welcome to lesson 1e vapor pressure and viscosity in this lesson we'll define vapor pressure cavitation and viscosity and we'll do some example problems what is vapor pressure here's a formal definition we're talking about a pure substance it's the pressure exerted by its vapor molecules when the system is in phase equilibrium with its liquid molecules at a given temperature here's an illustration for water some molecules evaporate and others come back into the water they're in equilibrium when the same amount goes out as comes in that happens when the air is saturated with water vapor molecules if there were fewer molecules than that more would come out in other words evaporate than would come in it would not be in equilibrium fluid mechanics people like to say vapor pressure but it's exactly the same as saturation pressure psat which thermodynamicists prefer it is a pressure so its dimensions are force per length squared and its units are typically pascals or kilopascals an interesting phenomenon is when the pressure in a liquid drops below the vapor pressure then the liquid locally vaporizes into bubbles process called cavitation the little bubbles are called cavitation bubbles let's do a quick example water at 20 degrees c flows at high speed through the narrow gap in a valve we find that the lowest pressure in the flow is 3-2-2-0 pascals let's determine if cavitation is likely to occur we look up pv or psat online or in some tables at 20 degrees c pv is 2.339 kpa in our valve the lowest pressure is 3220 pascals we multiply by a unity conversion factor so this lowest pressure is 3.220 kpa compared to pv this is greater since that's the lowest pressure we conclude since p is greater than pv everywhere we do not expect cavitation anywhere in this flow i have a short youtube video called cool consequences of cavitation i'll play some of it here here's an example of ship propeller cavitation cavitation is usually undesirable because when these bubbles move into a region of higher pressure they collapse rapidly these collapsing bubbles generate vibrations and noise here's an example of cavitation in a pipe you can both see the bubbles and hear them these collapsing bubbles may reduce performance that can severely damage nearby surfaces here's a slow motion video of bubbles growing and then now they collapse very rapidly this damage is called cavitation damage we see it in pumps in valves and in turbines here's the party trick that was mentioned if the bottle is filled with air it doesn't break if the bottle is filled with water it doesn't break but if the bottle's partially filled with water it breaks there's some slow-motion videography you can see the cavitation bubbles form collapse and break the bottle if you put an accelerometer on the bottle you see that it doesn't break when the hammer strikes but it does break with the cavitation collapse wow i never knew cavitation was so powerful that's awesome dude thank you sure now let's talk about viscosity viscosity is given the symbol mu although some authors use ada we'll use mu it's the fluid property that represents internal resistance of a fluid to motion some people call it dynamic viscosity its dimensions are mass over length over time typical units are kilogram per meter second or p which stands for poise or cp which stands for centipoise we'll always use these units kinematic viscosity nu is just mu divided by density this is just for convenience since this combination often occurs in fluid mechanics the dimensions of nu are l squared per time typical units are meters squared per second some people use st which stands for stokes a special unit for kinematic viscosity we'll always use this one as you can see in this plot the viscosity of gases increases with temperature as you see here whereas the viscosity of liquids decreases with temperature also mu of a liquid is typically much greater than mu of a gas as also seen in the figure for water flows we can find mu or nu in tables or online some empirical equations are also available but we won't discuss those here for gases like air you can also find mu or new in tables or online for air we will always use sutherland's law which is given here this gives us mu as a function of temperature here's the equation and these are the constants let's do a quick example let's calculate the viscosity of air at 50 degrees c and 1.33 kpa first a comment always use absolute temperature when using sutherland's law this is a good equation to put into excel or other software for when we do problems that require the viscosity of error so first let's convert t 50 degrees c becomes 323.15 k we'll use that here and here in sutherland's law plugging in the constants this is mu s up here and t s naught comes from here ts is 110.4 k this is our temperature and another ts notice that all the k's cancel my calculator gives me one point nine six six one times ten to the minus five kilograms per meter second we round to three digits for our final answer from a table in the appendix at 50 degrees c mu is given as 1.963 times 10 to the minus 5 kilogram per meter second comparing these two the error is about 0.2 percent which is excellent notice that this p was never used 1.33 kpa why it's because viscosity is approximately a function of t only mu is a very weak function of pressure i do an example with viscosity in a youtube video called block sliding down an incline on an oil film i'll show portions of that now i'll share a video about this here's the problem set up we have a block sliding down an incline of angle phi along an oil film of thickness each the surface area of the bottom of the block is a in contact with the oil oil viscosity is mute we are to calculate the speed v of the block to solve we draw a free body diagram of the block there's a weight w which we split into two parts there's a normal force n the oil acting on the block and there's a viscous force trying to slow down the block since v is constant there's no acceleration newton's second law says that sigma f has to be zero in the normal direction this n must be balanced by w cosine phi let's call this equation one in the tangential direction the viscous force must be balanced by w sine phi we'll call that equation two now let's take a close-up view of the oil film here's our magnifying glass tilt your head a little bit and you see this block moving at speed v the oil thickness h tau is the shear stress acting on the bottom surface of the block the no slip condition sets u equals zero at y equals zero and u equal v at y equal h you can prove that the velocity profile is linear so u is y over h times v for this simple linear velocity field tau is mu d u d y which simplifies to mu v over h and the viscous force is just tau times a or mu v over h times a we call this equation three now all we do is combine equation two this equation and three this equation so we get this simply solve for v our final equation is v is wh sine phi mu a this is our final solution for block speed v sliding down the incline thank you sir i understand it now but wouldn't there be a moment or torque on the block yes mr nerley good observation the net moment causes the block to tilt slightly until all the forces and moments balance i have another short video called fluid viscosity and its bearing on journal bearings i'll show some clips from that as well viscosity affects both normal and shear stresses now consider an axisymmetric version of this rotating inner cylinder and a stationary outer cylinder with the gap fluid in between this is not to scale but if the gap width is small now much less than r then the velocity profile is approximately linear just like with the parallel plates we can measure the torque required to turn this inner cylinder at a constant rpm then we can solve for mu we get mu proportional to torque an important application is for journal bearings the journal bearing consists of a housing a journal or a shaft and lubricant in the thin gap between the cylinders when the shaft is centered the previous equation still applies we can solve this equation for torque turns out that the torque on the rotating shaft is linearly proportional to the viscosity of the lubricant then why do they use high viscosity oils in journal bearings then man wouldn't it be better if they used like water or something i was just about to get to that when there's a load on this journal bearing the loaded supports is also proportional to the viscosity of the lubricant so to support high load you need a high viscosity fluid besides these things get hot and the water could boil thanks dude i mean professor yeah make sure you show up for class next time i'll try man see you later dude yeah they don't make students like they used to finally let's talk about newtonian versus non-newtonian fluids a newtonian fluid is defined as a fluid where the rate of deformation which is a strain rate is linearly proportional to shear stress tile for a newtonian fluid the rate of deformation is linear with shear stress tile as you can see here most fluids we'll use in this course water air oils gasoline these are all newtonian fluids for simple shear flows where there's a shear in velocity in the y direction tau is just mu d u d y as in the two video examples i just showed so we see that tau is linear with d u d y with the coefficient being mu which we assume is constant in this simple expression some fluids are non-newtonian in which tau and the rate of deformation are not linearly related we show several examples in this little diagram a dilatant fluid is called shear thickening by the way viscosity is proportional to the slope of this curve and viscosity increases as d u d y or rate of deformation increases an example of a dilatant fluid is starch in water or quicksand this is the curve for a pseudoplastic fluid where a shear thinning fluid examples are paint and blood bingham plastic looks fairly linear but there's a yield stress up to some certain towel the yield stress bingham plastic behaves like a solid once you reach that shear stress then it behaves like a fluid a good example is toothpaste toothpaste is an example of a bingham plastic you can have a finite shear stress and the toothpaste doesn't flow even upside down once you exceed a certain shear stress it starts flowing like a fluid this is definitely a non-newtonian fluid we will analyze newtonian fluids only in this course but you should be aware of these other kinds of non-newtonian fluids thank you for watching this video please subscribe to my youtube channel for more videos