all right so section 199 uh we're talking about pressure the pressure in of fluids um so we're saying it's the normal force exerted by a fluid per unit area so it's a force per unit area pressure is a scalar it doesn't have a it's not a vector quantity right it's just a scalar uh because it it has to be perpendicular to the surface perpendicular everywhere perpendicular to a surface so we're going to talk about uh the pressure of gases and liquids that are pushing on the wall of the tank the wall of the um you know whatever's holding the water or the fluid in okay uh the units of pressure it's remember it's forced over area force per area makes sense it might be newtons per meter squared a newton per meter square is a pascal our newton per meter square is a pascal a kilonewton per meter square would be a kilopascal also a newton per millimeter squared would be mega pascal uh kind of make sure you know your your si units um in english units whatever the force is divided by whatever the area is pounds per square inches uh this is pound psi right pounds per square inch if this was pounds per square foot it'd be psf um so generally in um english units whatever the whatever you have up here whatever you have down here just kind of leave it p s i p s f ksi would be kips per square inch k s i you know that a kip is 1 000 pounds i think hopefully you know that you know it now kept is 1000 pounds [Music] okay uh atmospheric pressure of the air right of the atmosphere at sea level is 101.325 kpas right 101.325 kpa or one atmosphere atmosphere is a unit of pressure um relative to atmospheric pressure and uh in psi 14.696 um psi okay the difference between absolute pressure and gauge pressure absolute pressure is relative to zero it's you know it's relative to zero there can be no um negative absolute pressure almost like absolute temperature but absolute pressure is the actual pressure relative to zero the gauge pressure is a pressure above or below atmospheric pressure all right so if the gauge pressure if the pressure gauge is 10 uh kpa then that means it is at atmospheric pressure plus 10. so that would mean the pressure absolute is 111.325 kpa right so this gauge pressure is um what a pressure gauge would read so this i like to think this is what a pressure gauge or a pressure device would read because it is in the atmosphere right it measures the pressure difference from atmospheric pressure so maybe we can call this the gauge pressure is the pressure above atmospheric pressure whereas the vacuum pressure is the pressure below atmospheric pressure or a negative gauge pressure a negative gauge pressure oh well that's sorry that's what it already said right here uh so for instance if p vacuum if the vacuum pressure [Music] was you know i don't know let's say 30 kpa then that means it's 101 minus 30 kpa so the absolute pressure would be whatever that is 71.325 kpa okay uh this right here is on your formula sheet um we need to kind of look at that conversion sheet that you will be able to use on the test okay so just some definitions right here we're looking at the pressure the force per area of a fluid and be careful did it say absolute pressure did it say gauge pressure absolute relative to zero gauge pressure is relative to absolute relative to sorry relative to local atmospheric pressure okay let's talk about the change in pressure with change in depth um and we're just going to talk about an incompressible fluid so this is in an incompressible fluid so i don't know i think you knew this hopefully you knew this or it makes sense that the further you go down in a body of water right the more you go under water the more pressure it has right that makes sense you have more fluid on top of you the further and further you go down uh if you were to look at the pressure on a wall so if you've got this huge you know tank of water this huge aquarium this huge body of water and if this wall is holding it you know keeping it in you can imagine if if you were a tiny particle on top of the wall you'd feel the pressure of that fluid a little bit but if you were a tiny particle on the bottom here you would feel a lot larger pressure and so the pressure increases pressure increases the pressure of a fluid increases with depth and it does increase linearly it increases linearly with depth all right so this is not parabolic exponential or anything this is increases linearly with depth okay what is the change of pressure with depth well rho g h memorize that box that in you can have a um little note card formula sheet on the test that's gonna be on your note card but you may have already known that you can memorize that not too hard the change in pressure is rho g h the let's write that down the change in pressure [Music] is rho rho would be the density of your fluid times gravity that's the acceleration due to gravity this would be 9.81 meters per second squared please don't use just 9.8 go ahead and use 9.81 or 32.2 feet per second squared if we're in english units and height is is really the the delta h the change in depth [Music] uh this is in the vertical so this is in the y direction it doesn't matter if it changes in depth i mean if it changes left or right it only matters vertical up down only matters its height that's why we kind of use an h right there so the change in pressure is rho g h so this is what i do i just add add rho gh to the original pressure as you go down as you go down if you get deeper and deeper under water or under whatever fluid add rho gh make sure your pressure is increasing as you get further and further down under the water pressure increases at rho gh as you go further and further under water and make sure that that makes sense make sure you're you're not subtracting if you're going down under the water the pressure's increasing you're adding rho gh to whatever pressure was above water so what would happen is you could take the pressure the atmospheric pressure or whatever pressure you have up here above water take whatever pressure one you have up here above water and if you want to know pressure two then say oh well to get pressure too let me take so equals let me take pressure one and add rho gh right easy enough add rho gh to the pressure above as you're going below the water okay a few things that will be helpful for us in these problems as we look at calculating the pressure of fluids [Music] let's look at this let's say we have some sort of youtube or something we have some fluid and the the pressure over here of the fluid at this height is p1 and maybe kind of i want to know the pressure over here p2 if it's the same height and the only difference is a horizontal change in position pressure at the same height of the same fluid is equal is equal right so p2 is equal to p1 there's no change in height there's no change in height there's also no change in fluid p1 would be equal to p2 all right so it doesn't matter it doesn't matter that you went down under here and then came back up doesn't matter if you went left and right it only matters the height you start at and the height you finish if it's the same height then it's the same pressure of the same fluid okay so when you are uh going down in the same fluid you add rho gh for instance you can take pressure one and add rho gh and you end up at pressure two right you can take pressure one add rho gh and get to pressure two what if you started at pressure two you would subtract rho gh and you would end up at pressure one you see those equations are actually the equivalent those equations are the same equation so if you are going here and then going down take pressure one and add rho gh if you're starting here and going up you subtract rho gh okay all right what if you have two different fluids and they're not a mix right they are you got one fluid here that's kind of butted up to another fluid here the pressure at the interface of two fluids is equal all right if they weren't equal they would be pushing on each other one would win you know against the other but they're in equilibrium and so the pressure right here at the bottom of the green fluid would be equal to the pressure right here at the top of the pink fluid so the pressure at the bottom of the green equals pressure at the top of the pink all right it's not equal to the pressure of green up here top no just the pressure at the bottom of the green is equal to the pressure at the top of the pink so we'll see how we can use that um to kind of jump from one pressure to another pressure all right the pressure change of the gas so let's say we've got a fluid here a flu sorry liquid here liquid here and a gas here technically the pressure change of a gas is still rho gh but the row of gases are orders of magnitude smaller very very very small compared to the row of liquids so in this class we're going to say the pressure change of the gas is negligible the pressure change of a gas is neglig let me spell this negligible compared to the pressure change of liquids so you could just say that p1 is approximately equal to p2 um you know you don't have to p1 plus rho gh [Music] equals p2 because that row is very very small compared to the pressures of the liquids so you can just jump straight from there to there and just assume it's approximately the same pressure all right so now we've got the notes i think we're ready to work some problems