Fluid Viscosity - ENGR 318, Class 2 (26 Aug 2021): transcript

hi everybody all right time marches on this is class number two for fluid mechanics this lecture is intended for thursday the 26th of august once again i apologize that we're not able to meet in person this week but we will be back to our normal class location and normal class time and meeting face to face on tuesday of next week let's go through a couple of announcements remember that it's important for you to get a copy of the textbook now the assignments that you're going to have this semester are largely ones that problems that i myself have written so you're not going to use the textbook most of the time for homework problems but it is an important source of information the author can explain things with a different perspective than i can and so i really think it's worth your while to rent or buy the textbook the introductory assignment that getting to know you short answer type uh

assignment is due before noon on friday the 27th and so please upload your responses to blackboard before then in order to get the 10 bonus points and then looking a little bit further down the road homework number one which you can look at right now on blackboard that should be submitted before 11am on thursday december excuse me thursday september 2nd so we'll have some office hour opportunities and a chance to talk over those homework problems before you need to turn it in but i just wanted to put it on your radar so that you can look a little bit further down the road the topic of today's lecture is viscosity and gas laws and so the rest of this presentation was recorded in an earlier semester but the material really remains the same i'll just uh before starting with that remind you that although i'm out of town this week i still would be happy to try and address your questions by email if you want to send me an s a message and

then next week i'll be back to my face to face in person office hours i wanted to point out that next semester i'm going to be throwing this slide into my presentation you may remember that we had a discussion about whether at the bottom of the ocean water compresses itself because of the weight of the water above the bottom of the ocean and i thought that was a really interesting thought question and so you know i learned from your great questions sometimes i learn you know what's interesting to students and how can i be more thought provoking and so i'm going to throw this slide in next semester and i just wanted to illustrate that you know even though we're talking remotely right now it still is possible for us to have a good interactive experience and so i appreciate the questions when you've got them it it makes it more easy from my perspective to teach okay now

this is a photograph and does anybody want to guess what this is a picture of is looks like honey to me it looks like what honey honey good that's right and what are the clues that that's honey there are bubbles trapped inside it as it's flowing good very good and so seeing those bubbles what does that imply like if if this was water we wouldn't see those bubbles so what does it mean when you have the bubbles they can't rest they can't readily escape good and so there's something about this fluid that makes it so that uh the air bubbles can't escape another interesting thing is if you look at the taper can you see my cursor it's never clear

to me whether students can see my mouse cursor i guess you can yeah i can see okay good that's a must be a new feature for blackboard collaborate ultra because in the spring students couldn't see my mouse cursor but you can now so another clue that this is not water besides the color obviously another clue is if you look at the taper there it's kind of if this was water it would be going into individual droplets you know the water accelerates fast enough it speeds away from the spoon as you pour it out of the spoon that it wouldn't be cohesive and pouring out into a sheet like this appears to be all right so there's something about this fluid that's a little bit different from water let's watch a video clip that also addresses the same issue all right so i have ah here we go bring it into full screen mode here i'm

going to mute it and all right so fluid on the left fluid on the right something's different the the person is shaking these two different fluids they're both clear there's the same amount they're in the same kind of container but when you shake the one on the left it sloshes around easily the one on the right doesn't slosh around so when you're shaking the container you're applying a force to the fluid when you apply the force to the fluid on the left the fluid responds to that force and so it's deforming the the force that's applied is causing the fluid to deform relatively easily it seems like but the fluid on the right isn't deforming as much you're applying a force but it's not sloshing around okay now let's see what happens if you

pour it the fluid on the left which is water pours easily the fluid on the right which is glycerin it pours really slowly that's thicker than honey it's thicker than syrup just looks so delicious i want to put it on a stack of pancakes glycerin and pancakes it's a winning combination so this illustrates the principle of viscosity so let's talk about viscosity in detail now to understand viscosity we have to define some terms here you may remember from previous courses that you've probably heard the word strain and so strain is the deformation of a physical body under the action of applied forces so we just saw in the picture forces being applied and the fluid deformed but solids also can deform when you

apply a uh stress i wonder if i have my ruler in here i do brilliant all right so i've got this metal ruler i don't know if you can see the uh the picture of me it's probably pretty small down there at the in the bottom of your screen but i'm holding up a metal ruler and if i press on that metal ruler i'm applying a force right now and it's deforming can everybody see it's it's formed into an arch now it's not moving anymore it's stationary but i am still applying a force so right now um the physical body is deforming and the strain is that deformation under the action of the applied force so a solid has this proportionality factor between the shear stress applied and the shear strain so the stress is the force the strain is the deformation

and the relationship between the two is defined by shear modulus so this is how do you think it would be different if this was titanium maybe we don't know a lot about pipe about titanium but maybe you do what do you know about titanium compared to steel it's more brittle it'll probably break it's more brittle um it would resist the deformation you know if i applied this much of a force i think it probably would but well if it deformed this much it probably would um break but just think about my my weak little fingers my weak engineer fingers i couldn't break a titanium with these little weak fingers but what would happen is it just wouldn't deform as much if this was like titanium so steel it deforms a lot titanium it deforms a little bit so there's this material property the relationship between

the stress that's applied and the strain that is experienced by that solid the proportionality factor is the shear modulus well there's a similar thing in fluids in a liquid that proportionality factor is called viscosity and the difference between one of the many differences between a liquid and a solid is that in the case of a liquid it continues to deform as long as the shear stress is applied so an example of that is if you put a propeller into a tank of water the water is going to continue to deform as long as the force is being applied whereas in the case of a solid it only deforms it stops deforming even though you're still applying a force and if i want it to deform more i have to apply a greater force but a liquid will continue to deform and so it stays in motion as long as the stress is applied so

the the reason why i compared the solid and the liquids is just so that you kind of understand that there's an analogy here the analogy between stress and strain in the solid and stress and strain in liquid we're going to look at some figures i hope that will will make this a little bit more clear gavin asks is there still a yield stress when dealing with liquids no there isn't all right so one of the principles that um that one of the applications of viscosity is the fact that a river has a different velocity at the top as it does at the bottom so we have a river here in huntington the ohio river and you maybe have noticed that when you look at the top of the water the water can be it looks like it's moving pretty quickly but if we went down to the bottom where the water is in contact with the

soil the velocity would actually be zero so when we talk about the velocity of the river there's not just one velocity there's a whole distribution of velocities there's a spectrum and um here is a velocity distribution and what it shows is that if we are down here at the bottom of a uh stream the velocity is zero but as you go higher up and further away from the bottom of the stream the velocity is increasing and so up at the top of the water the velocity is higher and so this slope d y d v is just how quickly the velocity is changing with an increase in depth so let's watch a video clip that introduces this idea that at the bottom

of flow where the water is in contact with a stationary solid the liquid velocity is zero all right now this is a little bit murky it's maybe hard to see what's going on so i'm going to explain it before i play the video i'm going to give you a sense of what we're actually looking at this is a straw so there's a straw that's going down into a flume and most of you went into the fluid mechanics lab this week and in the back of the room there was that big long channel you can think of it as like a a big plastic um it's like a plastic simulation of a river so there's clear acrylic on either side and then the bottom of it is plastic and so you're putting water down this channel and it's similar i guess to a rain gutter think about the rain gutters on your house it's just a long rectangular channel that carries water so in this case what's happening is that water is flowing

from the right to the left well i don't remember what direction the water is actually flowing we'll see so this is a straw and it's going to be injecting a dye and we're going to see what happens to the dye that's being injected okay so they're going to put the straw down at the bottom and right now that straw is touching the bottom of the channel so think about it's a simulated river and this straw full of dye they inject a little bit of the dye so can you see the green tracer so they're injecting some of that green tracer and so it's like a big blob of dye and it's not sticky it's a water soluble dye so it's not like it's glue or anything like that but it will stay at the bottom because the velocity down there is essentially zero now when you take the straw back up into the rest of the stream you can see that these ripples and turbulence kind of indicates that the water is flowing from the right

to the left and so the dye is acting as a tracer but there's still this big clump of dye down at the bottom because the velocity of the liquid is zero but when they put a spoon down in there and stir it around the dye goes away because you finally put enough velocity to make it go downstream so that's just an illustration of the no slip condition so the question is can it be assumed that the farther away the liquid particle is from the stationary surface the faster it goes yes that's a great question and yes that's the correct observation and this velocity distribution is kind of an illustration of that effect the farther away you get from the bottom where you have the no slip condition no slip boundary that just means that the bottom of the river isn't moving the base the bottom of the river is stationary and the farther away you get from the bottom the faster the liquid is because

that that solid surface down there is applying a resistance to the movement of the fluid all right so if we define some of the terms would this not be experienced on the sides as well yes it would be experienced on the sides so that was like a clear plastic acrylic on either side and you're right it's not just the bottom it's any place that the water is in contact with it's going to have that no slip boundary it's always true that the farther away from the stationary surface the fluid particles are the faster they'll be moving yeah okay i understand your point yeah you're right because for example the spoon when the spoon went down to the bottom and they he was swishing the spoon back and forth well then that's no longer true that that's the lowest velocity so there are you know like if you have external interventions like a propeller or the spoon then you can uh defy

this general velocity distribution trend okay so um viscosity is the resistance to flow remember when you had that glycerin in the uh in the beaker and it was being shake back and forth uh and it was resisting flow flow is the response to the forces that are applied and viscosity is re resistance to that deformation so in this figure v is velocity y is the distance from the bottom which is the no slip condition and then mu is viscosity and sometimes we call it absolute viscosity sometimes we call it dynamic viscosity those two things mean the same absolute viscosity dynamic viscosity those are two different names for the same

uh the same exact thing and sometimes we just call it viscosity so any three of those terms are interchangeable and it has units of newton seconds per meter squared the shear stress is the force that's applied per unit area and so if you think about the units of shear stress it's going to be force per area and so shear stress the relationship between shear stress the deformation and viscosity is this equation that's shown on the screen here so remember what i said earlier is that viscosity is the proportionality factor between the shear stress that's applied and then the response of the fluid so shear stress is force per area

and then dvdy is the rate of strain dvdy is basically how quickly the velocity is increasing the further away you get from the boundary so think about this velocity distribution right now let's say this figure is a river of water what if it was a river of pancake syrup well that would be delicious but what we know about pancake syrup is that it has a higher velocity viscosity than water does and so there wouldn't be as a steep a curve if this was pancake syrup you'd have to go further away and maybe the velocity would just be a little bit higher so it wouldn't be deforming as readily if it had a high viscosity so you can think of it that way another illustration example is just thinking about the fluids that you walk through

it's easy to walk through air but if you're in the swimming pool and you're trying to walk it's not as easy you can't walk four miles an hour through a swimming pool because the fluid is getting out of your way not as readily as air gets out of the way when you walk through air it deforms out of the way really easily now if you're driving a car at 100 miles an hour there's some serious wind resistance there the fluid is deforming and it's applying a resistance force but it doesn't require a very big velocity to have some resistance force through a more viscous fluid like water so water has a higher viscosity than a gas like air so why is it easier to walk through air because it has a lower viscosity so there's less friction you can think of it as resistance or drag force because of the viscosity of the fluid another way to think about it is that

it's deforming at a higher rate than water can because the viscosity is lower so back to this formula if you have a low viscosity then you can have a large dvdy for a certain amount of shear stress that's applied so for you know you're applying a shear force to a fluid a low viscosity will give you a big dvdy then if it's a big viscosity so if mu is large because it's pancake syrup then for the same force the rate of strain has to be lower air moves out of the quick rate when you apply a shear stress water and other liquids that have a greater viscosity will move out of the way more slowly so here's that equation again shear stress is viscosity multiplied by

dv dvdy which is the rate of deformation or rate of strain so if we graph it you can see the difference between air water and oil in this figure and what it's showing is think about this vertical axis which says shear stress remember the units of shear stress is force per area so a certain amount of force applied to a unit area is only going to get you a little bit of deformation for oil so here's the curve for the oil and so for a certain amount of shear stress the oil is just going to deform a little bit so think about shaking it side to side in the beaker you know sloshing it around you're not going to get as much of a response with a viscous fluid like oil compared to water water is going to slosh around really easily but for a certain amount of shear stress

what would deform the most is air and so in the horizontal axis here rate of deformation you can just think of this as the response to the shear stress that's applied and so the slope of the line you can see here that we're calling the shear stress is a and the rate of deformation is b and so shear stress divided by the rate of deformation is how we define viscosity all right so viscosity is the slope of the line if we're thinking about it in graphical terms which means it's the ratio of the shear stress to the rate of deformation and what i when we were just kind of doing some general definition terms earlier i suggested that one way to think about viscosity is it's resistance to flow because something with a high viscosity will have a high resistance to flow

a low viscosity will have a low this of low resistance to flow let's look at another video all right so this is an experiment where we have several different fluids here i think it's water and maybe an oil honey so what they're going to do to illustrate that there's differences in the viscosity is they're going to drop a ball into each one of them and how quickly the ball settles to the bottom of the liquid is a reflection of how easily the liquid is deforming out of the way and so wait for it it'll be worth it starting on the left the water dropping that marble i think that must have been air because it looked like it fell really quickly so air is a liquid a fluid right okay this looks like an oil and we could with a stop watch time how long it takes

for that ball to settle down to the bottom of the fluid and so there's different viscosities and different speeds that it settles and this one must be really thick because it is deforming out of the way so slowly so these are just another illustrations of viscosity and so you could characterize viscosity by how quickly the fluid deforms out of the way remember terminology wise what we've been talking about so far is absolute viscosity which is the same thing as dynamic viscosity and sometimes we just call that viscosity i'm going to introduce another term now and that is kinematic viscosity and kinematic viscosity corrects for the fact that some fluids are more viscous when they have a greater density so there's kind of a

co-varying relationship between density and viscosity so a lot of equations that we use in fluid mechanics will have both the viscosity term and also a density term and for that reason and also to be able to express viscosity independent of a fluid's density we sometimes use kinematic viscosity as a variable and it's the ratio of viscosity to fluid density so here's the formula for it the formula is we take mu and divide it by rho and so remember viscosity has units of newton's seconds per meter squared and density from our previous discussion has units of kilograms per cubic meter and so if we cancel those terms out remember a kilogram is a base unit but a newton

is a kilogram meter per second squared so if we're going to expand the units of the newton out to its full base units and then simplify what we get is that kinematic viscosity has a unit of meters squared per second so it's length squared per time so it's just another way of expressing a similar thing so here's the terminology absolute viscosity dynamic viscosity and viscosity all mean the same thing and we assign them the same variable mu but kinematic viscosity is something different it's where we're dividing that by the density now shear force is when you multiply shear stress over an area that it's being applied and so if we want to find out how to calculate the shear force for a fluid

that has a certain viscosity and is experiencing a certain rate of strain so d u d y here means the same thing as d v d y you probably already know from physics and statics and all that sort of thing that sometimes we use u for the velocity variable sometimes we use v but here what we mean is the rate of deformation d u d y so the way that we use this equation it's applied and of course units of force is newtons the way that we apply this formula is that sometimes there's a linear relationship between the change of velocity and the distance between two surfaces and so rather than assuming a curved velocity profile we just use a linear distribution of velocity with distance

to simplify and solve some problems so here's a like a physical instance that we can use viscosity to do some calculations let's say that we have glycerin in a tank remember from one of the earlier videos glycerin was the thing that poured out of the beaker really slowly so what we know about glycerin is it has a large viscosity it resists deformation when a shear force is applied so what we have is this sheet of metal it's a metal plate that's three meters by two meters and so what that means is it has a surface area on the top of six square meters and also a surface area on the bottom of six square meters so it has in total a surface area of 12 square meters

6 on the top 6 on the bottom now if we tow it through the glycerin we have to apply a certain shear force a yeah a force in order to get it to move through the liquid now what we're saying is we want to achieve 0.58 meters per second we want this metal plate to drag through the fluid at 0.58 meters per second and we're also given some technical data like the glycerin's viscosity is 0.15 newton seconds per meter squared and then also we know the distance that it looks like it's closer to the top of the tank than it is to the bottom of the tank so what the example says is it's 1.2 meters from the metal plate up to the top of this tank and then 2.4 meters down to the bottom so what we want to know is solve for f

how big of a force is required in order to achieve this total dis this total velocity of 0.58 meters per second so you can see i've given you a hint is we're going to be using this formula f is viscosity times area times d u d y and here i've said we can just use velocity divided by distance as d u d y but we've got two distances we've got the distance to the top and the distance to the bottom and so the total force is going to be the sum of the force on the top and the force on the bottom so what i'm going to do is pause for a moment give you a chance to get your calculator piece of scratch paper or you can solve this in the notes if you've printed those out but i'm going to pause i'm going to ask you to calculate f calculate the total force required

in order to us to get a velocity of the plate moving through the stationary liquid if the plate's moving at 0.58 all right so i'm going to stop talking if you want to type a guess there into the chat box once you think you've got the numbers i'd invite you to do that that would be great back we're trying to figure out the total force and [Music] um let me drag this solution over to this screen okay so what we're given we have the equation that defines force applied viscosity area and rate of strain we know the distance to the top is 1.2 the distance to the bottom is 2.4 the velocity the viscosity so those are all

of our nodes so if we want to calculate the force that's on the top of the plate because the top is closer it's closer to that location where the tank is stationary so there's going to be a greater shear force there because the distance is less than the bottom so you can see where i've substituted in the numbers and the top force is 0.4 newtons the bottom force 0.2175 because the distance is greater down to the bottom of the tank and then the combined force when we add those two together is 0.6525 so any questions about that [Music] all right

well great that is a taste of what you're going to need to know in order to solve the homework so question yeah can you go over how we calculated the area that we needed to calculate this for because i know you said we need to do the top and the bottom and we're doing three meters by two meters so we have six but i don't like why are we not just doing the the face like the surface area of the face that's dragging through the water or glycerin for that matter so um this is the thin plate you know the thickness of this plate is so small relative to its top and bottom area that there is going to be a drag force having to do with like the front face of that plate but it's going to be negligible compared to the drag force that arises due to

the area on the top so let's say for instance if this plate is a centimeter thick so you know that's a pretty substantial metal plate if it's a a centimeter thick but still the area of that if it's one centimeter by let's say two meters deep that's gonna have a really small area in contact with the fluid compared to six meters of area on the top and then another six meters of area on the bottom so we kind of neglect the thickness of the plate and the interface uh the like vertically oriented interface because what's going to be by far the dominant surface area is the the top and the bottom and so we we use 6 as a because we've calculated the forces on the top and the bottom separately because they have different distances because the dy is different for each of those

so hopefully that addresses your question all right are there any other questions so what about if the plate had like a uh a bit of convexity to it would we use the same type of formula well i guess uh you know if it's really convex then now the the drag force you know like the projected area from the front would be different and so you know depending on how convex it is we may no longer be able to like uh neglect that the like the profile drag that we did in this example so i guess it would just depend on how deformed it is let me give you another illustration and

this is of a homework problem that okay i got a question from harrison here does the formula only apply to surfaces parallel to movement could it be used for the front slash sides of a thick sided plate i'd say yeah it does only apply to forces that are parallel to the movement and i think that you'll get a sense for how it applies as we look at a couple more examples let me bring up the homework assignment here so in one of these problems in problem six you have a cylinder that's falling down through a a a different cylinder that has a hole in the middle of it and so there's oil that's inside that boundary and so that lubricating oil

is if you think about the distance it says here it's .003 inches thick so if this inner cylinder is falling downward then you're going to be able to have the velocity defined for you 0.5 feet per second and so thinking about this formula that we've just looked at you know that would be the du the given velocity and then the wrong way okay here it is and then the gap distance of .003 inches would be the the the dy and so here's the dv here's the d y and then the area so the question is about what area to use it's going to be the area that is in contact with the fluid and so

it's not going to be like if we think about a a cylinder i'm holding up a water bottle right now the applicable area isn't this bottom area of the cylinder it's the side area of the cylinder and so in this homework problem that you're going to have it's the area the outside area of the cylinder is first of all find the circumference so that's circumference pi d and then the distance so circumference times the distance would give you the outside area that's in contact with the fluid so that will be the applicable surface in the out in that homework problem and it's that one more problem is uh similar to a problem that i used to give out of a textbook you know in that textbook problem which you know this other one is similar to there was a uh a cylinder that was falling down through

a pipe and so it was a similar thing where there was a gap distance and so it's the the gap distance between the two is what defines the dy the dv is how quickly it's falling and then the area will be the area that's in contact with the fluid but not the top or the bottom area it's the outside surface area where you know what's close where's the gap the smallest is going to be what governs because of the in the formula the dy being small makes the means that you have a much greater force viscosity is independent of a fluid's pressure and so the viscosity of a fluid doesn't change if it is being compressed and pressurized terry asks by nature will the cylinders

always be concentric um [Music] i i'm afraid i don't know what you mean by that terry so here we have a cylinder what is it you're asking do you have a microphone terry yeah so what i'm asking is if you have that cylinder sliding down the pipe like by nature like would it be the path of least resistance for the cylinder to stay exactly in the middle of the pipe on its way down gotcha yeah that's a great question uh and i think you said it exactly right when you said the past the path of least resistance and so that cylinder wants to travel at the highest velocity it can not that it has like conscious preferences but it wouldn't go up against the side wall because then it would be falling more slowly and so just in the same way that water flows through the path of least resistance the cylinder would fall through the path of least resistance which is going to be to maximize the distance

around the edge there so yes it would it would fall down the center and it may like bang back and forth but uh in general it's going to um maximize its velocity okay so um fluids don't change their viscosity based on the pressure that they're experiencing and this viscosity arises out of the molecular forces within a fluid and so fluids that have high cohesive bonds molecular bonds inside of the fluid are going to have those cohesive forces decrease as the temperature goes up so viscosity does vary as a function of temperature and you probably have seen that before when you change the oil on a car if you've ever had the pleasure of sliding under a car and changing the oil

what you know is that if the oil is warm it pours out really quickly but on a cold winter day if you don't let your engine warm up before you empty the oil then it can drip out of there for hours it just drips really slowly because it doesn't have the same viscosity so the temperature dependency of viscosity is that in a liquid the viscosity decreases as the temperature goes up but ironically in gases the opposite is true that when a gas temperature goes up because the molecules are bouncing around more since the molecules have more kinetic energy that ends up having a slight effect that increases the viscosity of the fluid [Music] and before we get into the sutherland's equation let me just show you the figure of that relationship so this is showing

uh the kinematic viscosity of two different fluids it's showing that in oil the viscosity is decreasing as it gets warmer so down here on the horizontal axis is temperature so with the oil it's pretty dramatic when you're down near freezing the viscosity is high but as the oil heats the viscosity is much lower so if you look at the magnitude of these units it's uh it looks like about one tenth the viscosity by heating the oil from freezing up to 100 degrees celsius with air that slope isn't quite as steep it does experience an increase in viscosity but the effect isn't as dramatic as it was with oil but

i remember like when i was growing up there was this airplane that they wanted to do a continuous flight around the world i think it was called voyager you had a maybe you've seen it if you've been to the air and space museum i think they have it hanging up in washington dc has a propeller on the front a propeller in the back and what i remember about that is that they did it during the winter time because they wanted the air to be cool and have more viscosity because if the air has more viscosity then they're able to generate greater thrust with those propellers and so the reason why they didn't do their attempt in the summer is that in the summer the air would be warmer and therefore would have they wouldn't get quite the same thrust that they'd get in the other case so what supplements equation does is it allows you to estimate the effect of

temperature changes on changes in viscosity so it's an equation that's empirical in nature and it just allows you to estimate if you know the viscosity of a fluid at a certain temperature so in this example for instance let's say that we know the viscosity of air at 50 degrees celsius is 1.95 times 10 to the minus fifth newton seconds per meter squared what if we wanted to find out that same fluid at 95 celsius instead well what we have to do is use units of kelvin in order to solve this and so we're going to convert both of these temperatures from celsius to kelvin and then solve for the mu the velocity at the new temperature where we start off with the viscosity at a given temperature so this is another one of those where i'd like to pause for just a moment and give you a chance to try out sutherland's equation because there's a

homework problem where you do this let's try and find out what's the viscosity of air at 95 degrees celsius so that's going to be the unknown viscosity at a t of 95 and of course you have to convert it from 95 celsius to kelvin and the original viscosity of 1.95 times 10 to the minus fifth was at a t naught of 50 degrees celsius again converting over to kelvin all right so i'll stop talking give you a chance to exercise your calculators and i'll be giving out gold stars in the chat box to people get it right on the screen just in case you're stalled so that we can see where things are going with this all right so the the first thing we have

to do in this problem is convert the given temperatures into kelvin which is uh par for the course when we're dealing with gas type problems and so our givens is that the initial temperature for which we know the viscosity 323.16 kelvin the temperature where we want to know the viscosity 360 kelvin and then we're also given the initial viscosity and the uh supplements constant and then you can see the substitutions that i made in there now this is the first but certainly not the last time i'm going to point out a habit that i think is really important for engineers and i think it's an important habit for you to be really explicit when you're making substitutions and so in this

example what i did was i wrote the equation first and then i showed the direct substitution for every component of that equation including the units it's really worthwhile to write the units when you're substituting things in because for one thing it'll help you to avoid mistakes of maybe substituting the wrong variable in the wrong place you know for example if you write the temperature in celsius accidentally and so you had you know like 50 celsius and then this sutherland's constant is kelvin then you'd see oh these are different units i can't add it together but if you just wrote the numbers if you just wrote the number 50 and then the number 111 then you're not going to have that same like opportunity to recognize that the two shouldn't be combined so in other words what i'm saying is

include the units when you write down the numbers and you're going to make fewer mistakes also it's just more professional and more neat if you include the units and so the other thing i'll point out is that i don't try and do all the calculations in a single step i kind of take a few steps and so you'll notice that what i did here is i had the ratio of the temperatures and then i write that number there before i do to the 1.5 power and the advantage of having it in multiple steps is again you avoid mistakes and you can check your work more easily i think it's really a good habit on exams for example to check your calculations two or three times before you submit the work you just want to make sure you didn't make a calculation error and so if you do kind of like these intermediate steps it helps to check your work so in the end you can see what we end up with is 2.15 times 10 to the minus fifth

newton seconds per meter squared any questions on these calculations so you have this allows you to estimate the viscosity of the gas when you don't have it like in a table it's just a way to extrapolate all right so we already looked over these figures for the viscosity of air and oil and this is a kinematic so if you'll remember that the units for kinematic are length squared per time there are some other ways to classify fluids a newtonian fluid versus non-newtonian fluid and what we mean by that a newtonian fluid is where there is a linear relationship between shear stress

and shear strain so water is a new newtonian fluid the the slope of the line is dynamic viscosity in a newtonian fluid but there are certain fluids that are a little bit funny maybe let me just show you the video clip before we go through the definitions in too much more detail let me first of all let me see if i can copy that link and put it into my other browser all right look at these kids walking on a fluid have you seen something like this before sometimes this is called oobleck but really what it is is it's just cornstarch dissolved in water and so if they walk fast enough they can avoid falling down into the fluid

but if they stop for a second then they get stuck in the fluid they go down into it so this is a non-newtonian fluid where the viscosity of it responds to the uh to the shear stress that's being applied so let's look at this other video as well before we talk about it a little bit more so copy link and then i'll paste that over here i'd love to have a swimming pool full of that non-newtonian fluid oh those golden fries you didn't think you'd have to sit through commercials during fluid mechanics class right okay all right so this is a high-speed camera and that same thing it's the cornstarch water mixture and they've added some

food coloring to it in order to make it more visually appealing um when you apply a force to it then instantaneously the viscosity of the fluid changes like if you're not applying a force it has a low viscosity but as sar as soon as you start applying a force then the viscosity is higher so it has a greater resistance when you apply a shear force so look at the interesting patterns that arise because of the movement of that subwoofer and then they get it going with the high-speed camera kind of interesting shapes hopefully they'll show us the high speed footage here in a second all right here we go it almost looks like an animation right

but it's not this is the actual footage it looks fake but what's happening is is that as the subwoofer is moving it's applying a shear stress to that liquid and so the liquid's viscosity is changing as the force is applied to the liquid in the lab next week we're going to deal with this cornstarch water mixture so that you can get kind of a tactile experience of what does it mean when a fluid is non-newtonian so those are a couple of video clips now let's go back to these definitions a non-newtonian fluid could be a shear thinning fluid and so in a shear thinning fluid what happens is when you apply a shear stress then the viscosity decreases so ketchup is an example of that if you've ever pounded the back of a glass ketchup bottle what you're doing is you're applying a shear force to the liquid and temporarily the fluid becomes less viscous because of the force that

was applied that's a sheer thinning fluid a shear thickening fluid which is what we just looked at with those previous two youtube videos is where the fluid becomes more viscous as a shear force is applied so this graphical illustration is that a newtonian fluid is not affected its viscosity doesn't change depending on what force is applied but a shear thinning fluid becomes less viscous as the force is applied whereas a shear thickening fluid becomes more viscous so i'll give you a corn starch and water mixture in lab next week and a spoon and if you stir the spoon slowly then it's easy to stir but if you try to suddenly move the spoon really quickly through that cup of the liquid then the liquid resists the movement so it's kind of an interesting experience that we'll look at in the lab next week um

we are out of time we're going to have to talk about the gas laws in class on tuesday