Course Introduction, Fluid Properties, Elasticity - ENGR 318, Class 1 (24 Aug 2021): transcript

hi everybody i'm dr waite i am the instructor for engineering 318 fluid mechanics and today's class meeting and the class meeting for thursday is going to be delivered over the internet as a recorded video unfortunately i'm out of town and not able to be with you in person for the first week of class but we'll be back together face to face in our normal classroom location and at the normal class time starting next week what i'd like to do is go over a couple of announcements and then share some important information about the course with you so this class meeting is for the 24th of august that's a tuesday and i'm going to include one of these announcement slides at the beginning of each of our class meetings just to help make sure that we're all on the same page in terms of scheduling and due dates and that sort of thing the first thing that should be at the top of your mind if you haven't already obtained a copy of the textbook is to purchase or rent that it's engineering fluid mechanics 10th

edition and i'll show you the author and isbn when we're going through the syllabus in just a moment as far as submission deadlines go there's an introductory assignment that's available now on blackboard and that's worth 10 bonus points i don't give very much bonus credit through the semester in fact this is it so if you want to accumulate just a little bit of a cushion for your grade this is the way to do it it's a pretty easy assignment it's just kind of some getting to know you questions and so if you'd like to participate in that please submit it before noon on friday the 27th and you should upload your file that's responding to those questions to blackboard it's through blackboard that all of the assignments this semester are going to be submitted just to put it on your calendar the next real assignment of the semester homework number one that has to do with problem solving that should be submitted before class meaning before 11 a.m

on thursday september 2nd okay so we're going to go over a few matters of you know practical matters related to the course and then we'll get into some technical content related to fluid properties and elasticity so let's look at blackboard and just review some of the material that's available there right now first of all i wanted to point out that the lecture notes are posted already such that if you'd like to print a copy of the lecture notes and have them available as we go through the course then you're certainly welcome to do that and there's a variety of different formats available for instance if you want to print out the notes so that there are three slides per page with a little bit of free space on the right hand side for you to take your own notes that's an option if you want to save a little bit of paper and print fewer slides then here's six per page with less room for note taking so you can choose whichever of those works best for you i'd recommend that you print it

out maybe consider putting all of these materials into three ring binder the next thing i'd like to show you is the homework assignments that are there for the semester i need to rearrange this one that here's the homework zero down at the bottom let me just go ahead and drag that up to the top while i'm thinking of it all of the assignments for the whole semester are posted right now i don't expect that anybody will want to work ahead but at the very least you can see what the due dates are and get an early look at those assignments if you choose so this introductory assignment which is a an easy getting to know you type thing with a couple of short answer questions let me drag that over so you can get a look at what that is all right so it's just you know tell me a few things about yourself tell me what fluid relating engineering problems are there in this part of the country what classes you registered for that kind of thing pretty

straightforward i think all right so that is due as you can see before noon on friday the 27th and at noon this will become invisible so that you won't be able to submit the assignment any longer as i am going to point out in just a minute i have a pretty strict policy as far as late work goes and that is the assignments need to be turned in on time and i don't accept late work unless you have an official university excused absence and so if you've just simply forgotten or lost track of time please don't contact me asking permission to submit the assignment late because the answer will be no perhaps the most important thing that you could print out and have available would be our course schedule and i say that because here on the course schedule you can get at a glance all of the things that we're going to be doing through the semester such as what is the topic of each of the class meetings that we'll be having and you

can note that some of these are indicated as online classes and you know the first week is going to be online and there are a couple more through the semester where i'm not going to be able to be with you in person so we'll do a pre-recorded lecture you can see the assignment due dates in most cases the due date will be before class on the date that it's indicated so for instance homework number one it's due before 11 o'clock on thursday september 2nd homework number 2 is due before 11 o'clock on thursday september 9th and so on you can see which book chapters relate to certain parts of the course so that you're able to follow along in your reading and then you can see what are the topics of the accompanying labs that go with civil engineering 319 which is a co-requisite for this course so i would encourage you to look through this schedule it has everything for the

semester including thanksgiving and even the date and time of our final exam at the end of the semester all right so that's the schedule the syllabus we'll take a few moments to go through a few important points of the syllabus i'll ask you to read through the entirety of the syllabus on your own but i did want to point out for example that my office location is indicated on the syllabus as well as my telephone number my email address and then my office hours so i have office hours on monday wednesday and thursday from 1 to three and i'd be happy to talk to you at other times you can always reach out to me on microsoft teams or give me a phone call or stop by in person and if i'm available i'll be happy to help you if you send me email i'll also do my best to respond in a timely manner there's important university policies

related to covid19 and i'm sure that you will have already received a variety of emails reinforcing the university's expectations as far as that goes and so i won't reiterate that other than just to say i plan to follow the university's covet 19 policies and hope that you'll respect that here is our textbook information the title is called engineering fluid mechanics 10th edition so it's by clayton crowe and here is the isbn there are more recent editions of the textbook than that but i choose to stick with the older edition to help keep the cost down because the newer editions are only available in an electronic or a loose leaf format and the publisher does that because then you're not able to sell it back at the end of the semester and i just find that the durability of a normal printed book if you want to keep it is better than an e-book or loose leaf and if you don't want to keep it i'd like to give you the option to sell

it back or to rent the text so that's why i've stuck with the 10th edition the material is essentially the same and i think it works out for you from a business perspective here are the outcomes for the course and you can see here are each of the course learning outcomes and how each of them is practiced during the semester and how they're assessed and so these are just the things that you will know how to do by the end of the semester and they relate to a lot of the topics that you would find as you go through the schedule my grading policy is that the grade is determined on the basis of your homework assignments 25 and then three exams during the course of the semester each of which are weighted as 25 percent of the grade and you can go into the grade book on blackboard any point in the semester and see what is your weighted average and so if you ever want to know what's your grade you can just go straight to

blackboard and you'll find it there i do have a little bit of flexibility when it comes to homework and that is i drop the lowest grade when i'm calculating the average of your homework assignments so if you accidentally forget to do one of the assignments or turn it in or you know forget to turn it in on time then that won't affect your grade because you're able to drop the lowest assignment of the semester and of course i already mentioned my late work policy and that is that it's not accepted unless you have an official university excused absence and so the way that you get one of those is you go to student affairs with your medical note and then they would evaluate whether it meets the acceptable standards i'm not going to be taking attendance but i expect students to attend and participate in classes now the academic dishonesty policy is important so i wanted to spend a few moments talking about that

my expectation this semester is that anything you turn into be graded is your own work and that you're not copying another student or you're not using something you found online as the basis for your solution you should figure out how to solve the problems on your own or by asking me for assistance and it's okay to chat with other students and to discuss to discuss problems with them on kind of an informal basis but it wouldn't be okay if you stare at their paper and you copy down every step of what they did it's not okay if you go to chegg and you follow the form of a solution that you find there because if you do that you're not going through the personal growth and the mental strengthening process that you need in order to be successful on the exam and later on be successful in your career so i'd ask that you think carefully about the academic dishonesty

policy each semester it seems like someone doesn't take that seriously or forgets and then i end up having to penalize them for having cheated on their homework assignments so it's better to just not turn in an assignment than to cheat on the assignment because if you cheat on the assignment then you'd get negative points meaning a grade lower than zero so if you have any questions about my expectations after you've reviewed the entirety of this academic dishonesty policy please let me know and i'd be happy to talk about it with you a variety of other things in the syllabus here such as the academic environment statement where i ask that you arrive in class on time that you not play with your cell phone during class that you wait until class has concluded to leave that sort of thing the course schedule and so that is the syllabus that's maybe another thing that you could print out and include in the

three-ring binder that you're going to have that includes also your solved homework assignments and the lecture notes here is a link to the youtube channel where i have all of the class lecture recordings for the semester posted and i've got several previous semesters there as well and so you know if we looked at the videos we would find some from previous semesters but if you want to search for a particular class meeting let's say you're sick or maybe you're solving a homework problem and you want to go back and refresh your memory about a certain thing then you can search by the class number so for instance you could say 318 which is our class number class 7 and if you search for engineering 318 class 7 you'll see a couple of the previous semesters you want to find the one that's the most recent and then you'd be able to watch the lecture video for that so in videos they just appear chronologically but you can also search

for certain videos with that um magnifying glass all right so that's it for the course overview and if you have any questions about the policies or that sort of thing please let me know all right so for the rest of this recording what it's going to be is i'm going to be editing in the content related uh discussion and material that was recorded in a previous semester so it was the fluid properties and elasticity lecture from fall of 2020 and so there may be some incidental references to times or dates that don't quite match up but the material itself is the same from last semester to this semester and so i'll be editing that in and once again emphasizing that if you have any questions about the course material or the structure or anything at all please send me an email although i'm out of town i'm going to be doing my best to be responsive while i'm away so please

let me know all right well it was probably a long summer where you didn't spend a lot of time thinking about units and uh the difference between s i and traditional units much of this class i'm going to teach in the s-i unit system and i think that when you get a taste of what fluid mechanics is like with the traditional units you'll understand why a lot of the equations that we use to solve problems in fluid mechanics are just so much simpler if we solve in the s i system so you'll get a taste of that but let's just review some of the basics there are units of kilograms in si and the equivalent of that in traditional units when we're talking about mass is either pounds of mass or slugs and we'll review the relationship between pounds force pounds mass and slugs on a separate slide in just a moment

units of length is meter or feet inches yard mile and furlongs and all sorts of other bizarre stuff in the traditional units time is seconds in either unit system force in the s i a newton is when we want to accelerate one kilogram of mass at a rate of one meter per second squared so we're increasing its velocity at a rate of one meter per second in every second it requires a newton of force in order to cause that acceleration whereas in the traditional units it's a pound of force is the unit system and so it's kind of confusing because when somebody says a pound do they mean a pound of mass or a pound of force well if you're talking about the the force applied by a pound of mass under earth's gravitation then the two are the same but there are a lot of other

gravitational excuse me there are a lot of other accelerations besides 32.2 feet per second squared you know we can take a tank of water and accelerate it at any acceleration rate we prefer and so that's one of the reasons why it's a bit confusing to have the same name for both the mass and the force in traditional units gravity is about the same over the earth's surface it varies slightly based on your elevation but the unit that we're going to use for gravity in traditional excuse me in si units is 9.81 meters per second squared you know we'll use it just three digits of precision that's good enough for us in the traditional units i'm surprised i didn't write it it's 32.2 feet per second squared for the traditional gravitational acceleration all right so now this slide kind of gives us a bit of additional information

about pounds mass versus pounds-force um excuse me one second the air conditioner in this office is noisy but man it's starting to get sweltering in here it's probably like 85 degrees in this room um all right so in s-i units it's easy to know that a newton is a kilogram accelerated at a meter per second squared so if we want to know how many newtons are required you just take the product of the mass and the acceleration in the traditional units a pound of force is a slug that is accelerated at one foot per second squared and so what is a slug it's a strange name for a unit right so if you accelerate a slug at one foot per second squared that means it took a pound of force to achieve that acceleration

so a slug is 32.2 pounds of mass you know that that number of 32.2 hopefully that is uh seeming a little familiar because we were just talking about how gravitational acceleration is 32.2 feet per second squared so the way it works is that a pound of force is either a slug accelerated at one foot per second and so remember a slug is 32.2 pounds of mass so you can accelerate a slug at one foot per second squared and that's a pound of force or you know there's a whole range of possibilities but another of the possibilities is that you are accelerating a pound of mass at g where g is 32.2 feet per second squared so it's the same thing it's just you know um what acceleration are you using

so put a little star on this slide you know when you print it out we'll come back to the slide a couple of times through the semester when i'll i'll give you a problem that uses traditional units and you'll need to refresh your memory about what's a slug again how does that all work everything you need to know about the relationship between pounds mass force and slugs is here on this slide the weight is the effect of acceleration on mass and so it is the same as a force and so the weight of kilogram is 9.81 newtons in the temperature units we will often need to keep track of absolute units of temperature especially when we're doing gas law related problems you may remember back to your time in chemistry

using kelvin in the gas law calculations well here in fluid mechanics fluids encompasses both liquids and gases and so a lot of the calculations that we'll do works for both you can apply the principles of fluid mechanics to both liquids and gases and so sometimes the calculations will use kelvin and in the kelvin system zero kelvin is absolute zero the it's the absence of any kinetic energy in the molecules in question 273 is the freezing point of water so that if we want to convert between celsius and kelvin the relationship is that kelvin is 273.1 plus your degrees celsius and so the size of a kelvin degree and the size of a celsius degree are the same but they have a different zero point work and energy both of those have units

of joules and a joule is the amount of energy required to apply a newton of force over a meter of distance and then when we put a time component into that if we are doing a certain amount of work per unit time or exerting a certain amount of energy per unit time a watt is when you are exerting a joule per second or using a joule per second of energy so hopefully most of these units are familiar but you know we'll just begin with the basics and build from there quick refresher of the units that are going to be applicable for fluid mechanics so units conversion of course you could probably do many of these conversions built into your calculator and at the beginning of the textbook it also has units conversion between si and traditional units there's the foot conversion slug to

kilogram conversion foot pounds of force to newton-meter conversion conversion between foot pounds and horsepower of course we know 550 foot-pounds per second is a horsepower and that's equivalent to 746 watts as it ends up i don't expect you to memorize these conversions the conversion between the traditional and si units and temperature are a little bit tricky because the degree size is different when i was talking about kelvin and celsius what i mentioned there is that the size of a kelvin degree and the size of a celsius degree are the same but there that's not so in fahrenheit a fahrenheit degree is a smaller change in temperature so if it goes up by one degree fahrenheit that does not mean that it's gone up by one degree celsius it's only gone up by five ninths of a degree celsius if the

temperature increases by one degree fahrenheit and complicating mathers further is the differing zero point where water freezes at 32 fahrenheit and so if we want to convert between the absolute fahren excuse me the absolute units of temperature in traditional is raking and fahrenheit here is the formula for that so just for example to rest my voice for a minute to rest your brain from having to hear it let's pause for a moment and i'm going to encourage you during the semester to either have these notes printed out or have us a piece of paper handy and when i pause the lecture for you to work on an example go ahead go ahead and oh i'm hearing myself all of a sudden there did the connection drop for a moment all right well hopefully we're back now

um so i'm going to pause for a moment and what i'd like you to do is convert between 46 degrees celsius and what would that equivalent temperature be in raking so what you need to do is first of all convert from celsius to fahrenheit and then from fahrenheit into raking so see if you can do that with the information that's on the screen here uh and in a moment i'll bring up the solution on the slide and we'll we'll talk through it together take a look at why it was 574 degrees in dubai yesterday i don't know what the actual temperature was in dubai but that's not far off this time of year it gets hot over there all right so temperature conversion 46 degrees celsius first of all we have

to find out how many fahrenheit degrees that is and so we are converting for the size of the degrees and so 46 celsius degrees is the same as 82 fahrenheit degrees so that's just talking about how many increments can you see my finger how many increments there are you know how much the thermometer went up above the baseline now we need to add on the baseline which is the freezing point and in celsius that was zero but the freezing point in fahrenheit is 32 degrees fahrenheit so first of all converting between celsius and fahrenheit it is 114.8 fahrenheit in this example and i think i saw a headline the other day that they recorded 130 fahrenheit somewhere in death valley did anybody else see that a headline that's bananas

130 degrees so once we have the temperature in fahrenheit then we convert it over to raking just by simply adding so it's however many fahrenheit degrees there are plus 460 to get us to the raking so it's a two-step process first you go from celsius to fahrenheit then from fahrenheit to rakine all right next let's review some uh properties that are related to a system's mass or weight and um first of all when we talk about the density of a fluid what we mean by that specifically is the mass of fluid relative to the volume that is occupied that by that

fluid and so water for instance in one cubic meter of water the mass is at the standard temperature of uh i think 10 degrees celsius 10 degrees celsius is 1 000 kilograms so a cubic meter of water would have a mass of a thousand kilograms that's its mass density um a lot of people are familiar with the density of water as being one gram per centimeter we're going to be thinking in bigger terms you know a cubic centimeter is pretty small a cubic meter now you're talking some real water so density of a fluid is its mass divided by the volume so water at 10 degrees celsius is a thousand kilograms per cubic meter and that you know that's not coincidental that's kind of how they defined what a uh a kilogram was as they used

water as the baseline and and so they they set it so that it would be by definition a thousand kilograms per cubic meter or one kilogram per liter that's another you know a liter of water has a mass of one kilogram in the traditional units it's 1.94 slugs per cubic foot and that's not by definition that's just what it works out to be when you have uh you know some random amount of mass back in the middle ages it is was defined as a pound so it there wasn't you know it's not a unit system by design it's kind of a unit system by evolution whereas the si system is units by design specific weight is maybe something that you have maybe you haven't heard about it but we use it a lot in fluid mechanics this is really important and so we use the symbol gamma for that that's the greek symbol gamma and so it is the density multiplied by

the uh gravity that the fluid is experiencing and so it's the weight of the fluid divided by the unit volume and so in the case of water there are 9810 newtons per cubic meter at 10 degrees celsius and so that's the weight of the water per meter of volume whereas in the traditional units it's 62.4 pounds of water in a cubic foot that's pretty heavy right 62.4 pounds per cubic foot so that's specific weight so remember the relationship between specific weight and density is if you need the specific weight just multiply density by g so 1000 multiplied by g which is 9.81 that's where you get 9810 newtons per meter cubed i'm going to turn off that

air conditioner it's so noisy i think i'd rather roast than listen to it anymore i don't know if you could hear it but it was like a mosquito was inside my eardrum all right so one of the differences between liquids and gases both of which are fluids remember fluid mechanics encompasses liquids and gases one of the differences between those two different classifications of fluids is their compressibility and so just using one liquid and one gas as an illustration we know that water is not very well compressible some people call it incompressible but if you apply enough force it compresses a little bit just a little bit but so water is not very compressible but air is really compressible and so that's one of the ways that we can

distinguish between fluids and even though water is relatively incompressible that doesn't mean that its density is always the same because we could change the density of water depending on whether salts are dissolved in it and of course the density of water also varies as a function of temperature so both of these times when i was talking about the mass density and the specific weight you'll notice that it was saying what temperature that was at and so i'll show you a slide in just a moment that shows the effect of temperature on density and how fluids expand as they get warmer above a certain point so here's one more term that you need to be acquainted with and it'll just roll off the tongue and it'll be at the forefront of your mind through the entire semester because it's such an important and foundational concept specific gravity often abbreviated sg

is the ratio of some fluids either density or specific weight relative to the density or specific weight of water so for instance you know the oil floats on top of water right it's less dense than water that's why if you have a container of oil and water and you shake it up then the oil will separate to the top and the water will be down beneath it's because the oil is less dense and so from that if you divide the density of the oil by the density of water then you'd have a specific gravity of less than one so a typical oil density might be 750 kilograms per cubic meter well if you divide 750 kilograms per cubic meter by 1000 kilograms per cubic meter which is the density of water then that would give you a specific gravity of 0.75

so specific gravity is just a ratio and when it's greater than one it means that the object or fluid is more dense than water and if it's less than one it means it's less dense so it can give you a hint of whether the thing will float or sink in water any questions about these concepts of density weight and specific gravity when you repeat what you said about the ratio yep basically let's say that oil has a density of 750 i wish i could write on my screen more easily but i don't have one of those touch pad screens so if you have an oil where the density of the fluid is 750 so say 750 divided by the density of water which is

1000. so 750 divided by 1000 would say sg is 0.75 and so when the sg is below 1 that tells you that the fluid is going to float because it's less dense than water but if the sg is greater than one then that tells you that the fluid or the object is going to sink because it's more dense than water are there other questions okay now here's that table i was mentioning earlier it shows the the relationship between temperature and both density and specific weight so in a homework problem or on an exam

if i tell you what the temperature of the fluid is then you should look up its temperature specific fluid properties so if i tell you that it's water at 50 degrees celsius then that's a hint that i want you to use either the density or the specific weight at that certain temperature but if i just say water and i don't tell you what temperature it is then you can use the temperature that the typical density or specific weight for water and by the way the term specific gravity and specific weight remember they're not exactly the same because specific gravity is the ratio of specific weight of a fluid to the specific weight of water so don't confuse specific weight and specific gravity the gravity one is a ratio sometimes specific weights called unit

weight okay so you can see that what the relationship is is that fluids become uh less dense as they get warmer so the maximum density is at about five degrees celsius and depending on the charts like if you have a really detailed chart like this sometimes it'll show that the density at zero celsius while it's still a liquid is a little bit lower than a thousand this table maybe isn't as completely accurate as it could be it's at four degrees celsius that water has its maximum density of one thousand kilograms per cubic meter but then as it warms it becomes less dense the same trend is true for air that air density and specific weight vary as a function of temperature all right so the last thing we're going

to talk about today is elasticity and the effect of a change in pressure on a change in volume so earlier i mentioned that water is generally considered incompressible and with air quotes i don't know if you can see my fingers there we go water is incompressible that means that if you apply really a tremendous pressure to water it will contract a little bit and so the relationship that describes the volume change and a pressure change is called the bulk modulus of elasticity and so this is a this is a fluid property that says how much of a pressure change is going to cause a fractional change in volume and so a volume relative to its initial fluid volume and so here in the

numerator of this ratio you can see the pressure change from before and after and so dp just means the change in pressure so before this new pressure was applied versus the after the new pressure is applied and then in the denominator of this you can see is the in the denominator denominator of the ratio is a ratio itself the fractional volume change and so what this means is that down here in the denominator you need to have the the amount of volume change relative to the initial volume that was occupied by the fluid so maybe you had an original volume of some defined amount and we're going to work an example here in just a moment you know initial volume of 50 liters and then you know that you want to calculate how much volume is going to be

occupied afterwards you could solve this with the known bulk modulus of elasticity for water you could solve for the unknown dv all right so kc is typed a question here can water compress itself you have a deep enough tank with enough water in it will the water exert a great enough pressure on itself to experience a difference of density from the bottom to the top um that's an interesting question and we can calculate that after this example because we can look up where is the deepest point on earth it's in the marianas trench it's called challenger deep so let's find out what is the depth of challenger deep and then we'll calculate what's the pressure at the bottom of challenger deep and then we'll see is that enough pressure that it could cause a meaningful change in volume i think the answer is no i don't think there's enough pressure

like in a natural environment like that i think it has to be like an artificial environment where uh an engine or like uh you know we're creating additional force but we'll we'll crunch the numbers on that all right and uh jeremy asks isn't that how ocean pressures change in relation to depth no that's a good question but ocean pressure changes differently than this bulk modulus of elasticity this bulk modulus of elasticity does not describe the change of pressure with the change of depth it's a separate concept that we will get to all right so jeremy looked up the depth at the bottom of challenger deep it's 10 kilometers boy that's deep are you sure 10 kilometers no you set up zero two 10902 one zero nine two nine we'll look it up all right before we get

into challenger d ten kilometers all right so let's do this example uh let's say that we know the bulk modulus of elasticity is 2.2 times 10 to the ninth giga 2.2 times 10 to the ninth pascals so that is the bulk modulus of elasticity for water that is a constant fluid property that describes how much of a change in pressure is going to cause what change in volume so with that we can rearrange this equation for bulk modulus and the way that we can think about it if we rearrange that equation is that the bulk modulus is describing the change in pressure and the change in density of the fluid okay so here's this example we have 50 liters of water that's our initial volume of fluid so this v with the line through it you may be wondering why did i put the v through with the line through it

well we're going to use the letter v a couple of different ways this semester and without the line through it that is velocity uh with the line through it that means volume and you know sometimes i'll get sloppy and lazy or forget not you know won't put the line through it but like when we're being really precise and we want to you know classify whether we're distinguishing between volume or velocity the v with this line through it means volume all right so in this example you've got your scratch paper there in your scratch paper you've got that the initial volume of the fluid is 50 liters and it's initially open to the atmosphere and so then the pressure change of 5 megapascals is applied so 5 megapascals is 5 times 10 to the 6th pascals so if you rearrange

this equation this equation here rearrange it to solve for delta v then let's find out how much does the volume decrease and by the way i neglected to mention earlier why there's a minus sign here in the equation that's to kind of indicate the directionality of an increasing pressure causes a decrease in volume so i mean it's it's obvious if you think about it that you know when you're compressing the liquid it's going to reduce its volume but that is made explicit with the minus sign in the equation there so in this what i'd like you to do is here we're given the bulk modulus we are given the initial volume we want to solve for delta v so i'll pause for a moment and see if you can calculate what is the change in volume and therefore what is

the final volume so delta v and then compare that to the initial volume and find out instead of 50 liters how much space will that water occupy after we apply this pressure i generally will pause the recording for those moments where i'm not talking just so that if you are watching at home you know you can pause it and then when you work through the calculation you can resume it again all right so i have the solution here eric's got it 49.8 liters right so what we did was uh we started with the original equation for

the relationship of bulk modulus incremental pressure change and unit change in volume and uh rearranged that down here to solve for the change in volume so you can see once we rearranged that then i substituted in the the given pressure that's applied to 5 megapascals applied the initial known volume of 50 liters the bulk modulus of 2.2 times 10 to the ninth and so what that tells us is that 50 liters of water is going to have a volume reduction of 0.114 liters so that's not very much 50 liters of water just for perspective i don't know that's like uh a trash can is about 50 liters of water you know like a standard curbside trash can and so it's going to go down by a tenth

of a liter and you know a tenth of a liter is you could swallow that really easily you know like that's um this water bottle is 500 milliliters and we're talking their reduction volume is only 100 so it's you know a fifth of this bottle of water is how much it compressed when it started off with the same amount of water that you'd find in the trash can so that's the final volume 49.88 because what we do is we subtract the change in volume from the original given volume all right so any questions about that all right now as to can the pressure at the bottom of the ocean compress the water as it turns out after running the numbers i think the answer is yes and let me show you why now we're jumping way ahead into the course to

to address this question but because it's interesting and because we've got the time let's go ahead and do it anyway um there is an equation called the hydrostatic equation that we're going to learn later in the semester and with apologies for my sloppy handwriting here's how things work in the hydrostatic equation what we're talking about is the change of water depth is 1000 excuse me 10 000 meters and did i have that right that's challenger deep the depth of let me just google that challenger d [Music] yeah 36 000 feet so that's at least 10 000 meters right in meters 10 984 so that's even more than i've written but let's just say for sake of argument if you go 10 000 meters down into the ocean what is the pressure there so the breath

the pressure 10 000 meters down into the ocean this hydrostatic equation is you multiply the unit weight of the water which is 9810 newtons per meter cubed if you multiply that by the depth then that will tell you the pressure at that depth and so if you go 10 000 meters down into the ocean the pressure is 98 megapascals so let's go back to our example the example that we just solved it was 5 megapascals of pressure and so like what was the percent reduction in volume here like if we calculated on a percent basis we saw 0.114 liters out of 50.

multiply that by a hundred it's basically a 0.2 percent reduction we'd see more than that it you know that's very little reduction in volume a very slight increase in density but uh i think that down at the bottom of the ocean yeah uh you know if we saw a reduction from five megapascals you're certainly going to see a reduction from 98 megapascals so if you go down to there bring enough submarine for sure all right