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# Venturi effect and Pitot tubes

## Video transcript

let's talk about the venturi effect this has to do with water or any fluid flowing through a pipe and turns out let's say this water is flowing right here minding its own business having a good day for that matter when it meets a constriction what's going to happen here well the waters got to keep flowing but it's going to start flowing faster through the constricted region and the reason is well there's a certain amount of fluid that's flowing through this pipe let's say all the fluid in this region right here let's say this front part of the water I mean this whole thing is filled up but just say this cross-section of the water happen to make it from this back portion to this front portion and I don't know let's just say one second so this entire volume moved through this section of the pipe in one second well there's a law in physics that says that same volumes got to make it through each portion of this pipe because if it didn't where I mean where is it going to go this pipe would have to break or something this water's got to go somewhere that much flowed through here in one second then this much has to flow through this little tiny region in one second but the only way that that's possible is for the front surface instead of just traveling from there to there in one second the front surface it's gonna have to change its shape but the front part of the waters can have to travel from here to here maybe in a quarter of a second because all of this has got to cram through here in the same amount of time now water still coming behind it there's more water coming and the volume flow rate got to stay the same the volume per time flowing through one region of the pipe has got to be the same as the volume flow rate through some other region of the pipe because this water has got to go somewhere it doesn't just disappear in here it's got to keep flowing that means the important part is the water flows faster through the constricted region sometimes much faster through the constricted region the smaller this is compared to this original radius the faster the fluid will flow through here why do we care well because faster moving fluid also means lower pressure why do faster moving fluid mean lower pressure well if we look at the Bernoulli equation Bernoulli's equation says p1 plus rho g h1 plus one-half Rho v1 squared equals p2 plus Rho gh 2 plus 1/2 Rho v2 squared home my goodness this looks frightening but look at p1 we just pick some point in the pipe let's just pick this point right here I'll call that point 1 so all these ones this whole side refers to that point let's just pick point 2 right here all this whole side refers to that point now notice something these are like basically the same height and assume Heights not really a big difference here so let's cross out the heights is they're the same height so I don't have to worry about that this says that all right if there's some pressure at 1 and some velocity of the water at 1 you can plug those in here and get this side but now look at over here we know the velocity at 2 is bigger we just said that it has to be because the volume flow rates got to stay the same so this speeds up in here so this is bigger this quantity here but we know the whole thing equals this side so if this term increased that means the pressures got to decrease so that when they add up they get the same as this side over here this is actually called Bernoulli's principle Bernoulli's principle says that when a fluid speeds up its pressure goes down it's totally counterintuitive we always expect the opposite we think fast moving fluid that's got to have a lot of pressure but it's the exact opposite fast moving fluid actually has a smaller pressure and it's due to Bernoulli's equation and this is what causes the venturi effect the venturi effect refers to the fact that if you have a tube and you want a smaller pressure region you want the pressure to drop for some reason which actually comes up in a lot of cases just cause a narrow constriction in that tube in this narrow constriction faster moving fluid and it will cause a lower pressure this is the idea behind the venturi effect so the venturi effect basically says for a constriction a pipe you're going to get a lower pressure while we're talking about fluid flow we should talk about one more thing let me get rid of this here imagine you just had a brick wall with fluid flowing towards it maybe it's air here so they've got some fluid flowing towards this brick wall this seems like a really dumb example of Bernoulli's principle but I'm going somewhere with this to stay with me this is flowing towards here what's going to happen well can't go through the wall he's got to go somewhere maybe this just goes up like that and this you know I'm going to go this way it's closer to go that way this side maybe just goes down this is actually kind of what happens but there'll be a portion in the middle it basically just terminates it hits here and kind of just get stuck so there'll be some air right near here in the middle where it's just not moving what if we wanted to know what the pressure was there based on the variables involved in this problem we can use Bernoulli's equation again pick two points let's pick this one point one let's pick this one point two use Bernoulli's equation it says this and again let's say these are basically the same height so that height is not a big factor and if these terms are the same then we can just cross them out because we can subtract them from both sides they're identical now what can we say we know the velocity of the air at - it's not move it got stuck here it got stagnant and so v2 is just zero and we get this statement that the pressure at two which is sometimes called the stagnation pressure so I'm going to call it the stagnation pressure because the air right here gets stuck and it's not moving you might object you some might say away hold on I thought the air had to go somewhere well it's all going somewhere the point is there's some air right here they get stuck it gets stuck and air starts passing it by and so what's this pressure here well up here we just read it off all these went away p2 which is what I'm calling the stagnation pressure got to equal p1 the pressure over here plus one-half Rho Oh v1 squared and we get this formula you might think why why would we care about this who is regularly shooting air at a brick wall people do it all the time because you can build a pretty important instrument with this called a pitot tube and the pitot tube looks something like this let's get rid of that so why would someone use this system it's called a pitot tube people use it to measure fluid velocity or if you're moving through the fluid it's a way to measure your velocity or your speed so what happens is you've got this setup let's say you're in an airplane you mount this on the airplane you're flying through the fluid which is the air so that means air is rushing towards this section here rushing past you let's say you're flying to the left so you'll notice air flying past you a pitot tube always has this section that's facing into the wind or into the air this air be directed straight toward this region and the key is this is blocked off at the end so there's air in here but it can't be moving the air in the section can't be moving all the way to the front because I mean where is he going to go we just said if fluid flows in fluids got to flow out there's no out here and then there's another region up here you've got a second chamber where the air flows over the top and this is directed at a right angle to that air flow you've got another chamber and again in here fluids not flowing the key is this gives you a way to determine the difference between the pressure here and the pressure there if you had some sort of membrane in here or something dividing these two sections that could tell you the pressure differential right if the pressure on this side is a little bigger than the pressure on this side and this would bow outward one of these is measuring the pressure here and one of them is measuring the pressure there how do what is the mathematically how what's the relationship it's the one we just found right here this is the stagnation pressure right the air is not moving in here it flows straight in we know the V is zero right here and so the stagnation pressure equals the pressure up here at scan ups assuming there's very little height difference let's say this is a very small device and it's not like 10 meters tall so any height differences are miniscule and we would just have our same equation before this would just equal the pressure plus one-half Rho V squared and this is how you determine the velocity or the speed because now we can just solve this for V I get that V 1 equals P s the stagnation pressure minus the pressure at 1 that whole thing times 2 divided by the density of the air and then a square root because you have to solve for the V 1 so this device lets you determine this pressure differential right here check you need to know what the density of air is and this gives you a way to determine the velocity of the fluid or in other words the velocity of your aircraft flying through the air