Transcript for:
Fluid Mechanics Concepts and Applications

years welcome aboard to this special session we are in the nurture series and nurture series is for all the 11 standard students also for the dropper and the 12 standard students who want to revise their 11 standard topics today is lecture number one of fluid mechanics and this is your captain this is your master teacher streas and i'm going live from valencia so welcome aboard to this special session and this is a part of your long term series on your favorite channel via enthuse so let me just quickly tell you what we are going to do today and then we are going to start the session so in this lecture number one of fluid mechanics we're going to talk about what is pressure what is hydrostatic pressure how to calculate variations of pressure with height and depth and the gradient we are going to also talk about pascal's law and it's beautiful application and then we are going to go to two very special instruments called barometer and manometer see they're working and their variations and then yes we are going to go to force on the walls of container and also i'm going to give you homework questions all of this with me shreyas your physics master teacher at vidantu hello everyone how is everyone doing hi aisha madhav roshni good evening dakshin ramya madhav nivegi welcome aboard vikki vivek so this session is for all 11th and 12th standard students as well and i'm pretty sure most of you would have completed your term one examination and if you haven't completed it yet don't worry we need to start with the term two syllabus of your 11th standard because we can't keep waiting number one and number two we are preparing for jail remember that all right and also thanks a lot for hitting that subscribe button and also thanks thanks a lot for smashing that like button down there good evening everyone yup yup yup i will uh complete lightweight zoom yeah and then i will start there is one more lecture which is of uh young's double set experiment and then i will do that yes vk i'm going to do reoptics also for 12 standard all right so let's get going are you all ready full of josh how many of you have already studied the job a chapter honestly let me know okay and i have a question for you in fact i'm going to answer this question towards the end of the class you will understand how this works it's a very interesting problem if i ask you to drink some juice from a straw okay if i ask you to drink some juice from a straw let's say this is your container this has some juice and there is some straw in it and that is you okay that is pandu or that is you okay and you're going to put this straw in your mouth my question is how high can this straw be high do you think this straw can be hello kaneshma hello mother welcome welcome karthik hi loges hi molesh welcome aboard okay so some of you have not studied no problem it's okay so this is a very interesting question i'm going to ask you this now but the answer for this will be disclosed towards the end of the class so how high do you think you can elongate the straw so that you can still sip it without any you know problems okay you're saying 0.8 meet atm related uh pressure will be decide the height according to capacity okay i give you one more option you can suck it stop again suck it stop that's okay you can hold the straw you do not have to suck it in one go you can suck it stop it relax chill yeah breathe somewhere and then again suck it and again then press it you can keep doing that then what is your answer then is it more than certain height can it be three storage building can it be five storage building can it be infinity what do you guys say hello speed okay it depends on atmospheric pressure all right so we're going to talk about it i'm going to disclose the answer you know somewhere in the session so stay tuned so i hope you have already smashed the like button so now what is a fluid so remember a lot of people always think fluid means water water is just an example of fluid fluid is anything which flows it could be gas it could be liquid but not solid because it cannot assume the shape of the container so all the things which can assume the shape of the container and which can flow they have very similar alike properties and that's why we categorize them as fluids now you might be wondering how exactly is this chapter going to flow in the nurture series so let me give you a small breakup see fluid mechanics is actually divided into you know generally three categories first is fluid statics hydro fluid yes very similar static status means it will be stationary it will be at rest okay so you're going to see static fluids where things are floating or you're finding the pressure in a container where the gas is at rest something like that hydrodynamics dynamics means moving so when fluids start flowing through capillaries through tunnels through canals through pipes so that is fluid dynamics and then we have non-ideal fluids where you have certain non-ideal behavior like viscosity like viscosity okay yep so when did i start fluid mechanics today is the first lecture lalites okay yeah thermo will be done after this yep so now yes liquid disturbance will be stock talked about in hydrodynamics the disturbance the turbulence we are going to talk about it briefly in hydrodynamics now what categorizes like we have ideal student right so in a class full of students right you have somebody who is very ideal an ideal student completes the homework on time he sits on the first bench and maybe he answers all the questions asked by the teachers and then i don't know he takes part in all the competitions so probably this is what an ideal student looks like so this is an ideal student this is how he looks like okay so this is how an ideal student looks like this is how it is how many of your ideal students please raise your hands now what is an ideal fluid what is an ideal fluid okay yes yes wiki this is enough for everything yep this is once you study for g you also study for ct you also study for vit you also study for neet you also study for srm you also study for bitset you also study for kvpy you also study for blah blah blah okay now uh well great now what are the characteristics of an ideal fluid the characteristics of an ideal fluid look something like this first of all understand it cannot be compressed or expanded yep it cannot be compressed or expanded that's one assumption we generally make in most of the cases so gases to certain degree will not be ideal because you can easily compress gases so an ideal fluid okay so you cannot compress it you cannot expand it okay so you cannot compress it or expand it so this is not allowed then understand one more thing there is no viscosity there is no viscosity what is viscosity viscosity is not there honey sauce ketchup have you ever drank honey or have you used sauce or ketchup how it is when you throw when you pour that sauce or ketchup it hardly flows right it hardly flows but if you have a bottle of water like this if you have a bottle of water and you pour the water it flows everywhere it easily flows because it is less viscous when the fluid is thick in and you know there are a lot of drag forces a lot of forces which take away that kinetic energy of the fluid then it is viscous fluid i hope this is clear mother used it just some time back correct mother yep so newton don't worry the camera results will be out hold on okay very good saja now i know it's the class timings are seven o'clock so viscosity is not there there are no dissipative there are no forces which take away the energy of that fluid then that is an ideal fluid so viscosity is absent and there are certain more characteristics like density will not change um i mean that's obvious from this because i mean think about it if it cannot be compressed or expanded the density also won't change i hope that is clear all right otherwise joining bacha even if you're a little bit late it's okay it's okay okay very good very good and basically it flows very easily it flows or basically it can slide so this is something which is an ideal fluid it slides and flows very easily it can take the shape of the container so that's what it is perfect okay so what is the most important criteria that we are going to study in this particular segment of fluid mechanics like i told you fluid mechanics is divided into three parts you're first going to start with hydrostatics and like i said that statics means it is basically at rest so what it means is look at this liquid which is in this container if i take any part of that fluid so what is this this is nothing but a system this is nothing but a system the net force on it should be how much come on put it up in the chat box my warriors what do you think the answer should be what do you think the answer should be what do you think the answer should be the net force should be and what do you think the net torque should be what do you think the network should be it should be zero and the net force should be also zero makes sense perfect harita good evening kalyani long time very good we will be doing at least one lecture and probably another class on monday definitely it will be zero net force is zero net torque is also zero and this automatically means acceleration is zero this automatically means alpha is zero that means it is not translating it is not rotating okay so we do not study those things under the purview of hydrostatics you will always see this will be obeyed it will be almost at rest it will be hardly moving great so that's the first segment remember after this after two classes we are going to start with hydrodynamics everybody i think is clear about this okay so after uh two lectures we're going to start with dynamics very good my warriors perfecto i can see all the zeros in the chat box now there are some important properties that you should know about fluid now everybody knows about density so i although i have put up over here hydrostatic pressure this is one of the important properties so when i talk about properties of fluids everybody should know about this property which is density and everybody knows the density is how closely packed it is generally the symbol is rho and it is nothing but mass by volume obviously it is expressed in kg per meter cube now you also have another you know way of writing density that is relative density relative density uh generally is also referred with respect to water so what is the density of water the density of water is 1 gram per cc that is in cgs but you can also write it as 10 to the power 3 kg per meter cube this is some standard value which you should remember density of water is 1000 kg per meter cube or 1 gram per cc so relative density is nothing but density of that object upon density of the standard material that we usually choose and that is also basically nothing but water sometimes it is also called as specific gravity specific gravity okay so specific gravity talks about relative density so guys think about it if i tell you the specific gravity is 1 if the specific gravity is 1 that means it's as dense as water if the specific gravity is 1.3 if the specific gravity is 1.3 then what do you think will happen come on put it up in the chat box what do you think will happen if the specific gravity is 1.3 come on put it up come on come on come on come on i know you didn't you're very curious but as soon as i find out something i'll definitely put it up and reply to your comments so what do you think will happen if specific gravity is 1.3 by common sense by general knowledge by your past experiences what do you think will happen okay so dakshin we are going to talk about that in thermal expansion okay so we're going to talk about it not now not right so what do you think will happen obviously if the density is higher than that of water then if you put such an object in liquid like water it will sink yes 1.3 is more than water definitely it will definitely sink and if it is less than one obviously it will float perfect that's one thing second thing is pressure you always talk about pressure of a gas pressure of a liquid so you don't generally you know talk about force by a liquid there are cases where we discuss force but generally we talk about a property called as pressure and this pressure is nothing but the intensity of the force what is it called intensity of force pressure is a word used only for fluids you never talk about pressure for a solid so fluids means both gas as well as liquid so you only talk about pressure for liquids or gases when i say intensity of force it means force per meter square for satin per unit area and that means the unit of this the unit of this will be newton per meter square you can also write basically pascal okay so atm all these are other units and pressure is nothing but the force divided by area but remember one thing if the force is at an angle if the force is at an angle then only choose the perpendicular component of the force the parallel component of the force should not be considered so whenever you write pressure is force by area keep this in mind it is perpendicular force divided by area fair enough everyone clear about this shall we go ahead yep very good very good let's get moving everybody clear give me a thumbs up give me a yo all right very good alka very good excellent deduction moving ahead so don't worry you're going to get all the things in the you know pdf as well pressure is forced by area now there are some interesting properties pressure and let's talk about it now okay there are some interesting properties about pressure and here it is that is called as pascal's law one of the first things that you do when you wake up in the morning and there could be many things but one of the first things is you brush your teeth and before you brush your teeth you open the cap off your toothpaste and you squeeze it on one side right you squeeze it on one side and you have fun especially when the toothpaste is about to be over so just imagine this this is your test tube uh which is your favorite toothpaste i don't know which one is your favorite toothbrush hi mohan hi simple girl good evening everyone okay hello so think about it what okay what's your favorite tool let me just put up i don't know close up okay close up okay so that's your toothpaste and you squeeze it you squeeze it on one side with your hands okay this is your hand this is the hand of pandu this is pandu he's trying to squeeze it what happens the fluid flows to the other side right it flows to the other side and even if there is a cap if you squeeze it on one side even if the cap is there the other side starts bulging what has happened is basically any change in the pressure on one side of the compartment or the container immediately flows to the other side immediately flows to the other side because when you squeeze over here the pressure increases but here the pressure is low so immediately the liquid will flow from high pressure to low pressure and it will try to equalize the pressure and the other side will bulge out other side will bulge out correct so basically what has happened is any changes in pressure in a closed container that's very important closed container because if the cap was open imagine if the cap was open you squeeze it this won't bulge out this will just come out it will probably go stick on this wall and then again you will get a flying slipper from your mother correct because the toothpaste has just gone and stuck on the wall and then you have to clean it so if it is closed then you will see the pressure will adjust itself now this principle is called as pascal's law and it is used in day-to-day life and you will see a lot of phenomena based on pascal's law pascal's law tells that whenever you change the pressure you know it tries to adjust itself it equalizes it normalizes everywhere till the pressures on all the parts of the container including the fluid become the same yes it tries to maintain that pressure and one other good example is right over here look at this this is a piston look at this this is a piston somebody is trying to push it somebody is trying to pressurize it the moment you try to pressurize it over here other parts of the container won't stay quiet other parts of the fluid won't stay quiet what will happen the moment you try to increase the pressure everywhere the pressure will equalize it okay so everywhere the pressure will increase and everywhere you will see the same pressure so in a closed container enclosed liquid at equilibrium the pressure change at one point is transmitted to all other points of the liquid till the pressure normalizes yes we are going to solve problems now one of the best examples is this one how many of you have played with syringes in your um in your childhood how many of you played with syringes by connecting them and how many of you have seen this in your car showroom or maybe a garage somewhere this is very interesting phenomena very interesting phenomena thank you uma this is very interesting look at this such a big expensive heavy car look at this guy who do you think is heavier pandu or car come on put it up in the chat box simple girl has played lalites has played who do you think is heavier pandu or the car who do you think is heavier okay roshni also has blade there are two objects this is called as a hydraulic lift okay car is heavier obvious you'll be like sir what are you saying i mean this is such an easy question you are asking such obvious things obviously car is heavier but look at the interesting thing out here the person the pandu standing over here is able to lift the car why is it so why is this pandu able to lift that car okay let me just get the pandu back okay please where is that pandu oops where is that panda one okay there we have the pandu let's get this pandu okay this is all because of pascal's law what does pascal's law say if any changes in pressure happen it will get transmitted everywhere the pressure becomes equal correct so can i say the pressure of the piston or this piston or this piston so basically pistons is pressure on the pipe is also the pressure of the fluid is also the pressure on the walls of the container that means the cylinder can i say this how am i able to say this is only because of pascal's law everybody agrees with this particular concept everybody agrees with this particular concept pressure of this piston pressure on the liquid pressure on the walls pressure on the pipe pressure on the cylinder everything is same it's normalizing it now what is the pressure on the piston see this pandu has some weight correct so he is applying some force f1 so what is f1 f1 is basically the weight the weight of this particular pandu the weight of this particular pandu what is this f2 this f2 is nothing but the weight of that particular car so can i not say the pressure here and pressure here are equal so therefore f1 by a1 is equal to f 2 by a 2 f 1 by a 1 is equal to f 2 by a 2 now just rearrange this terms and see what do you get just rearrange these terms so f 1 by f 2 will be a 1 by a2 now out of a1 sorry this is a1 and this is a2 a1 and a2 who is more out of a1 and a2 who is more obviously we can see that a1 is less and a2 is more if a1 is less and a2 is more that also means f1 is less than f2 so that means that means what it means that a small force can equalize a large force a small force can balance a large force that's all it means and you can check by putting some values for example if this a 1 is 1 a 2 is let's say 100 then if f2 is 100 kg then f1 can be 1 kg crazy right here if you put 1 kg mass you can support 100 kg mass on this side because the area of cross section is one is 200 that's how fascinating this is that's how fascinating this is this is the best example of pascal's law everybody has understood this can we now switch on to problems everybody please give me a yo if you guys have got this it looks very non-intuitive so how is it possible but this is how it works the force per unit area is same not the force the force per unit area is same let's start doing some questions okay so this is one good example out here i have put it up in the pdf don't worry you're going to get all of this okay so i've put it right over here whatever i have done pascal's principle okay come on quickly answer this okay for an ideal fluid but i am the father of all of you because you are my bachelor maybe okay for an ideal fluid viscosity is absent volume and density remains constant bulk modulus is infinity rigidity modulus is zero come on what do you think it is yes nani aspirin mechanical solids have been completed theory and basic problem wise but you will have another problem solving session very soon problem solving session will be there on solids later on okay alka saying hey okay i'll give you one hint more than one may be correct more than one may be correct be careful more than one ideal fluid what are the characteristics think about it yes i am going to give you weak wise time table come and then tomorrow's class definitely yep yep okay acd abd okay very interesting and the correct answer is actually all of them and all of you are wrong because all of them were correct so viscosity is absent i just mentioned about viscosity no drag forces no losses no loss that is the characteristic of ideal fluid volume and density remains constant because it is not compressible you cannot compress it so it is not compressible so this is also correct bulk modulus is infinity this also comes from this if bulk modulus if bulk modulus is higher then it means because bulk modulus was one by compressibility the compressibility is less so if this goes to infinity this goes to zero so it is basically not compressible very very important and last thing yes unexpected to its rigidity modulus super extra what why is the rigidity modulus even coming over here i'll tell you what rigidity modulus was all about if you have forgotten rigidity modulus has got to do with shear remember this was nothing but shear modulus and what is shear got to do with it's got to do with sliding so if you have layers of fluid if you have layers of fluid they can slide with respect to each other easily if they can slide easily they can sure they can bend they can take the shape very easily and when once things can slide their shear modulus is less if shear modulus is more it's very difficult to slide one over the other they won't bend i hope you understand this so hence it is zero another example for that would be imagine you know this is a book with lots of pages in it if i apply a force like this you can see the pages slide over it there is some sheer modulus but if this was a liquid all the layers will tuck tuck tuck tuck they will start sliding and they will flow and they'll spread everywhere so that's why shear modulus is basically zero perfect what is bulk modulus calories just watch my previous class it's got to do with the property of the fluid related to compressibility previous class on properties mechanical properties of solids watch it next question coming up on your screen all right yes velocity gradient creates that low rigidity modulus perfecto yep yup nani aspirant i'm going to create a timetable for all of you tomorrow for 2022 warriors and for 2023 i'm going to come up with another strategy session don't worry stay tuned in a fluid of bulk modulus b density rho naught if it is compressed by changing pressure delta p then the new density is going to be interesting question bulk modulus is given change in the pressure is given what is the new density okay so think about it there is a liquid whose mass is m volume is v okay and there is some pressure acting on it maybe okay there is some pressure acting on it maybe atmospheric pressure whatever now what happens is you change the volume so this was your initial volume or v naught now you change the volume how by applying some pressure and the volume decreases this is your final volume but even when the volume changes what will remain same volume might get smaller because you have compressed it mass will remain same is the same mass correct so that has happened because of change in the pressure fair enough so let us go by the definition of bulk modulus and start doing the problem what is bulk modulus it is change in the pressure divided by negative sign change in the volume upon original volume do you remember this this was the formula yes mass will remain same okay now here is what will happen just take this delta v by v over here so it will and take this v over here let's see what happens so because i want change sorry i want the new density so delta v by v will be negative delta p by b now what is delta v its final volume final volume minus initial volume and this is also initial volume v stands for initial volume delta v stands for change in the volume this is equal to minus delta p by b take this minus sign inside so it will become v naught minus v f divided by v naught is equal to delta p by b now just do a simple math v naught by v naught is nothing but 1 this will become minus v f by v naught is equal to delta p by b interesting once i get this i can shift this guy over there this guy over here so it will become one minus so delta p by b is equal to v f by v naught okay now till here i have simplified the only thing that i need to do is somehow convert volume into density and i think i know what to do density initially is mass by volume final density because the density would have changed is same mass by that new volume sorry by that new volume which is v f correct so now think about it just substitute v f over here and v naught from there so what was vf from there just just check this out what is vf just from here vf is nothing but m by final density density goes below and vf comes on the top and what is v naught v naught is again mass by initial density you can just swap the terms and you can see that clearly what is happening mass mass goes off and you're just getting rho naught by rho and this is nothing but 1 minus delta p by b swap the terms take row on the top take this below so rho will be nothing but rho naught divided by 1 minus del p by b so i think that's our final result i have got what i wanted this is initial density this is change in the pressure this is bulk modulus this gives me the final density very interesting problem and it is very very important problem there were questions in mains advanced bits at so many times on this particular concept is that clear just check this out so what we did initial mass initial density initial volume final mass final density final volume mass remains same go by the definition of bulk modulus bulk stress by bulk strain this was the formula i just gave you few days back that negative sign comes because you have to always keep it positive and all of that just rearrange it it's just pure maths after this basic algebra which anybody can do okay perfecto let's get moving and here is the answer rho naught by one minus delta p by b okay here is the next question on pascal's law this was asked in february 2021 previous year question let's see how many of you if you are giving the je 2021 exam in february how many of you can actually crack this there is a hydraulic press the same what is this hydraulic press exactly the same diagram this diagram over here is a hydraulic press hydraulics okay that's what you should visualize where it can lift 100 kg when a mass mkg is placed on the smaller piston it can lift how many kgs when the diameter of the larger piston is increased four times and that of the smaller piston is decreased by four times keeping m on the smaller piston same very interesting let me give you a time for solving this within one minute you are supposed to solve this let's see if we can solve this within one minute i've started the timer now okay so i'll just draw the diagram for you so this was the smaller piston right over here this is the tube okay and this is the bigger piston right over here perfecto and yep you had that mass m over here and over here you had basically a different mass so earlier this was 100 kg now if you change the areas as mentioned what do you think will be the new load that you can lift that's the question come on my warriors figure this out hardly a few more seconds remaining do the math quickly in your rough books i'm pretty sure you can crack it within the stipulated time come on 10 seconds to go figure this out come on come on come on my warriors think think think all righty the time is up the time is up now let's calculate this in pascal's law i told you using pascal's law pascal's law i told you pressure at point one will be pressure at point two pressure at point one will be m g divided by smaller area here the area will be smaller and here the area will be larger okay and on pressure at point 2 will be that force force will be whatever 100 g divided by that larger area anyways g gets cancelled now is the nice trick mass is the same only we need to figure out what will happen with this hundred okay here is one simple trick what i am going to do keep that hundred as it is take the take that a over here so m capital a by small a is equal to 100 now this 100 is nothing but your old weight which can be lifted which can be lifted now see what is happening the diameter of the larger piston is changed four times if you recollect area area is basically pi r square which is pi r is diameter by two so it will be diameter square by four so can you see that the area is actually proportional to the square of the diameter it is proportional to the square of the diameter so think if larger pistons diameter is increased four times so the area will increase four square times which is nothing but 16 times do you agree with this a will capital a will increase 16 times what about small a my warriors what about small a smaller piston is decreased four times so if the diameter decreases four times the area will become one by two square one by four square times which is one by sixteen times agreed with this it will become one by sixteen times kuipativya just join in you've missed some part but you can always go back and you can always catch up hence think about it numerator has become 16 times denominator has become 1 by 16 times so totally as a ratio how many times has it become 16 into 16 how much is 16 into 16 256 times 256 times everybody agrees so lhs became how many times 256 times so rhs how many times should it become rhs should also become 256 times so what is 256 into 100 2560 we are doing fluid mechanics fluid statics that's the first part and today we are doing pascal's law and then hydrostatic pressure barometer manometer okay so don't worry we're going to complete this uh hydrostatics part in two days and monday's class all right join in i just completed pascal's law okay and now we are going to go to hydrostatic pressure all right cool amazing go moving ahead to the next one what a brilliant question yes satya i can see your chat definitely mission iit is our last year series this year we're going to have different series okay now let me also tell you whatever i'm teaching you the questions etc will be available to all of you in the telegram channel the link is there in the description box so do not forget to join it because all important announcements and pdfs are shared over there and remember all those of you who want to join vedanthu and who want to cover up their backlogs there is still an opportunity a window of opportunities there for all of you because there is a crash course starting especially for 11th standard students so go ahead check out the link in the description box for 2023 there is a pro subscription link i'll show that to you towards the end of the class so stay tuned okay so now let's talk about some more things about hydrostatic pressure now what is this hydrostatic pressure i'll tell you hijaram welcome very good gaurav now here it is see imagine i'll tell you a simple story imagine there is a pandu okay there is a pandu he's carrying a book on his head like this he's carrying a burden right if he's carrying a book on his head what is he carrying he's carrying a burden right now just imagine a pandu like this and you ask him to carry more and more books there will be more and more burden on his head and he will probably disappear great very glad nanda okay now imagine even you guys even me i am carrying a burden you are carrying a burden but not of books but of something else you might be wondering sir which burden am i carrying sir that is something which is not seen by you but it is there even right now you are carrying that burden that is basically the weight of the air above you and this extends till wherever that atmosphere is so this is where the atmosphere ends and the entire column of air the all that air above you is responsible for creating that pressure over you exactly now like oh my god this is breaking news sir i need to get rid of this pressure so what pandu does he starts running for his life he starts running he's like i don't want this burden over my head he starts running and he takes shelter under a roof and this pandu now becomes very very happy as pandu becomes now very very happy he's like yes hooray i don't have that burden of this atmosphere because the only amount of air above me is this much so now the burden on me is less do you think this pandu is correct or wrong what do you guys say what do you guys say what do you guys say espandu who ran away to escape the burden of the weight of the air supported over his head he ran under a roof under a shelter he's like okay now i do not have that burden anymore what do you guys say is he correct or is he wrong command my warriors think about it you two are under a roof i'm pretty sure unless you're watching this lecture right in the open in some garden what do you guys say what do you think is spun right in thinking about this or is he wrong do you think he has escaped the burden do you think he has not escaped the burden come on put it up you could be wrong it's okay nobody's judging you what do you think is he wrong is he correct has he escaped the burden or not well well well the answer is the answer is no right not escaped says nada okay dakshin says no the answer is he has not escaped the burden you'll be like what why did you didn't pan do i escape the bird and sir because there is a shelter the shelter will prevent the weight of the air you guys forgot that there is air besides as well there is air besides as well and it extends till infinity so this burden is there like okay so that will fall over here it will not affect this thing again think again if this part has for example low pressure this part example has high pressure what will happen liquid will flow pascal's law liquid will flow from high pressure to low pressure tuck and it will immediately increase the pressure so you technically can't escape it even right now over your head you might be thinking sir only this much air is there but don't forget there is some air gap somewhere inside your room there is some way the air from outside is escaping inside and that's the reason why that pressure which was there outside has got transmitted inside and that's why you indirectly have the burden of the air which is you know outside the room as well so basically what has happened is this imagine another pando over here this panda over here both of them will have the same burden because assume that you are assuming that this has low pressure just assume then this pandu has high pressure this one was low pressure so what will air do it will start flowing but remember air should not flow why because we are discussing which topic hydrostatics so basically this cannot be at low pressure this cannot be at high pressure both the pressure should be same that means both the pandus will have the same amount of pressure that's what it is is that now understood is that now clear my warriors got it so you cannot escape no matter where you are no matter where you are you cannot escape the burden of the air column above you this burden of that air column is called as hydrostatic pressure so this is the burden of the fluid in this case basically the atmosphere column column and it is created because of gravity gravity is responsible for that particular weight so gravity creates the weight and that weight creates the burden it cannot escape it now vivek is asking a very interesting question sir what if the room is packed with doors very interesting question will be tell me one thing before packing the room with doors wasn't the door open so the air has already escaped so already the pressure inside is the same as the pressure outside got it so you cannot escape it unless you go out in space you become an astronaut you go outside in space and then you remove all the air inside and then you pack the doors you pack the windows you make it airtight and then again come back from space onto earth and then outside and inside the pressure will be different that's a different story because you have not allowed the air to enter inside in the first place is that clear my warriors perfect question as well awake okay now like i was telling you before that pressure is always the perpendicular force my area so in a fluid which has pressure look at this container it has some liquid and there is some body inside that liquid that body could be floating sinking doesn't matter the point over here is there is pressure everywhere there's pressure here there's pressure here there is pressure here because it's under the influence of gravity there is pressure everywhere and it always acts in all the directions the pressure will act in all the directions so the moment it finds a surface it will act perpendicular to it so if you take a surface here it will act perpendicular to it if you take a surface here it will act perpendicular to it if you take a surface here it will act perpendicular to it so the pressure acts in all the directions and the force due to the pressure is always perpendicular to the area got it so it's always perpendicular to that surface area and it always acts in all the directions and it's same okay so that's what it is let's do some interesting derivation horizontal variation and very good vivek and vertical variation variation of pressure with you know horizontal and variation of pressure with vertical distance there is a very interesting thing which happens if there is a liquid and you move horizontally then you will find that the pressure here pressure there and pressure there will all be the same why there is a very simple explanation imagine pandu one imagine pandu two imagine pandu three respond to one pandu three one two two and one two three come on imagine the burden on them imagine the burden of air column over them what do you think will the burden be same or not when they are at the same height what do you think will one be equal to two b equal to three will one be more than two more than three and imagine another pando over here which is let's say pandu four okay what do you think about that guy's burden what do you think about that guys burden and imagine another pandu fight another pandu five think logically about the burden of the air column it's very obvious 1 will be equal to 2 will be equal to 3 4 will be equal to 5 but 1 2 3 burden will be less than 4 and 5 makes sense because 4 and five are at same level so they should have the same burden same pressure one two three are at the same level so same pressure but four and five are deeper inside so more pressure so what happens is when you move horizontally the burden the weight of the air column remains the same so there is no change in pressure so only when you change height only then there is variation in pressure also keep this in mind this is a more general rule actually better word for horizontal is here in this case when gravity is down then in a direction which is perpendicular to gravity in a direction which is perpendicular to gravity pressure is same so just imagine for some reason gravity is at an angle gravity is at an angle do you think the pressure will be same along this line line number one or do you think the pressure will same along this line line number two which is perpendicular what do you guys say what do you guys say come on think about it yes kalka kitchen definitely okay come on think think think come on think think think what do you think will the pressure be same on line number one or will the pressure be same on line number two think yes because yes very good roshni yep yep so people with height have less burden yes we wait but the burden change will be hardly anything because pressure variations are very small for that height it has to go by large heights for changing that pressure yeah so line two will have basically the same pressure keep this in mind they will have the same pressure it's always perpendicular yep perfecto line two will have this will not have keep this in mind so that's the variation of pressure with horizontal now let's talk about the variation of pressure with height we als saw that as as you go in the direction of gravity so what should i put in the direction of gravity the pressure should i put increases or decreases come on in the direction of gravity should the pressure increase or decrease come on quickly put it up in the chat box quickly put it up in the chat box in the direction of gravity that means you go down down down so when you go down down down should the pressure increase or decrease so as you go down there is more burden and if there is more button it should increase so definitely it should increase the best way to calculate that is by taking an element of the fluid taking an element of the fluid and i'll just mark this height as let's say dh okay so dh is the element of the fluid okay which i have taken it's a cylindrical element i hope you can see that the top area over here is a the bottom area is also a pressure let's say on the top forget this pressure on the top let's say is different and on the bottom also it is different so let's say at the bottom it is p okay at the bottom it is p and at the top it is p plus d p p plus d p d p is the small change in the pressure bottom it is p as you go up dp dp dpdp change is the change in the pressure now the force acting on the bottom and the force acting from the top will be p plus dp into a and p into it because pressure is force by area so force will be pressure into area so pressure into area is force pressure into areas force so from the top there is more force from the bottom there is less force like sir this is wrong you said the net force should be zero so how is it possible from the top there is more force from bottom there is less force guys the answer is simple you missed out on one more force think about it so that one more force is nothing but the gravity one more force is nothing but the gravity yes weight so you should also show the weight of it the weight of it will be also there and how much will be that weight the weight will be think mass into gravity but the mass think about it it will be mass into gravity the mass is given by density into volume density into volume density is rho volume of that cylinder calculate the volume of that cylinder it will be area of cross section into the height which is vdh and gravity is nothing but g so that's what it is that's what it is now just use the concept that it is a hydrostatic fluid hydrostatic fluid means net force will be zero i know some of you are still wondering sir eight minutes something is wrong weight is down larger force is also down smaller forces on the top does not make sense guys think dp will be actually a negative value yeah dp is negative but i just put it as you know lower height p a higher height p plus dp don't worry it will automatically turn out you will see when i solve the problem net force will be zero so the forces from the top will be p plus dp into a p plus d p into a plus the weight what is the weight it is rho a d h into g will be equal to force from the bottom how much it is p a now can you see p into a and p into a will get cancelled so only thing remaining is dp into a plus a rho a dhg is equal to 0 shift this over there but before that do one small favor cancel this a also so just shift this over there so what will you get you will get dp is equal to minus rho g dh shift dh below so dp by dh is equal to minus rho g now this is a very important relationship which you should know what is this dp by dh this is called as the pressure gradient pressure gradient with respect to or with height okay pressure gradient with height this is the most important formula pressure gradient with height what does this mean it tells you what is the rate of change of pressure dp is change in pressure with respect to height my height changes by one centimeter how much does my pressure change by and that comes out to be minus rho g why is this minus coming out over here the reason why this minus comes is because the pressure does not the pressure does not increase with height it decreases with height so the sim this minus signifies the pressure the pressure decreases the pressure decreases with height that's the reason for that as the height increases the pressure decreases as simple as that very good pranayama remove i hope you get well and i hope everything is fine i mean i hope you have got your medicines and please take care bacha please take care i hope everything is recovered very soon yep okay so no problems even if you are late you can always replay the session and start from the beginning and catch up to wherever we are all right very good so this is what it is dp by dh is called pressure gradient minus because the pressure decreases with height rho and g is the density and gravity at that place perfecto now using this you can calculate using this you can calculate the pressure at any depth h so we can just do that pressure variation you know inside of fluid okay so by the way do you know the value of something called as the atmospheric pressure this p naught is also called as the atmospheric pressure that has been mentioned over here the approximate value although the exact value is 1.01 1.012 into 10 to the power 5 pascal you can approximately take it as 10 to the power 5 pascals for most of the calculations for most of the calculations okay hi nv18 hello motivator welcome aboard very good now the next thing is what is the pressure at any depth we know at the sea level what is this p naught p naught is called as the atmospheric pressure when you go inside the liquid then the pressure will change correct the pressure will change that pressure variation with height can be derived from dp by dh i'll leave that up to you so using this relationship and integrating integrating with proper limits what you get is pressure at any depth is the pressure at the fluid level which is exposed to the atmosphere plus rho g h that's exactly what you get and if you're wondering what this h is h is nothing but the depth depth inside the liquid surface how deep are you in is that understood perfecto hi ravish yes vedanti is good for everything need olympiads jay everything yeah yep so that's what it is cool so remember this formula p naught plus rho g h what is p naught p naught is the atmospheric pressure rough value remember it 10 to the power 5 pascals rho density of that liquid g gravity h is the height or depth inside this uh liquid yes mangalam obviously we are doing more than cbse it will be obviously useful for cbse once you prepare for j all right so guys remember one thing now onwards my timings of the class will be 7 p.m onwards tk 7 p.m onwards so please make changes now onwards it is 7 so that we finish our classes somewhere around 8 30 8 45 you also get a break and you know shimon says class starts at nine so all of that so we can also have longer lectures that's another interesting thing that happens because of the change cool no problem pbx i am so glad that at least you watch the recordings that's good and i'm pretty sure you will have a different experience today just because you're attending it live all right now this hydrostatic paradox very interesting thing now let me give you a brief about this so just imagine a situation where there is a pipe which is bent in certain manner okay that pipe is bent into certain manner now here which is this part which is exposed to the atmosphere that has atmospheric pressure p naught ok this is exposed to the atmosphere so basically this is nothing but your atmospheric pressure there is liquid inside this okay there is liquid inside this of density rho you see that there is a tank here it could be any random shape and there is a point x and at that point x i am asking you to find the pressure that point x is at a depth h below this level what do you think the answer will be will it depend on the shape of that container shape of that pipe think about it i just mentioned the pressure at any point only depends on the depth it does not change with horizontal level right in the same liquid if you go from one point to the other point to the next point you will not see any variations that means that means it should not matter what is the shape only the height should matter so this should be just p naught plus rho g h it should be just p naught plus rho g h correct makes sense hi q takancha welcome welcome tamil hello so this means that if i have multiple containers one big one small one wide one narrow one of some random shape doesn't matter the shape the size of the container what should happen is that irrespective of the shape irrespective of the size irrespective of how bent it is as long as they are connected to each other as long as they are connected to each other all the lick all the containers should have the liquid till the same level all the container should have the liquid till the same level yes that means the pressure at this point pressure at this point pressure at this point pressure at this point should all be equal yes it will be more than p naught but they will all be equal they will all be equal and the reason why they should be equal this this this this why should they be equal think if they are not equal imagine a situation just imagine if they are not equal then what will happen there will be pressure difference and the moment there is pressure difference what will happen the liquid will start flowing from high pressure to low pressure so if there is high pressure here low pressure here immediately the liquid will flow and they will equalize it so they will start flowing till there is equal amount of height in all the containers glad to know that sarvana excellent day and don't worry all the 12 standard warriors all the 12 standard students don't worry we are going to start our remaining portions immediately after your chemistry exam so stay tuned and tomorrow there is a special class just for all of you you know on how to strategize for the je 2022 exam so this is called as hydrostatic paradox paradox because a lot of people think that depending on the shape and the size the liquid level will adjust bigger container will have maybe more fluid or less height no it doesn't work that way it only depends on the height nothing else independent of the area independent of the shape okay here are the questions coming up on your screen okay i think it should be there but i'm not sure it should be there it should be starting somewhere around 8 o'clock why the damn water reservoir is thick at the bottom what do you think welcome money welcome okay nice name money money um pesa okay envy 18 saying c saying c roshi also saying see no answer modern physics is yet to be done in the pathfinder series i am just doing light waves i just did two classes i'll do more two classes and then we'll go to modern physics hold on stay tuned i'm going to do everything i remember everything i made a promise and tomorrow i'm going to announce something special even for 2023 students it's going to be very interesting so attend that class it's going to be very interesting because there is some series launch which i'm going to do tomorrow spread the word spread it everywhere for 12 standard for 11 standard that there is something new coming up for especially you know revision and increasing your level in your board examination and j means examination and j advance okay all of you are saying c yes the correct answer is c you have if you have seen the cross section of a dam it looks like this and the reason is very obvious because here the pressure is p naught so atmospheric pressure will act perpendicular to the surface of the wall as you go below the pressure increases increases increases increases so more force here so if there is more force over here that's why to hold it you need a thicker wall so the pressure increases that's why the force increases and that's why you know the dam should be wider here is the next question this was asked in march 2021 pyq question how many of you are going to crack this question let's see this is a pyq okay let's see how many if you can crack this the pressure acting on a submarine wow 3 into 10 to the power 5 pascal at a certain depth now the depth is doubled you go deeper the percentage increase in the pressure acting on the submarine would be g is 10 density is 1000 atmospheric pressure is 10 to the power 5 pascals let's draw the diagram vishal i was not going to myself so sad no yes please ask shimon sir why he did not carry me to myself i am very angry with shimon sir he did not take me to myself i'm very angry ask shimon sir everybody should spam in today's class or tomorrow's class whenever shimon sir is going to take why you did not take stress spam you guys have to make this promise okay cool thank you bharath it means a lot and it means that means a lot because you came here and said that thank you too all the best bacha stay tuned there is a special announcement tomorrow for all the 12 standard students so be there at 11 o'clock in the morning on sunday interesting now what do we have over here is that at certain depth h the pressure is uh three into 10 to the power 5 interesting now if you double the depth you have gone to 2h then what is that new pressure that's what the sorry not the new pressure what's the percentage change in the pressure all right here is my logic see when you are here right then 3 into 10 to the power of 5 will be p naught p naught is the pressure over here right okay plus rho g h correct will be p naught plus rho g h fair enough now think p naught is nothing but 10 to the power 5 we already know that atmospheric pressure is just 10 to the power 5 plus rho gh so basically rho gh take the 10 to the power 5 here take that 10 to the power 5 here what will it become 3 minus 1 2 2 into 10 to the power 5 pascals now let's talk about this point for that point the pressure will be again p naught plus rho g but 2h p naught is 10 to the power 5 2 comes as it is what is rho g h rho g h is 2 into 10 to the power 5 so 2 into 2 4 4 plus 1 5 so 5 into 10 to the power 5 pascals that's what you got the pressure is but the question demands to find the change in the pressure percentage change ramanaya saying option adduction saying okay oh option a let's see so percentage change in the pressure will be final pressure 5 into 10 to the power 5 minus initial pressure 3 into 10 to the power 5 divided by initial pressure which was again 3 into 10 to the power 5 into 100 into 100 10 to the power 5 10 to the power 5 10 to the power five gone five minus three guys two two by three into hundred two into hundred two hundred by three percentage is it there yes it is some of you got those marks very good money very good dakshin harita excellent my warriors very good auri bachchan don't worry your rm cash you've got 28 months you stay with me till the end term 2 and j you see what happens just have trust on me imagine just in the last few days if it would make such a big difference staying with me for the next three four months till your till your boats is going to make a hell of a difference and i saw all your lovely comments which you guys posted in my sessions in the last few days so i'm always there for you and it's also something for your juniors 11 standard kids so guys remember share sir is always there it's not a journey for one lecture you have not come over here for one lecture you have come here for two years you have come here for three years maybe or four years depending on which standard you are in and watching this video so this is a long term journey this is not a 40 minutes one hour one and a half hour class it's a long journey it's a bond that you're going to have with me for yours because you're going to treasure this and you're going to enjoy this and you're going to remember this when you enter into iit's remember that all right let's get moving to the next one coming up on your screen here it is hello nishant welcome aboard if the pressure at half the depth of a lake is two thirds the pressure at bottom of the lake what is the depth of the lake let's see if you can solve this question in one minute meanwhile i'll start drinking water here we go right equations even if you're watching this lecture in a recorded form it's okay pause the video think how you can do this at half the depth of the lake is two thirds of pressure at the bottom of the leg assume the depth of the lake to be h or h by 2 or something like that and then start solving eliminate the options and i'll give you a hint take atmospheric pressure as 10 to the power 5 take density of water as 1000 take g as 10 g standard 10 density is 1000 atmospheric pressure 10 to the power 5 that's it use it it will help you only then you'll get the answer come on let's see how many can do this question 10 seconds to go let's see how many if we can do this five four three two and there we go time is up oops looks like not many people could make this but okay let's solve this together what do we do so we have the liquid surface let's say we go down the pressure at half the depth is equal to two thirds the pressure at the bottom of the lake so what will you do guys first you will start assuming right so let's just assume the depth of the leg to be h so this is at h by 2 the pressure over here is let's say p1 and at a depth of h let's say the pressure is p2 okay so this is basically at the bottom this is basically the surface of the liquid now according to the question the pressure at half the depth that means here p1 is two-thirds of the pressure at the bottom of the lake that means p2 that's what the question means so understanding the statement and making the equation is what you should develop that art is something which you should slowly develop that's the skill that's the e statement you created an equation now what is p1 try to remember the formula pressure at depth h so p naught p naught is the pressure over here right on the surface so p1 is nothing but p naught plus rho g but not h h is height or the depth which is h by two this is two thirds pressure at that that will be again p naught plus rho g just h fair enough what you do next cross multiply take that 3 over here so 3 p naught plus 3 by 2 rho g h is equal to 2 p naught plus 2 rho g h 3 2 s cancel can you see that here and here take that 2 p not here so it will just become p naught take this dude over here so it will become 2 minus 3 by 2 times of rho g h interesting 2 minus 1.5 is 0.5 0.5 is half so this is just going to be rho g h by 2 is p naught but what's the question the question is the depth of the lake so what is being asked h is being asked so h will be 2 times of p naught by rho g substitute p naught is 10 to the power 5 your row is 10 to the power 3 g is 10. one two three four zeros five zeros so one zero remaining with a two so that's going to be 2 into 10 which is 20 meters that's it that's it it looked difficult it looked difficult but it is easy it looked difficult it's just a matter of making the equation and solving it do not give up have patience that's all i have patience got it shall we move ahead to the next part perfecto yep there we go option b is correct interesting now we're going to talk about a special device and in fact there are two devices that is called as a barometer and mammometer barrow mano what does barrow do and what does manu do now i'm pretty sure you would have done this in the bathroom and do not lie about this what would you have done that would be many things but this is one of the crazy things you could do in the bathroom that is taking a mug inverting it and then dipping it inside the water it's upside down upside down and then you try to lift that mug above the surface of the liquid how many of you have tried doing this how many of you have tried lifting fill that mug completely with water put it immerse it completely inside the water and then try to lift it up if you have not done it do it right now leave water quickly run towards the bathroom leave that water image a mug and completely fill it with water and try to lift it upside down just try to do this okay come on think what has happened what what is your experience say what does your experience say what has happened you would have experienced a lot of difficulty in taking that out yep you would have definitely experienced a lot of difficulty now the mug is not so tall but imagine you had a tall test tube if i had a tall mug and that entire mug or the tube can be immersed in water and you slowly take it out you slowly take it out you will see that the water will gush inside that tube it's going to yeah duction if no water has come out that something has gone wrong out here maybe some there is a leakage some gap is there some air has gone inside if air goes inside then it will not come up so make sure that there is no air inside yeah it's going to be little tricky but you can try it out you see if you take a tube and if you pull it the water will go inside but that does not mean if you keep pulling the tube the water will just continuously keep on going up now that's not what is going to happen there comes a point where even if you pull the tube beyond a certain point certain extent you will see the water will not fill the tube completely it's not going to go till here you will see there will be kind of a vacuum created there then kind of vacuum yes it's like something was pulling the mug back into the water what is pulling that mug back into the water if you cannot feel it you will not understand it and you have to feel it by going to the bathroom that's your homework that's your try and home experiment very well you get such kind of homework i'm a crazy physics teacher anytime so what happens is basically this water is what you're holding when you try to hold the mug what's happening is this vacuum is created that vacuum is trying to pull it and basically you are trying to hold this water which is stuck because of that vacuum so when you try to pull the tube indirectly while that vacuum you're trying to hold that water and lifting that water is a pain so it's like the water is pulling you down because of its own weight because of its own weight that's what is happening now there is a limit till which it can go and that limit is let's say height h fair enough now what's exactly happening let's say the water reaches this height so this is your height not this one not this one just ignore this is a vacuum created over here we all know this is fluid at rest in a fluid okay oops in a fluid at rest what should happen everything net force should be zero pressure at same height pressure at same height should be same should be same correct pressure at same height should be same now look at all the points over here there's one interesting thing that is happening this point this point this point this point this point this point this point all are at the same height so shouldn't the pressure be equal shouldn't the pressure be equal come on my worries what do you guys say it should be right so can i not say the pressure at point a and the pressure at point b should be equal pressure at point a and pressure at point b should be equal correct so the pressure at point a and pressure at point b is equal think what is the pressure at point a guys pressure at point a is open to the atmosphere so what is the pressure at point a it is just the atmospheric pressure it is just the atmospheric pressure correct next what is the pressure at point b oh wait a minute it is inside a liquid so it will be pressure at this point plus a rho g h pressure at this point plus rho g h think again what do you think is the pressure at this point this is vacuum there is nothing there so the pressure over there is zero it's zero correct no it will not be greater than atmosphere it will be equal to you are on the surface you are not inside you are on the surface of the liquid so it will be equal so think about it it will be nothing but 0 0 plus rho g h why is this 0 because there is vacuum over there got it now think about this if i rearrange this i will get h is equal to p naught by rho g and this is a very interesting equation because because if you put the exact values like you know 1.01 into 10 to the power 5 and the row you put it as for mercury mercury is 13.6 times heavier than water yes it is 13 times 13.6 times heavier than water it's a metal so very very heavy metal it's in the liquid form if you take liquid mercury that's 13.6 into 10 to the power 3 into g g is 9.8 if you put the exact values in all of that guess what this is going to come out to be 0.76 meters okay so if you're wondering what this 13.6 is this is basically density of mercury density of mercury now my wondering wait 0.76 it's a very familiar number what is 0.76 0.76 meters is 76 centimeters that's right you can see that right over here yes arul you can definitely watch it 76 centimeters and that's nothing but the unit of pressure so that's where it comes from so essentially one atmospheric pressure is 76 centimeters when you fill a barometer with the mercury so 76 centimeters of hg that's where the unit comes from exactly the action i even even i had the same doubt and your doubt will be clarified in the next question there's a question which is going to come up on the screen and that will definitely yeah clarify your doubt hold on is that clear how this unit of pressure came one atm is equal to 76 or 760 millimeters of hedging that's the same thing so what is barometer used for a barometer is used to measure atmospheric pressure what is it used for it is used for measuring atmospheric pressure keep this in mind perfect shall we go to some questions and here it comes on your screen and by the way i have put all the theory right over here all right here it comes if water is used instead of mercury in the tube what is the length of the water column in the tube if the tube is very long assume the tube is very long what do you think if instead some guy decides man you decide okay i'm not going to use mercury i don't have mercury i want to use water fair enough how much do you think the height of that column will be approximately approximately make some suitable assumptions and do this come on my worries figure this out it's not that crazy what is the formula we just learned we learned p naught is equal to rho g h for a barometer for a barometer p naught is roughly 10 to the power 5 density is 10 to the power 3 g is 10 i know over there i had taken 9.8 and 1.01 and all of that yeah it's okay fair enough assumptions into height so guess what this height comes out to be approximately as 10 meters oh my god oh my god 10 meters do you know what's the height of your room you know what's the height of your room around 4 meters three meters around that 10 meters it's like a two story building goodness will you have a two story long test tube as a barometer obviously not you're going to break it you cannot handle it you cannot handle a 10 centimeter test you what are you going to handle a two story test tube you cannot it's practically not feasible it's not good to have such a long test tube so that's why you use a denser liquid is that clear everyone got it perfecto moving on to the next question okay yes is h constant very interesting question is this h constant well this h is constant only if the outside pressure is constant if the pressure changes then h will change sometimes you go to a hill station if you go to a hill station guys come on what will happen if you go to a hill station what will happen to this edge what will happen to this edge will this edge go down or will this edge go up you take this barometer you take this device patch it in your bag and take it to a hill station what do you think will this h decrease or increase come on my subject is i talk about hills and geography and hill station so i'm a traveler and that's my subject so i'm teaching how to travel to the hills using barometer that's that's what i teach yep yeah pahadi they usually call the subject as party subject all right so decrease yes perfect it will not increase so as you go up in the atmosphere the pressure decreases so the pressure decreases this will decrease if this will decrease h will decrease if pressure decreases h will also decrease that's it as simple as that got it okay i have another question for you just imagine just imagine just imagine just imagine you put this barometer you put this barometer in one lift you put this barometer in a lift now the lift starts accelerating upwards it starts accelerating upwards inside you have your normal air okay inside you have normal air what do you think will happen to this h yes j advance you have to study deeply for g mains what an irony wow we have j advance here interesting very good congratulations so if it accelerates upwards what do you think will happen yes nv18 what happens is if you look at this equation p is equal to rho g h g will no longer remain g it will become g plus a that means this has increased that means h has decreased so it will decrease it will decrease it will not remain constant this the air is the same the air is the same there is no change air is still the same it will be p naught but you will see less than 76 so imagine a pandu inside this lift look at this pandu he's thinking what the hell i should actually see 76 but he will see 74 centimeters instead of 76 centimeter what will this pando think inside the lift what do you think will this panda visualize or conclude in this lift by looking at the barometer you will see instead of 76 it's showing 74. you will think oh the pressure has decreased but actually has the pressure decreased think about that the actually pressure has not decreased that's the funny part have you understood this pando will feel inside this lift the pressure has gone down but strictly speaking it's just what he's perceiving but actually it has not actually the pressure the air is the same is just that the reading shown is less so that's an error in that measurement do you guys get it everyone got it perfecto let's get moving to the next question but before that i think we have mano meter manometers what does a manometer do this is like a youtube that's it youtube like the one you're watching right now no not that one this is u-shaped tube u-shaped tube so what's a manometer got to do look at this very interesting device you take a u-tube okay and you pour some liquid okay now if you just take a youtube and you pour some liquid so what will happen my warriors the liquid will be same in both the arms this is the arm of u tube this is the arm of the youtube the liquid inside will be of the same height the liquid will be of the same height why is the liquid till the same height because the pressure from here pressure from here both are same so there is no reason why the pressure why the height should be different rain mind so i would request you to go watch it there but yes if you are an english medium student you should definitely watch it over here but imagine somebody increases the pressure more pressure over here it will push the liquid down it will push the liquid up here so if there is some chamber if there is some container which has some gas or liquid then what will happen is that this high pressure will push that liquid down and that liquid will go up and that creates the height difference and using this height difference you can find out what is the pressure difference on both sides don't believe me check this out check this out do you guys agree this is the same liquid and at the same height the pressure should be same so this point and this point same pressure this point and this point same pressure this point and this point also same pressure so but okay pressure is same at same horizontal level in the same liquid so i can just say pa is equal to pb what is pa is exposed to the gas over here so this is basically the pressure of that particular gas because a is directly exposed to the gas what is pressure at point b it is deep inside this liquid and at this point it has atmospheric pressure so it is p atm plus a rho g h so interesting thing is p gas minus p atm divided by rho g oops divided by rho g is what you get over here very interesting very interesting okay yes definitely definitely calm killer hi siva what is this this is nothing but delta p this is rho g and this is h this has a very interesting formula this is called as the gauge pressure this is called as a gauge pressure gauge pressure tells you how much is the difference of the actual pressure as compared to the atmospheric pressure for example imagine just for an example the pressure of the gas is 1.2 atm and the atmospheric pressure is or let's say at that location is 0.9 atm possible right possible you are on the hill station so the gauge pressure the gauge pressure is basically 0.3 atm this is kind of an excess pressure how much more than the atmosphere do you know one interesting fact that when you fill air in the tube of your vehicle tires which pressure do you measure when you fill air in the tube of your vehicle tires which pressure do you actually measure yes gauche pressure can be negative also it can be negative it can be zero the pressure that you always refer to is the gauge pressure why gorge pressure because every place might have different pressure somebody might be staying at the hill somebody might be staying near the sea somebody might be staying near a hurricane somebody might be staying in some random location so everywhere there could be different climate so to standardize it we define relatively so if the atmospheric pressure is this much you need to have this much excess pressure that's it it's a standard so you always talk with respect to the atmospheric pressure that's what is used to fill the air in the tubes of your vehicle tires very very important perfectly yep i don't know what you are saying all right so here we have a question right up on your screen to immiscible means they do not mix like oil and water yep but fanta and coke that is miscible okay so two immiscible liquids having different densities are filled under youtube as shown comment on the pressure add a b c d f look at this this is a different liquid this is a different liquid come on what do you guys think is that that that's it that's a manometer so what does the magnemite i do it measures gauge pressure what is a barometer to actual pressure keep this in your head barrow measures actual atmospheric pressure manu measures difference of the pressure the relative pressure that's it okay okay so what do you guys think oh no no no comment means which one is more which one is less so pressure at point a pressure at point b pressure at point c pressure at point d pressure at point e pressure at point o f what symbol should i put over here more or less equal to that's what the question is it's not about c and d what should i put for let's say e and f or a and b now the logic for solving immiscible liquid problems remember this i'm teaching you a trick so what is the trick whenever you see okay immiscible liquids okay immiscible liquids in a youtube in a youtube what you should do start start this is the trick start from start from bottom what you should do always start from bottom very very important because when you start from the bottom you generally will find the same liquid over here do you see the same liquid this light greenish color light greenish color liquid and it's the same liquid so the pressure should be same so e and f should definitely have the same pressure obviously as you go up in this liquid this point this point same pressure this point this point same pressure this point this point same pressure this also same pressure this also same pressure c and d yes we are technically still inside the light green liquid so c and d should also have the same pressure got it my warriors perfect now comes the problem as soon as you go up as soon as you go up over here here is the problem yeah see you are going in a different liquid here you are going in a different liquid that is the problem my warriors so here the pressures won't be equal that's very important in spite of being at the same level so lot of people think just because two points are at the same level the pressure should be equal that is incorrect my dear warriors the pressures are equal at the same height if it is in the same fluid the fluid is the same here cd ef that's why they are equal but a and b they are not equal got it so that's the condition a lot of people make that mistake i wanted you to point point out this to you okay now the question is a numerical one a similar concept two immiscible liquids heights are mentioned the blue one is density row two the green one is density row 1 the common line also has been drawn question is find the ratio of the densities yep does it have to be of the same vessel basically i am me oh my god what is this i am me the thing is it should be a continuous liquid doesn't matter uh whether it's same vessel or not even if the vessels are different as long as there is a pipe connecting it if you have a connecting path then it works okay perfect let's have a look at this now two immiscible ah liquids are there and the densities are given the question is what is rho 1 by rho 2 we know that this point a and this point b will have the same pressure just from the previous logic so pressure at point a will be pressure at point b because this point and this point are in the same liquid at this point the pressure will be assuming atmospheric pressure to be p naught it will be nothing but p naught plus rho which is rho 2 into g okay g is g h is 4 h fair enough pressure at point b will be again p naught plus rho is rho 1 g is g h is 2h interesting thing p naught p naught goes wow gg also goes wow h h also goes wow so 4 row 2 is equal to 2 row 1 so row 1 by row 2 is 4 by 2 which is 2 by 1 which is just 2 then the nardon s and v18 perfecto gauge pressure ravi shake it means the pressure difference between pressure in a container minus outside or atmospheric pressure so the difference of the pressure inside the container minus the pressure outside or atmospheric the difference is called as the gauge pressure so all those of you are joining in late make sure that you watch the complete class after this okay that's it very good calm killer that's the spirit that's how you should help all the new warriors who are joining in and yes thanks a lot for smashing that subscribe button and thanks a lot for also loving this video and helping us grow it means a lot when you hit that like and you hit that subscribe button there we go find the force on the bottom surface of a container due to the liquid neglect atmospheric pressure density is rho look at this container do you see height h width w length l there is a liquid filled till this much point what's the force on the base so we are shifting to the forces on the walls of the container should we take atm pressure always yes definitely always always it will come okay now here the question says find the force due to the liquid so this liquid will apply some force on the base of the container this is how the base of the container will look like and there will be obviously some pressure over there so it will be exerting some force definitely on it correct that force the force on the base can be written down as pressure on the base into the area of the base now when i write pressure on the base there is one small catch many students make a mistake pressure on the base is not p naught plus rho g h it is just rho g h why because it says due to liquid only due to liquid see if the container was empty anyways the base would experience p naught agreed if the container was empty on the base i air would still exert that force so when you pour that liquid that extra force comes because of whom it comes because of the liquid so because of the liquid it is just ogh got it my warriors got it my warriors perfecto into area what is the area of the base w into l that's it rho g h w l do we have it yes we have it in option c perfect a b arjun done very good now we have a slightly modified question what is this find the force on one of the side walls due to the liquid side walls that's the catch sidewalls okay i'm not going to look at the options it's not needed let's just solve it independently sidewall could be something like this over here just going to mark this over here okay this is the side wall on this because anyways the air is there on the top liquid is only there at the bottom so only this much part is going to experience force hmm now i have a problem you know what my problem is no you don't know what my problem is my problem is i cannot say force on the wall is pressure into area like so why the pressure is not same why is the pressure not same yeah the pressure will change with depth right so pressure is different so over here the force will be less pressure is less at the bottom the pressure will be more and as you go deeper and deeper the force is going to increase the pressure is going to increase so it is going to be a varying diagram so the force will be different at different places like you see over here correct something like that like how the dams the shape is wider at the base so that means i need to account for the variation of pressure so what i'm going to do i'm going to divide it into small small strips yep no no viscosity you know you have to just divide it into small small strips so let me just consider a strip right over here okay so imagine a strip right over here okay just going to assume this as a strip so imagine this is the strip that i have chosen on that strip everywhere the pressure is same because it is at the same horizontal level that strip okay it's at the same horizontal level so the pressure is same so i think i can calculate the force on that strip and i have multiple such strips right from the top to the bottom if i add all the forces on all sorts strips if i add the forces on this this this this all the strips i will get the total force on the net container as well yes roshni you got it integration so i first need the force on the strip i just need the force on the strip the strip force will be the pressure near that strip into area of the strip interesting i don't know any values let's just assume certain values like for example let's just say this is depth let's say x if that is x this width will be dx are you getting it if that is x that is dx if this is y that is v y so that's how it works x is the depth dx is the width this is the length of the strip so think what should be the area of the strip what should be the area of the strip the width is dx length is l so it should be l into dx do you get that why is the area height into the length that's it fair enough all my warriors perfecto shall we go ahead now what is the pressure add to that strip due to the liquid only don't take into account because it just says due to liquid don't take it to account the atmospheric pressure hi sundar so it is just going to be rho g x rho g x rho g depth no p naught over there that's it so this is the force on the strip and since it's not just f it will be dn why this decay because it's a small teeny mini force on a small strip there are many such strips so the net force on the vertical on the vertical wall is basically the sum of forces on all the strips that means it is integration of df that means it is integration of these guys rho g x l dx okay let me just show these people away who are constants like rho g and l are constants x dx i need to integrate with respect to x how does x vary look at this the strip starts from the topmost point the strip starts from the topmost point so x is zero and the last strip that you take is at the bottom it is at a depth of h so the first strip is when x is zero the last strip is when x is h what is the integration of x dx x raised to 1 integration is x raise to 1 plus 1 by 1 plus 1 x raised to 1 plus 1 is x raised to 1 plus 1 2 and the limits are 0 and h so therefore the net force will be i am just going to do it over here it is rho g l and you will have h square by 2 minus 0 square by 2 that's how you do the integration right put the this is definite integration you put h over here then you put 0 over here and then subtract both of them so this is just going to be rho h square by 2 this is the force acting on the wall rho g l h square by 2 what a brilliant question perfect o swiss t very good roshni excellent arjun you guys got the limits so that's how you involve integration as well in fluids and that's the answer option a now i have posted some homework questions just for you so you have to post all the answers in the comment section i'm going to read all the names next time so this is the first homework question do not forget to solve and post it asap oops should not be shown oh my god why was the answer shown ignore okay i cannot help it now now there's a very special announcement in fact i have two announcements for all of you okay uh one of the announcement is the announcement of an announcement which is going to happen tomorrow so yes i'm going to announce certain interesting things and yes there is something in store for even the 11 standard students 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thousand rupees per month that's how it works so i would be really looking forward to all of you because you will be joining my courses as well at prices as low as 1350 rupees 1800 rupees and 2700 rupees these are much more affordable than your regular coaching centers thank you guys very much for being here do not forget to post all the answers in the comment section i'll be reading out all the names next time and remember stay tuned for the term 2 syllabus yep because we have to eventually target the g2023 get your friends see you again and again at 7 o'clock that's my new timing thank you very much for liking and sharing and also hitting the subscribe button you can also get in touch with me on my instagram handle stress underscore with antu take care bye bye nivi bye bye calm killer roshni take care bye bye uh septima's heap take care everyone have a great time production have a lovely time stay safe stay cool stay calm and keep studying bye bye abhishek take care good night bye shalom this was your captoshia signing off bye bye hasta la vista