps you make that decision let your salesmen know that you saw the video that it was helpful and that Brett sent you back rim no scuffs or scrapes on there and the back tires have just as much tread as the front tires this one does have rear airbag suspension and the frame and underbody is in very nice shape has all the remaining factory exhaust so it hasn't been altered in any way and once again lower rockers and cab corners all look really good comes with a really nice set of factory chrome step bars and it does have the side box steps coming around to the back of the vehicle you will notice that the rear bumper is in perfect condition it does have the backup parking sensors rear bumper steps full towing package which includes the receiver hitch and seven pin wiring these are for additional cameras to any trailer that you hook up and the tailgate is in really nice condition as well didn't see any dents or dings and there comes with an access soft roll-up tonneau cover and that tailgate is a power drop down tailgate you get a bnw companion fifth wheel hitch included with this truck spray and bedliner seven pin and four pin wiring back here you also get led bedlights and then it does have a plug-in right here and let's see what that is that is 120 volt 400 watt plug-in that spray and bedliner is in really nice shape goes into or onto the tailgate as well and this is a power up tailgate too but because of the tonneau cover it didn't want to close that happens led tail lamps as well coming around to the back rear tire or rim I should say is in excellent shape as well and down the rest of the side of the truck doors and cab all look really good does come with the telescopic tow mirrors built-in blind spot monitoring directional signals and led side lights they do telescope out and fold in this one also has the 360 cam these mirrors are power telescope out so you can see they go out like so I always like showing both sides so you know that both sides are working properly and then they do power fold in as well and out inside the LTZ package gives you the black leather interior you get the bucket seats in the front both of these seats are heated and cool no rips or tears on there smells very clean inside this truck I don't think it's ever been smoked in you also get factory all-weather floor mats this one does have heads up display auto head lamps fog lights cargo lamps push button four-wheel drive power windows locks and mirrors memory driver seat and these are the controls to control those power folding and telescoping mirrors back seats are just as clean as front seats these back seats are heated on the outboard side as well you do get the latch child safety system for any child car seats you may have power sliding rear window with the built-in rear defrost you also get little storage compartments behind the back seats on the driver and passengers side these seats fold up for extra storage there is a confined storage area a cord for an engine block heater covers for your fifth wheel and gooseneck prep package and a winter front also has a fifth wheel and goose excuse me fifth wheel and goose neck case right there we're probably just a goose neck case there your heated seat buttons as well as a USB USB-C and a 12 volt power point seats fold down like so child safety locks on the back doors and bottoms and inside of the doors all look fantastic on this truck we'll hop inside check out the miles the radio and everything that this truck has to offer on the interior if I can get the miles to come out there we go you can see that this one only has four thousand five hundred and forty four miles on it you get the nice digital instrument cluster there you get the heated leather wrap steering wheel cruise controls on the left Bluetooth and information center controls on the right it does have the Alice in 10 speed automatic transmission and it comes with the Chevy infotainment system that is a touchscreen it also has the factory navigation system on it right there you can see that is working nicely there's highway 41 you also get AM FM and Sirius XM radio capabilities and you do have all your different apps on here including Apple CarPlay and Android Auto you also have all your different cameras that you can do including the 360 cam the front cam you can do down the sides you can do a look at the back just a look at the front you can check out what's going on in the bed can zoom in on your receiver hitch and all that good stuff even add cameras to the trailer and then check those out so just a lot of stuff you can do with this radio and this camera system really a nice system on here down here you're more tactile climate and audio and tune controls volume and tune controls get your dual climate controls there heated and cooled seat buttons some comes with the factory exhaust break lane departure warning parking sensors power drop-down tailgate or power up tailgate hazard lights stability control that's the turn on the plug that's in the bed and put all the windows down at once factory brake controller USB USB-C 12-volt powerpoint and a hundred 10 hundred 20 volt 150 watt plug-in down here is a wireless cell phone charge pad two cup holders you also have your keyless entry with remote start and you can power drop down that tailgate as well passenger side format and seat are in excellent condition no rips or tears on there smells very clean inside this truck I don't think it's ever been smoked in and the headliner is in very nice condition as well you do get home link buttons for your garage door security systems and lighting systems on star and SOS buttons in the review mirror this one also has the digital review mirror display so it actually will portray a video of what's going on behind you it's kind of neat you can raise it lower it brighten it dim it as well I'm gonna show you the tire and loading information sticker as well as the trailering information sticker I like that GM puts these on their trucks so you can see how much you can tow and all that good stuff and there is your min sticker all right we'll start it up and take a look under the hood also check out all those LED lights in the front starts right up no check engine lights or anything like that you can see your heads up display right there I turn the lights on as well as the fog lights so you can check all those out I would personally like to thank you for checking out the video today and hopefully from this HD video you got LED side lights on the mirrors as well and hopefully from this HD video you've been able to verify the quality condition options and of course cleanliness of the truck all the way around inside and out there are those LED fog lamps running lights and headlights under the hood once again we have the 6.6 liter Duramax diesel engine this is the L5P with 445 horsepower engine base very clean runs very smooth once again this truck has been fully safe and inspected by our service shop has a fresh oil and filter change all the fluids have been checked and topped off this truck is 100% ready to go there's the emission sticker so the air comes in through the cull induction goes down to the side in this tube here and then goes right into the air cleaner for your cold air intake and I would highly recommend this truck for make quality and condition standpoint and to see more pictures of this truck or one rather 550 new and used cars trucks SCVs minivans Wranglers half tons three quarter tons one tons you name it we got to go to that website right there full pictures and descriptions of every single vehicle from two locations all at summit auto.com and if you'd like to check out more HD videos you can go to youtube.com slash summit auto remember to like subscribe and share on this video and all the videos that you see there click the bell notifications to get updates on the videos I do each and every day here at Summit Automotive fact in a second you will see a link to subscribe to my YouTube channel the upper left or link to more Chevy 2500 truck videos like this one the upper right link to this vehicle on our website and lower left and a link to one of our latest YouTube videos on the lower right click those check us out we're super excited to help you with this ultra clean 2021 Chevy Silverado 2500 crew cab short box LTZ in North sky blue metallic thanks again for checking out the video remember like subscribe and share on the YouTube channel I really appreciate it thanks again


Yn nhw'n ei ddweud yn cael eu cychwyn leol y ffordd nesaf, wrthy yn creu cyfreuion mewn gwybwysydd. Mae'r gwaith gan y bydd yn ein mwyafol, a'r gweld gwyeb y gallwn i chi fod i'i'n gwybwysedd. Mae'r chi'n maelod eu pwysig, mae'n gair i'ch gael eu mwyddor agor. Mae hynny'n cymryd ar gyfer mwyafol, ond rwy'n meddwl y gwasanaeth gwyddiadau I will have a word with them afterwards. There is only one item on today's agenda. It is stage 2 of the interests of members of the Scottish Parliament amendment bill. I would like to welcome to the meeting Stuart Stevenson, a convener of the Standards, Procedures and Public Appointments Committee and the member in charge of the bill. Basically, everyone should have the bill and marshaled list of amendments with you. There is also a groupings list. It is quite straightforward. Two amendments to be disposed of today and they have been grouped together as you will know. Firstly, the question basically is sections 1 to 8 of the bill. Are we all agreed that these can be agreed? Thank you very much. Section 9 of the bill is prohibition of paid advocacy. I would like to call amendment 1 in the name of Stuart Stevenson grouped with amendment 2. Mr Stevenson. Thank you very much indeed, convener. I will start by outlining the context for the provisions. The present position is that paid advocacy is where an individual uses their position as an MSP to advocate a particular matter in return for a payment, including a benefitting kind, or to urge any other MSP to do so. It is a criminal offence and a breach of the interest set for an MSP to undertake paid advocacy. It is worth noting that no MSP has ever been found to breach these rules. The Standards, Procedures and Public Appointments Committee is very clear, given the gravity with which paid advocacy should be treated that the criminal offence remains appropriate. The committee's consultation paper proposed that the definition of paid advocacy should be amended for greater consistency with the bribery act 2010. In particular, we noted that the bribery act incorporated the act of agreeing to receive inducements within the offence of being bribed. The paid advocacy offence currently requires actual receipt of an inducement by an MSP or by an MSP's partner, where this is in connection with the member's parliamentary role and results in some benefit to the MSP. It does not currently incorporate payments of benefits in kind that a member agrees to receive. The bill amends the definition of paid advocacy so that agreeing to receive inducements as well as actually receiving them would be an offence and thus a breach of the interest act. During stage 1 of the debate, Tavish Scott asked whether the offence of paid advocacy, as expanded by the provisions in the bill, would cover a scenario where a member requested payment to undertake paid advocacy. There is no doubt that receiving, agreeing to receive and requesting an inducement in exchange for carrying out paid advocacy actually or before or after the event is an offence under section 2 of the bribery act 2010. This is a complex but comprehensive provision covering corruption in a wide range of public and private sector settings. The paid advocacy offence in this bill is a much simpler provision, which is more specifically geared towards abuses of the procedures of this Parliament. Requesting an inducement is also covered by the paid advocacy offence as a member by section 9 of this bill, but only where some form of agreement flows from it and action is taken by the member on the basis of that. In other words, it does not matter who made the initial approach in this context. A purely unilateral request for an inducement would not be covered, however. This is partly because of the absence of any specific reference to requesting, as opposed to receiving or agreeing to receive. It is also because undertaking the advocacy part of the paid advocacy is an essential part of the element. It is not currently an offence to receive an inducement so long as the member does not in fact do anything in response to receipt of the inducement or are some another member to do something. Similarly, even if the bill is enacted, it will still not be an offence to agree to receive an inducement so long as nothing is thereafter actually done on the basis of that. Where a unilateral request for an inducement is concerned, it is unlikely that the requirements of this section will be satisfied because if the member is rebuffed or simply ignored, he or she is not likely to proceed to do anything on the basis of an inducement, he or she could have no expectation of actually receiving. There are possible alternatives to this. One is to do nothing on the basis that all of this is criminal under the Brivary Act and the pay advocacy offence is specifically about abuse of all the new procedures and facilities. However, I have decided to propose amendments to ensure that the offence covers a member requesting an inducement to carry out advocacy, but only where the advocacy actually takes place. I believe that these amendments put these matters beyond doubt. Specifically, the First Amendment amends section 9 of the bill, which in turn amends section 14 of the 2000 act. This amendment restructures subsection 2B of section 14, and essentially there are two things. Firstly, it adds to the reference to requesting a payment or benefiting kind for carrying out paid advocacy. Secondly, it introduces a conditional element to the provision, namely the payment or benefiting kind results, or if, when made or given, would result in some benefit to the member. This puts beyond doubt that the payment or benefit does not actually have to have been received for the offence to be committed. This ensures that where a member agrees to receive or requests a payment or benefit, the offence is committed even when the inducement has not been received. That ties up the provision in the bill so that it sits better with the addition of agrees to receive and requests. The second amendment simply adds a reference to requesting to subsection 3 of section 14 of the 2006 act, which sets out the exceptions to these provisions. Assistance in the provision of member's bill or assistance with amendments to any bill or a debate on subordinate legislation or a legislative consent motion will not be considered as paid advocacy. I have a pleasure in moving amendment 1. Thank you very much, Mr Stevenson. I am now going to allow other members to make a comment. Mary Scanlon. Thank you, I appreciate that. I would like to thank Mr Stevenson for his comprehensive explanation of his amendments, as I would expect nothing less. I think that we are all absolutely clear about advocacy in return for payment. I think that that is absolutely crystal clear. I think that what I would like a bit more information on, I think that it is perhaps a more grey area, is including a benefit in kind. If I can just give you an example. Somewhere in my diary we have got a dinner with the BMA and they are likely to be asking or suggesting things for the NHS. If I accept a dinner from the BMA in next week, I mentioned something in Parliament that resulted from that conversation. Then I have had a benefit in kind and I would be asking a question on the basis of that. So I think just to be helpful to all MSPs, can you tell us exactly, can you perhaps be helpful, convener, if the member could give us some examples of benefits in kind? What is a communication flow? What is a briefing? If you sit down and have a coffee or a dinner over that briefing, you have received a benefit in kind and you may go forward and ask something, advocate on that organisation's behalf. I just wonder, convener, if I could seek some clarity around the issue of benefit in kind. Can I just hold on a second, please, Mr Stevenson? Thank you very much, Mary. Can I just ask if there is anyone else has any questions for Mr Stevenson? Okay, that seems to be the only question. Mr Stevenson, could you enlighten us, please? Thank you and that is a good question to ask. I will just make the very general point that a member should always have any doubt about whether provisions of the member's interest or the standards generally that apply to members should always seek the advice of the clerks who will be very happy to advise in advance, but turning to the very specific circumstances that Mrs Scanlon has described, I think the important point to bear in mind is that the benefit is conditional upon an act. There has to be an offer or a solicitation of a benefit, is the first test that has to be applied before the paid advocacy rules kick in. Secondly, the paid advocacy needs to be consequential upon that agreement and it needs to be undertaken. However, the benefit does not need to be delivered. Now, the benefit in the case that is given being at a dinner is incidental to the action that was taken. That benefit, that dinner was taking place in any event and what happened at that dinner as a result of a conversation was not linking the provision of the dinner to that benefit that the member received. I think that is the test, but at the end of the day I do come back to that it is always a good idea for members to drop by room TG1 for the clerks are happy to answer questions. I think that answers the question and I am getting nodding heads on both sides of me so I have captured the essence of it. Is that link, that conditionality between the benefit that is delivered and the action that the member has taken, which I think in the circumstances which the member describes probably quite common circumstances, that link is absent and therefore it would not be caught by the provisions that we are seeking to introduce here. That is very helpful. Thank you very much. To Mary Scanlon, thank you to Stuart Stevenson. There being no other members wishing to ask a question of Mr Stevenson. Stuart Stevenson, would you like to press or withdraw amendment 1? I would like to press amendment 1. Amendment 1, thank you very much. The question is that amendment 1 be agreed to. Are we all agreed? Yes, we are. Thank you very much. I call amendment 2 in the name of Stuart Stevenson. I am ready to debate with amendment 1. Stuart Stevenson to move formally. Thank you very much. Okay, that is section 9. The question is that amendment 2 be agreed to. Are we all agreed? Agreed. Thank you. The right question is that section 9 be agreed to. Are we all agreed? Agreed. Okay, section 10 to 19. The question is that section 10 to 19 be agreed to. Are we all agreed? Agreed. Thank you. Finally, I believe that the question is that the long title be agreed to. Are we all agreed? Agreed. Thank you. At end stage 2 consideration of the bill. Thank you to everyone who has put in the onerous task of being here today. Thank you very much.


Snow plows keep roads open during winter storms, but their clumsiness can be dangerous. Plows throw snow every which way, blocking the vision of the driver as well as nearby motorists. Accidents involving snow plows are common, and the force of the snow against the plow blade can make controlling the truck difficult. Public agencies spend millions of dollars on snow removal that's not safe or efficient. But it doesn't have to be this way. New plow designs developed under the Strategic Highway Research Program can prevent snow from being thrown out of the windshield of the truck or nearby vehicles. These new designs make it easier for the plow driver to control the truck, and they're more efficient than current plows, allowing snow to be cleared faster and at a lower cost. Because of Sharp's research, there may soon be plows like this one, plows of the future. Three-quarters of the snow plows, operated by state DOTs, municipalities and airports, incorporate reversible nose plows. Many of them are inefficient, provide poor cast performance, and can create visibility problems. Plowed snow blows into the windshield of the plow truck and often causes snow to blow into the windshields of passing and trailing motorists. Surveys of state highway agencies have found snow and ice control operations account for the largest percentage of accidents involving maintenance operations. In addition, it's difficult to control cast distance, and strong lateral forces on plows adversely affect control of the vehicle and therefore the safety of its driver. So Sharp examined various parts of the plow for possible improvements. They looked at the mold board, they investigated the snow and ice blade, and they tried a new snow scoop. Sharp studied the mold board using computer simulation, water flow experiments, and field testing. Proper trajectory of snow on the mold board is important to minimize re-handling and blow by. Snow that rolls around in front is re-handled and reduces the plow's efficiency. Snow that the mold board can't contain blows in the face of the operator or other drivers. Using this information they began to design an improved plow. The improved design increases the board's height. The lower flat portion tilts back 10 degrees from vertical, and the upper mold board has a semi-circular section. All of the experimental plows tested had a polymer surface which improved the flow of snow on the mold board. Their cast performance was better than steel surfaces. Traditional plows have their blades perpendicular to the road. Paint marks on the snow show the effect of this plow design. Observe the results as the blade approaches the marks. Perpendicular blades create a compression zone in the snow. As the snow strikes the blade, it compacts and then churns dramatically. The marks are lost in the turbulence. The higher the velocity, the higher the energy required because of this compaction and churning. Experiences taught us that blades oriented at 90 degrees to the road remove compacted snow and ice the best. On the other hand, laboratory and field tests reveal that a snow plow blade inclined 50 degrees to the road surface is much more efficient. To deal with this conflict, the research team developed a retrofitable snow scoop. It fits in front of the plow blade and improves snow removal efficiency. And it allows the current near vertical blade to continue to remove compacted snow and ice. Using a snow scoop, they found that the plow needed less power and it experienced lower side forces, meaning increased stability and control. As shown here, when moving from an area of no snow to plowing snow, there is no loss of steering control of the truck. And the paint marks flow smoothly up the mold board. Field tests confirmed laboratory predictions. There was a 20% savings in energy required to plow snow. When they used the scoop, there was a significant decrease in lateral plow forces. The scoop clearly provided the driver with improved steering control. The scoop reduced blow by, thus greatly enhancing visibility and reducing the chance of a clogged radiator. They also found that with the snow scoop on, the plow cast snow further than without it. In short, with the scoop and the redesigned mold board, you'll need less force to move snow. That means reduced fuel costs and cleaner air, plus you'll have improved plow control. Another big advantage of the scoop is that it's inexpensive and you can retrofit it easily to most existing plows. Kit materials cost approximately $600 each. Initial installation takes about eight labor hours, but replacement of the scoop panels takes less than one hour. Together, these breakthroughs add up to a vastly improved snow plow. Plants for the snow scoop are available now from Sharp. Keep your eyes open for commercially available versions of both the scoop and the plow. In this presentation, we've covered only some of the snow plow innovations recommended by Sharp. Here's a brief summary of all of them. Use scoops angled approximately 50 degrees to the road surface. Use a tall mold board with a half-cylinder shape at the top. Surface with a polymer-based material such as ultra-high molecular weight polyethylene for low surface friction. Use a tripping edge rather than a full tripping mold board. It allows better control of the vehicle. Researchers tested hinges as close as possible to a vertical location above the cutting edge. They also used air springs to provide the tripping force. Truck air can provide adjustable force, and in the event of failure, there is no debris on the road. And keep your plow frame short so that the plow will be closer to the truck. It allows better vehicle control, better operator visibility, and reduced stress on the front axle. Soon, plows like this one with a blade that throws snow up in your face will be antiques. They'll be replaced by plows like this one that directs snow away from the windshield and other drivers. Plows that are safer and more efficient. Plows of the future. For more information on these advances in snow plowing technology, contact FHWA at the number on your screen.


Hello and welcome to lecture number 19 of this lecture series on jet aircraft preparation. We have been discussing about the basic cycles of jet engines and during the last few lectures we have also initiated discussion on various components of jet engine and we have already discussed about axial flow compressors. In the last lecture we had some discussion on centrifugal compressors and in today's lecture we are going to continue our discussion on centrifugal compressors. We are going to basically talk about performance characteristics of centrifugal flow compressors and how we can analyze centrifugal compressors. And we will also be discussing a little bit on the various instabilities that affect the performance of centrifugal compressors. Basically the mechanisms that we have already discussed for axial compressors very much are valid for this as well, but we will take a look at these mechanisms once again. Subsequent to that we will also have some time for solving a couple of problems related to centrifugal compressors which means that today we are going to have part of the lecture devoted towards discussion on performance characteristics and subsequently we will also have some discussion on solving problems on centrifugal compressors. So, let us begin our discussion on performance characteristics and if you recall during our discussion on axial compressors what we had realized is that the performance of axial compressors very much is a function of variety of other parameters that is the exit of the delivery stagnation pressure or the pressure ratio and the efficiency or functions of a host of other parameters like the rotational speed, the geometric parameters and so on and of course the mass flow rate. So, in centrifugal compressors to the performance is very much dependent on these parameters which means that the performance characteristics would be at least the parameters that are used in evaluating the performance characteristics are identical to what is used in axial compressors. We would basically be looking at these stagnation pressure ratio across the compressor or developed by the compressor as a function of mass flow rate for different rotational speeds. At the same time we will also be looking at efficiency versus mass flow rate at different speeds and that would give us an idea of the performance map of centrifugal flow compressors. This is pretty much what we had done for axial compressors as well. So, let us take a look at what we had discussed during axial compressors we will discuss that in brief with regard to centrifugal flow compressors. Now in the performance characteristics I think the derivation of performance characteristics is exactly identical to what we had discussed for axial compressors and we would basically be looking at the dependence of pressure ratio and efficiency on mass flow rates at different speeds. And what we will very soon realize is that centrifugal compressors also suffer from instability problems like surge and rotating star. So, that we will also take up for discussion after we talk about the performance characteristics. So for a centrifugal compressor the outlet pressure that is P02 and the isentropic efficiency depend upon several physical variables which is what we had discussed for axial compressors as well. Let me just quickly discuss that once again. So, P02 and efficiency are functions of mass flow rate and the inlet stagnation pressure that is P01, inlet stagnation temperature then the rotational speed or the angular velocity omega, the ratio of specific heats gamma, the gas constant R, then the viscosity nu, the design of the compressor itself and the diameter D. So, these parameters if we were to carry out a dimensional analysis then we can reduce these set of variables to a set of non dimensional parameters. And these are basically the pressure ratio P02 by P01 and efficiency as functions of mass flow rate which has been non dimensionalized m dot in the square root of gamma or T01 divided by P01 D square and omega D by square root of gamma or T01 omega D square by nu gamma and design. This of course reduces to what is written here that is pressure ratio and efficiency can basically be expressed as functions of m dot into root T01 by P01 and n by root T01. This is because for a given compressor the diameter does not really change and so omega D is n and gamma and R are fixed. So, based on that we can reduce this set of non dimensional parameters for a given design to P02 by P01 and efficiency as functions of m dot root T01 by P01 and n by root T01. This we will further reduce and this is basically processed in terms of standard day pressure and temperature that is the temperature is taken with reference to temperature on a standard day and pressure is taken as the ratio of pressure between that as compared to that of a standard day stagnation pressure. So, P02 by P01 and efficiency would become functions of m dot root theta by delta where theta is T01 by T01 standard day and n by root theta where theta is basically the temperature ratios and delta is the pressure ratio P01 by P01 standard day. And here the standard day temperature and pressure are T01 standard day is usually taken as 288.15 and P01 standard day as 101.325 kilopascals. So, I think if you recall our discussion for axial compressors this is exactly what we have done for axial compressors as well that we can express the pressure ratio and efficiency which are the performance parameters which we are interested in in terms of certain parameters which we can associate with the compressor that is mass flow rate and temperature and the speed. So, pressure ratio and efficiency express just functions of m dot root T01 or m dot root theta by delta and n divided by root theta. So, performance map or performance characteristic would involve looking at variations of pressure ratio and efficiency as functions of mass flow rate and the non-dimensional speed. And then what we will see very soon is that the performance characteristics are limited by two extreme operations at a given speed. One limiting factor occurs on towards the left hand side of the performance curve that is known as the surge limit and on the right hand side the performance is limited by maximum mass flow rate and that is known as the choking. So, these two parameters or these two phenomenon restrict the operation of centrifugal compressors to a certain band within which the operation is stable and outside of which obviously the operation is not desirable. So, let us take first a look at the performance characteristic at a given speed and then subsequently we will take up the discussion for a range of speeds. So, pressure ratio versus mass flow rate for a given speed. Let us take a look at what happens as we change mass flow rate what happens to the pressure ratio and basically theoretically what is it that should happen as we change this. So, if you look at mass flow variation of pressure ratio as a function of mass flow rate at a given speed. So, this line this curve that is shown here indicates what is known as the constant speed line. So, for a given speed of rotation or rotation of the rotor the characteristic would look like this pressure ratio and mass flow rate. So, I have indicated a few points salient points on this curve and we will take up these the significance of these points in detail. So, what happens let us take a look at what happens at the extreme cases at one case and you can see it is marked as C where we have a certain mass flow, but the pressure ratio is 0. We will take up that why that is so little later on the other hand we have a certain pressure ratio mass flow rate is 0 and what I have indicated as two distinct points are these points B and E. The point B is basically referred to as the surging limit point E is known as the choking limit. So, let us take a look at what happens between points A and B. So, if let us say the compressor is operating at point B and then we further reduce mass flow rate. So, as the reduce mass flow rate what should happen is that according to this curve the pressure ratio drops. So, as the pressure ratio drops it means that the pressure downstream if it does not reduce corresponding to what is shown in this curve then there is a likelihood that because the pressure downstream has not reduced as per what is shown here there could be a reverse flow from downstream towards the upstream. And as this flow occurs the pressure downstream would have dropped and immediately there is a movement of mass flow from upstream towards the downstream and this continues back and forth. And this basically occurs at a fairly high frequency and it affects the entire annulus of the compressor it is not a localized phenomenon it affects the entire annulus. And we had discussed that this occurs even for an axial compressor and that was referred to as surge for an axial compressor that the same thing happens here as well that under certain operating condition that is on pressure ratio versus mass flow rate curve on the positive slope of this curve as mass flow reduces there is also a drop in pressure ratio leading to this problem of surge that is surge is associated with violent fluctuation or oscillation of mass flow rate back and forth. And it is axis symmetric that is it is all over the annulus of the compressor which means that between these two points A and B operation of the compressor is unstable. So, you would not want to operate your compressor in a range where there is a positive slope for the pressure ratio versus mass flow characteristic. On the other side of the curve that is after the point B towards the right hand side what happens is that as we increase mass flow it is as it is accompanied by a reduced pressure ratio there is a reduction in pressure ratio which is fine because the pressure downstream is lower than what is upstream. And so there is not issue of a back flow which is likely to happen as in this case. So, the operation of the compressor from point B onwards does not really have restriction in terms of what happens between points A and B, but there is also a limit for operation on this curve from B onwards that is from point B onwards I have indicated a limit here which is indicated by letter E and this is known as the choking limit. So, what basically happens after this point is that as we keep reduce increasing mass flow rate there is a drop in pressure ratio and then beyond a certain level what happens is that the maximum amount of mass flow which the compressor can discharge has already taken place. And which means that no matter how much you try to increase the mass flow the mass flow has reached its maximum level. And beyond that point you would not really get an increase in mass flow, but obviously if we try to do that there could be a reduction in pressure ratio leading to loss of performance. So, there is a certain limit on the right hand side of the stable curve where the operation is supposed to be stable, but what limits is the maximum mass flow which the compressor can handle and that is known as choking. And choking on one hand one side of the curve limits the performance surging limits the performance on the other side. So, these are two limiting parameters that affect the performance of centrifugal flow compressors the same way this was affecting an axial flow compressor as well. But what we will see later on little later is the performance characteristics of a typical centrifugal flow compressor for a variety of speeds. So, we will get to see more details of the performance characteristics a little later. So, as I mentioned there are basically two limits which affect the performance of the compressor operation between points A and B limited due to surge where in there is a sudden drop in delivery pressure and also accompanied by violent aerodynamic pulsations. And which means that operation on the positive slope of the curve is unstable. And it is observed that most of the time surging usually begins to occur in the diffuser passages primarily because of the effect of the effect of boundary layer separation on the diffuser passages. I think when we discussed about diffusers in the last lecture I specifically mentioned that the performance of diffusers is very sensitive to the occurrence of boundary layer separation. And therefore, surges often initiated in the diffuser passages. Now, the other instability that might affect the performance is rotating stall we have already discussed about rotating stall for an axial compressor rotating stall may also affect the performance of a centrifugal compressor. What basically happens is that if one or more adjacent blades are undergoing stall the stall cell will rotate within the annulus. And if allowed to grow these stall cells might propagate and affect the entire annulus eventually leading to surge rotating stall on its own can itself lead to aerodynamically induced vibrations and eventually fatigue failure of the compressor components. So, rotating stall basically involves I think we have discussed this in the last class I will just go through it very quickly once again. In rotating stall what happens is that if there is a flow non-uniformity which is entering into the compressor in this case the impeller and that non-uniformity initiates separation boundary layer separation on one of the vanes of the impeller that would lead to a deflection of the flow approaching the adjacent set of vanes which means that if this is the vane that is undergoing stall because of the fact that the vanes themselves are rotating. And because of the fact that this blade is undergoing stall the flow approaching the adjacent blade also experiences in higher incidence. So, because of this what happens is that the stall cell would now shift to the adjacent blade or set of vanes or vanes and because the vanes are rotating the stall cell continues to rotate along the annulus of the compressor. So, this stall cell continues to rotate and in some cases the stall cell might propagate and expand and affect more number of vanes adjacent vanes and eventually the entire annulus can be affected by stall and the compressor might be forced into surge. So, the difference between what we see here and for a centrifugal compressor is that what I have shown here is basically a set of aerofoil blades which is not really the case in a centrifugal compressor we normally do not have aerofoil blades for the impeller impeller blades are basically vanes and not necessarily aerofoil sections, but the phenomenon is the same that affects a centrifugal compressor as well. So, rotating stall is the other instability that could affect the performance of a centrifugal compressor besides the fact that the surge and choking on the other side that is the performance characteristics gets limited on account of occurrence of these instabilities. So, choking I think we have already discussed that on the right hand side of the performance characteristics the mass flow reaches the maximum level beyond which we cannot really increase mass flow and that puts a limit on the performance of the compressor on one side of the on one side of the performance characteristic. So, let us now look at pressure ratio versus mass flow characteristics of a typical centrifugal compressor. So, what we see here is that on the y axis we have the pressure ratio the stagnation pressure ratio and on the x axis we have the mass flow rate the non dimensional mass flow rate m dot into root theta by delta and the characteristics have been plotted in terms of varying non dimensional speed. So, all these lines that we see here for 0.6, 0.7 and so on corresponds to different values of n by root theta and there are two lines which have been shown here one is the surge line and the other is of course, the point of maximum efficiency. Now, surge line is the locus of all the points on these performance characteristics which correspond to the surge point which we had discussed for a single characteristic. So, if you join all those lines we get what is known as the surge line and what we also see is that on the other side or the right hand side especially as we go towards higher speeds we have a very sharp sharply drooping characteristic which is because of choking that is as we approach higher and higher speeds the performance is affected by choking which means that we have a very narrow band of operation between surge and choke for higher speeds which is not the case at lower speeds. The lower speeds we can see that the performance characteristics are flatter and there is a larger band of operation of the compressor for lower speeds. And the other thing to notice here is that typically we may have pressure ratios which are much higher than what we get for an axial compressor per stage. And so, we can see that the pressure ratios can be on the higher side something we have discussed in the last class that the per stage pressure ratio for centrifugal compressors can be higher than an axial compressor for the same mass flow rate. So, this characteristics although looks very similar to what an axial compressor characteristics would look like. Of course, both these compressors are affected by surge and rotating stall as well as choke. And so, a designer would like to keep the operating line operating line is the line which corresponds to the point where the compressor has been designed to operate as close as possible to maximum efficiency and at the same time keep a safe distance between the operating line and the surge line. Because if the operating line or operating point is very close to the surge line then the possibility that under certain off design conditions the compressor might go into surge is very high. So, one would like to keep a certain margin between the surge line and the operating line and that is usually referred to as the surge margin which is basically a margin that the designer would like to keep to ensure that the compressor has a safe band of operation and that the risk of the compressor entering into surge is minimal. So, the other characteristic which we are also interested in is the efficiency, efficiency versus mass flow rate for different speeds. And we can again see that these efficiency points those which have been indicated here are those lines which have been joined and as the locus of points of maximum efficiency. So, we see that even in the case of efficiency as we approach higher speeds the efficiency characteristics also attain a drastic droop which means that the band of high efficiency drastically drops as the compressor is operating at higher speeds and as it approaches choke. Whereas, for lower speeds we have a relatively higher larger band of high efficiency operation. So, what we have discussed so far are the performance characteristics of centrifugal compressors as well as the performance penalties which a compressor is likely to pay especially as we change the operating range for a given speed. So, on one side it gets affected by surge or even before that the compressor might enter into rotating stall and also choking which affects the performance on the other end. So, a compressor designer obviously has to keep these things in mind especially because the compressor for an aircraft engine has to operate for a variety of speeds and range of operation starting from takeoff to cruise and then landing. So, the range of operation for aircraft engines is substantially more than for example, a land based power generating unit where of course, they are designed for a certain set of speeds. So, there the performance characteristics in the case of aircraft engines becomes even more significant because the compressor is usually is likely to go through all these different stages of operations of the compressor for these speeds. So, the similarities between axial compressor performance characteristics and centrifugal compressor characteristics are quite visible that we know that performance characteristics can be evaluated very much the same way as for an axial compressor and centrifugal compressor, but there are certain inherent differences as well between these two compressors in terms of their operation and also the the mechanism of pressure rise in both these compressors. So, I so with this I will wind up the discussion on centrifugal compressors. We have discussed about the components of centrifugal compressor, the mechanism of pressure rise, performance characteristics and also the instability aspects of centrifugal flow compressors. So, the next few minutes what we will do is to quickly discuss about a few tutorial problems where I have two problems which I will I will solve for you and then a few exercise problems which you can take up and solve based on our discussion in today's lecture as well as what we had discussed in the last lecture. So, let us take a look at the first problem that I have for you which we shall solve that is basically a centrifugal compressor with a given pressure ratio. Here the pressure ratio is given as 4 is to 1 here the pressure ratio is given as 4 is to 1 with an isentropic efficiency of 80 percent when running at 15,000 rpm and inducing air at 293 Kelvin. Curved vanes at the inlet give air a pre world of 25 degrees to the axial direction at all radii. The tip diameter of the eye of the impeller is 250 millimeters, the absolute velocity at the inlet is 150 meters per second and the impeller diameter is 600 millimeters. Calculate this slip factor. So, here we have a centrifugal compressor with a certain pressure ratio, its efficiency is given the rpm is given and we have some in information about the inflow direction of the incoming air. Some of the geometric parameters are given that is the impeller diameter and the axial velocity these are specified we are required to calculate what is the slip factor. Now, slip factor if you recall is the ratio of the tangential component of the absolute velocity at the outlet of the impeller that is C w 2 divided by the rotor speed or the impeller speed at the outlet that is u 2. So, C w 2 by u 2 refers to the slip factor. So, we are required to calculate this based on the data provided to us. So, as always I have mentioned even for an axial compressor the very first step towards solving these problems would be to draw the velocity triangles and then try to see what are the aspects of the velocity triangle which have been specified in the problem and that is that should be the starting point first solving such problems pertaining to axial flow compressors as well as to centrifugal compressors. So, let us first take a look at what the velocity triangle should look like at the inlet give based on what information we have been specified. So, at the inlet it is given that the absolute velocity the flow is given a pre world of 25 degrees with reference to the axial direction. So, this is the axial direction the flow enters the blade in this direction and it is mentioned that there is a pre world given and therefore, this angle which the absolute velocity makes with the axial direction is 25 degrees. And therefore, we have the velocity triangle as given here we have C 1 at 25 degrees u 1 is the blade speed at the I of the impeller and therefore, u plus v is C and that completes the velocity triangle at the inlet. And this part of this component of the absolute velocity is the world component or the tangential component C w 1 which is this component of C in the tangential direction in the direction of u 1. So, this is the velocity triangle at the inlet and so based on this we can based on the velocity and the angle specified we could probably solve the velocity triangle here. And then we can also move towards solving the velocity triangle at the outlet. Now, it is mentioned that the stagnation pressure ratio is 4 and the inlet stagnation temperature is also specified which means that the exit stagnation temperature can be calculated based on isentropic relations. Therefore, this temperature is basically the isentropic temperature. So, that is 293 into 4 which is the pressure ratio raise to gamma minus 1 1.4 minus 1 by 1.4 this is 435.56 Kelvin. Therefore, the isentropic temperature rises 435.56 minus 293 that is 142.56 Kelvin. So, this is the isentropic temperature rise we need to calculate the actual temperature rise which will be this temperature divided by the isentropic efficiency. Therefore, actual temperature rise is delta T naught s which is the isentropic temperature rise divided by efficiency that is eta c. So, that comes out to be 178.2 Kelvin. So, we can calculate the work done per unit mass which is C p times delta T actual and C p is 1.005 kilojoules per kilogram Kelvin multiplied by delta T naught that is 178.2. Therefore, work done per unit mass by the compressor is 179 kilojoules per kilogram. So, what we have just now calculated is based on the pressure ratio and the efficiency specified. We can calculate first the actual temperature rise which is well the isentropic temperature rise because we know the stagnation pressure ratio and from isentropic relations we can calculate the exit stagnation temperature T02 is T01 into pi c raise to gamma minus 1 by gamma. Subsequently we can then calculate the actual temperature rise which will be the isentropic temperature rise delta T naught s that is T02 minus T01 divided by efficiency. So, that we get the actual temperature rise and then work done per unit mass will be specific at constant pressure multiplied by the delta T naught actual and so we get the work done by the compressor per unit mass. Now, the purpose of calculating this is that work done per unit mass is also equal to U2 times Cw2 minus U1 times Cw1 and so we know U2 and U1 Cw1 we can calculate from the velocity triangle at the inlet therefore, we can calculate Cw2 and therefore, slip factor would be Cw2 divided by U2. So, we would be equating the work done which we have just now calculated that is Cp times delta T naught equated to U2 Cw2 minus U1 Cw1. So, let us calculate that. So, the peripheral velocity at the tip of the I that is U1 is pi dn by 60 where d is the diameter at the outlet or at the tip of the I of the impeller which is given as 250 millimeters. So, pi into 0.25 and n is 15,000 15,000 divided by 60. So, U1 is 196.25 meters per second Cw1 we can calculate because C1 is given as 150 and the angle is given as 25. So, C1 sin 25 is equal to Cw1. So, Cw1 we can calculate as 63.4 meters per second. Similarly, we calculate the blade speed at the tip of the impeller U2 it would be pi into capital Dn divided by 60 where capital D is the diameter of the tip of the impeller. So, pi into 0.6 into 15,000 divided by 60. So, that is 471.2 meters per second. So, this is the blade speed at the tip of the impeller. So, as I mentioned work done is also equal to U2 Cw2 minus U1 Cw1 and we have already calculated work done per unit mass from Cp times delta T0 which was 179 kilo joules per kilogram. So, work done 179 into 10 raise to 3 is equal to U2 which is 471.24 into Cw2 minus U1 that is 196.35 into Cw1 that is 63.4. So, from this we can calculate Cw2 which is the tangential component of the absolute velocity at the outlet of the impeller. Therefore, slip factor is basically the ratio of Cw2 and U2 Cw2 is 406.27 U2 we have calculated earlier that is 471.24. So, we can calculate the slip factor as 0.862. So, 0.862 corresponds to the slip factor which is basically the ratio of the whirl component of the velocity and the blade speed at the impeller outlet. So, we already discussed the significance of slip factor it is basically as a consequence of the disappearance of the Coriolis acceleration towards the outlet of the impeller leading to a tangential variation in the relative velocity. So, there is a difference between the whirl component of absolute velocity and the blade speed at the outlet. If that was not there the whirl component would basically be well Cw2 will basically be equal to U2 if the Coriolis acceleration were not to be considered. So, the next question that we are going to solve is the following at the inlet of centrifugal compressor I the relative Mach number is to be limited to 0.97 the hub to tip radius ratio of the inducer is 0.4 the I tip diameter is 20 centimeter. If the inlet velocity is axial determine the maximum mass flow rate for a rotational speed of 29 160 rpm and part b the blade angle at the inducer tip for this mass flow. The inlet conditions can be taken as 101.3 kilopascals and the temperature as 288 Kelvin. So, here what is mentioned is that the relative Mach number has to be limited to 0.97 and we have been given some geometric details like hub to tip ratio of the inducer as 0.4 the tip diameter at the I is 20 centimeters and also the rotational speed of 29 160 rpm. So, given these conditions and parameters we need to find the maximum mass flow rate if the Mach number is to be limited to 0.97 we also need to find the blade angle at the inducer tip for this particular mass flow rate. So, let us first start with the velocity triangles as we have been doing all ways let us get the velocity triangles first and then proceed towards solving this problem. So, what is specified in this case is that this is the inducer inlet and we have been given the radius ratio for the inducer in this case the radius ratio has been given as 0.4 and the I tip diameter is given as 20 centimeters. So, R T is given as 20 centimeters radius ratio is specified the revolution speed of rotation is specified and the relative Mach number at the tip has to be limited to 0.97. So, if we look at the velocity triangles we should be getting a velocity triangle as shown here at the inlet and we have the blade speed at the inducer inlet the absolute velocity which is assumed to enter axially and the relative velocity at the inlet of the inducer. So, in this case the rotational speed is given the tip diameter of the inducer is given as 20 centimeters and therefore, we can calculate the blade speed u 1 which is pi into d n divided by 60 which is pi into 0.2 into 29 160 divided by 60 where 29 160 is the speed of rotation in rpm. So, we get the blade speed as 305.36 meters per second and from the velocity triangle which I have just shown we can see that the relative Mach number which is the ratio of the relative speed to speed of sound at the inlet that is v 1 divided by square root of gamma R T 1 which is basically equal to square root of c 1 square plus u 1 square. So, v 1 square is the ratio of these two square root of u 1 square plus c 1 square divided by square root of gamma R T 1. Now, at the inlet we have this stagnation temperature which is given as 288 Kelvin and so T 1 is basically T 0 1 minus c 1 square by 2 C p where T 0 1 is 288 C 1 is not known and the specific heat at constant pressure is 1005 joules per kilogram Kelvin therefore, we get c 1 square by 2 0 1 0. So, relative Mach number is equal to square root of c 1 square plus u 1 square where u 1 we have just now calculated 305.36 divided by a square root of gamma R and we will replace T 1 by T 0 1 minus c 1 square by 2 C p and relative Mach number we know the limit which is 0.97. So, we substitute for m relative as 0.97 and therefore, we get 0.97 square is equal to c 1 square plus 305.63 square divided by this gamma R times 288 that is 115718.4 minus 0.2 c 1 square. So, if you simplify this we can calculate what c 1 should be c 1 comes out to be 114.62 meters per second so the absolute velocity at the inlet of the inducer is 114.62 meters per second. So, having calculated that we can now calculate T 1 at the inlet that is static temperature at the inlet because we need to calculate density because that will be required for calculating the mass flow rate. So, T 1 is equal to T 0 1 minus c 1 square by 2 C p and if we substitute for these values here we get T 1 as 281.464 Kelvin and from isentropic relations we also have P 0 1 by P 1 is equal to T 0 1 by T 1 raise to gamma by gamma minus 1 P 0 1 is given T 0 1 is known T 1 we have just now calculated. So, if you substitute all these three values we can simplify and calculate P 1 which is static temperature at the inlet and that comes to be 93.48 kilo Pascal. So, if you substitute for P 1 and T 1 we can calculate density at the inlet this is 1.157 kilograms per meter cube. Now, the other aspect we need to calculate is the annulus area for mass flow rate we need the speed axial velocity which we have calculated as c 1 then density we have just now calculated the next thing is the annulus area. So, annulus area at the inlet is pi d square by 4 into 1 minus the half to tip ratio. So, d is given as 0.2 meters half to tip ratio is 0.4. So, if you substitute for d and half to tip ratio we get the area a 1 as 0.0264 meter square. So, this is the annulus area at the inlet and since the inlet flow is axial the axial velocity and the absolute velocity are the same. So, mass flow rate is rho times rho 1 a 1 c 1 we have calculated all the 3 now. So, rho 1 is 1.157 a 1 is 0.0264 and c 1 is 114.62. So, the mass flow rate can be calculated as 3.5 kilograms per second. The other parameter to be calculated is blade angle at the tip of the i which is beta 1. So, tan beta 1 from the velocity triangle is c 1 by u 1 if you substitute for both these we can calculate beta 1 as 20.57 degrees. So, this is the blade angle at the tip of the inducer. So, in this problem what we have done is this was a problem which was concerning just the inducer. We were not looking at what happens at the outlet of the impeller. In the previous problem we were looking at the slip factor where we were required to calculate the impeller exit velocity triangle. We were required to solve the exit velocity triangle. In this case we were just solving the inducer of the compressor and we calculated the mass flow rate and also the blade angle at the inlet of the inducer. So, we have solved two problems today on centrifugal flow compressors one pertaining to the impeller and the other pertaining to the inducer of the centrifugal compressor. So, we will now take up a few exercise problems and then I shall leave it to you for solving these problems based on what we have discussed just now and also based on our discussion in the last lecture. So, the first exercise problem is on a centrifugal compressor is the following. The design mass flow rate of a centrifugal compressor is 7.5 kgs per second with an inlet stagnation temperature of 300 Kelvin and a pressure of 100 kilopascals. The compressor has straight radial blades at the outlet. The blade angle at the inducer inlet tip is 50 degrees and the hub to tip ratio is 0.5. The impeller is designed to have a relative Mach number of 0.9 at the inducer inlet tip. If the tip speed is 450 meters per second determine the density at density at the inducer inlet, the inducer inlet diameter, the rotor rpm and the impeller outlet diameter. So, this is a question very similar to what we just now solved the second problem that we had solved and here we are required of course, the mass flow rate is specified the inlet conditions are given the angles are also given. Hub to tip ratio is given Mach number is specified. So, based on this we are required to calculate the air then air density which is as which we can calculate and it will come out to be 0.988 kilograms per meter cube. The second part is inducer inlet diameter that will that would come out to be 0.258 meters. Then the rotor rpm would be 17100 rpm and the impeller outlet diameter that is 0.502 meters. So, this problem I am sure you will be able to solve because we already solved a problem on these lines the second one that we have solved was very similar to this. The second question exercise problem is a centrifugal compressor runs at 10000 rpm and delivers 600 meter cube per minute of air at a pressure ratio of 4 is to 1. The isentropic efficiency of the compressor is 0.82. The outer radius of the impeller is twice the inner radius and the axial velocity is 60 meters per second. If the ambient conditions are 1 bar and 293 Kelvin determine part a impeller diameter at inlet and outlet part b power input and part c the impeller and diffuser angles at the inlet. So, in this case we need to calculate we are required to calculate the impeller diameters at the inlet and outlet and the power output based on the rpm and mass flow rate the flow rate given pressure ratio is also given efficiency of the compressor is known to us and also it is mentioned that the inlet the outer radius of the impeller is twice the inner radius. So, this will help you in calculating the mass flow rate calculating the diameters at the inlet and outlet. So, diameter comes out to be outlet at the outlet it is 0.92 meters at the inlet 0.461 meters power input is 2044 kilo watts impeller and diffuser angles are 13.9 degrees and 7.1 degrees. The third exercise problem that you can solve is 30 kilograms of air per second is compressed in a centrifugal compressor at a rotational speed of 15000 rpm air enters the compressor axially. The compressor has a tip radius of 60 centimeter 30 centimeters the air leaves the tip with the relative velocity of 100 meters per second at an angle of 80 degrees assuming an inlet stagnation pressure and temperature of 1 bar and 300 Kelvin respectively find part a torque required to drive the compressor part b power required and part c the compressor delivery pressure. So, here in this question the part a and part b are very much related torque required and power required are quite related and straight forward and the mass flow rate is specified the speed of rotation 15000 rpm and the compressor tip radius is also given and the outlet velocity triangle we have the relative velocity and also the angle which it makes with the outlet that is also specified. So, the torque required in this case would be 4085 Newton meters power required would be 6.417 megawatts and the compressor delivery pressure would be 6.531 bar. So, if you were to solve this problem you would be getting these the answers that have been specified here. So, there are three problems that I had given for and as an exercise based on the tutorial we had during part of this lecture that we had today. And so, what we have completed so far is one component of the aircraft engine that is the axial compressor and then subsequently we are going to take up the combustion chamber then the turbine and also we will be discussing about the intakes and the nozzles of axial compressor jet engine. So, the next part that we shall be discussing would be about combustion chambers and then turbines subsequently we will also take up two other important components which constitute a jet engine that is the intake and also the nozzle. So, all these components put together constitutes the jet engine as a whole. So, in the next lecture that we shall be discussing that would be combustion chambers subsequently the turbines and then I shall be talking about air intake. So, in the next part of my lecture we would be talking about air intakes and we shall have three lectures on air intakes where we shall be talking about air intakes which are used in transport aircraft, air intakes used in military aircraft and also intakes which are used in subsonic flows and how they are different from supersonic intakes and what are the geometric differences between these types of intakes. So, we will take up some of these topics for discussion during our next lecture where we shall initiate discussion on intakes. So, that brings us to the end of this lecture and also the end of this chapter on centrifugal compressors. We have already discussed about axial compressors and so this would be the end of our discussion on centrifugal flow compressors.