1 00:00:01,268 --> 00:00:03,111 - Let's talk about the Venturi effect. 2 00:00:03,111 --> 00:00:05,688 This has to do with water or any fluid 3 00:00:05,688 --> 00:00:07,360 flowing through a pipe. 4 00:00:07,360 --> 00:00:10,263 And it turns out, let's say this water's flowing right here. 5 00:00:10,263 --> 00:00:13,744 Minding its own business, having a good day for that matter, 6 00:00:13,744 --> 00:00:16,128 when it meets a constriction. 7 00:00:16,128 --> 00:00:17,591 What's gonna happen here? 8 00:00:17,591 --> 00:00:19,359 Well, the water's gotta keep flowing, 9 00:00:19,359 --> 00:00:22,079 but it's gonna start flowing faster 10 00:00:22,079 --> 00:00:23,632 through the constricted region. 11 00:00:23,632 --> 00:00:26,151 And the reason is, well, there's a certain amount of 12 00:00:26,151 --> 00:00:28,103 fluid that's flowing through this pipe. 13 00:00:28,103 --> 00:00:32,023 Let's say all the fluid in this region right here. 14 00:00:32,023 --> 00:00:34,401 Let's say this front part of the water. 15 00:00:34,401 --> 00:00:35,615 I mean, this whole thing's filled up, 16 00:00:35,615 --> 00:00:38,614 but just say this cross-section of the water 17 00:00:38,614 --> 00:00:40,966 happened to make it from this back portion 18 00:00:40,966 --> 00:00:43,751 to this front portion in, I don't know, 19 00:00:43,751 --> 00:00:45,327 let's just say one second. 20 00:00:45,327 --> 00:00:49,583 So this entire volume moved through this section 21 00:00:49,583 --> 00:00:51,254 of the pipe in one second. 22 00:00:51,254 --> 00:00:54,677 Well, there's a law in physics that says that same volume's 23 00:00:54,677 --> 00:00:57,647 gotta make it through each portion of this pipe. 24 00:00:57,647 --> 00:01:00,596 Because if it didn't, where's it gonna go? 25 00:01:00,596 --> 00:01:02,412 This pipe would have to break or something. 26 00:01:02,412 --> 00:01:04,077 This water's gotta go somewhere. 27 00:01:04,077 --> 00:01:06,724 If that much flowed through here in one second, 28 00:01:06,724 --> 00:01:08,509 then this much has to flow through this 29 00:01:08,509 --> 00:01:12,101 little tiny region in one second, 30 00:01:12,101 --> 00:01:15,101 but the only way that that's possible is for this 31 00:01:15,101 --> 00:01:16,981 front surface, instead of just traveling from 32 00:01:16,981 --> 00:01:20,573 there to there in one second, the front surface 33 00:01:20,589 --> 00:01:21,807 is gonna have to change it's shape. 34 00:01:21,807 --> 00:01:23,351 But the front part of the water's gonna have to 35 00:01:23,351 --> 00:01:26,534 travel from here to here maybe in 1/4 of a second 36 00:01:26,534 --> 00:01:29,191 because all of this has gotta cram through here 37 00:01:29,191 --> 00:01:30,551 in the same amount of time. 38 00:01:30,551 --> 00:01:31,927 Because that water's still coming behind it. 39 00:01:31,927 --> 00:01:33,263 There's more water coming. 40 00:01:33,263 --> 00:01:36,351 And the volume flow rate has got to stay the same. 41 00:01:36,351 --> 00:01:39,063 The volume per time flowing through one region 42 00:01:39,063 --> 00:01:41,087 of the pipe has got to be the same as 43 00:01:41,087 --> 00:01:44,719 the volume flow rate through some other region of the pipe 44 00:01:44,719 --> 00:01:46,894 because this water's got to go somewhere. 45 00:01:46,894 --> 00:01:48,799 It doesn't just disappear in here. 46 00:01:48,799 --> 00:01:50,286 It's gotta keep flowing. 47 00:01:50,286 --> 00:01:51,662 That means... 48 00:01:51,662 --> 00:01:54,823 The important part is the water flows faster 49 00:01:54,823 --> 00:01:56,606 through the constricted region. 50 00:01:56,606 --> 00:02:00,381 Sometimes much faster through the constricted region. 51 00:02:00,381 --> 00:02:03,679 The smaller this is compared to this original radius, 52 00:02:03,679 --> 00:02:06,350 the faster the fluid will flow through here. 53 00:02:06,350 --> 00:02:07,654 Why do we care? 54 00:02:07,654 --> 00:02:12,654 Well, because faster moving fluid also means lower pressure. 55 00:02:13,757 --> 00:02:16,575 Why does faster moving fluid mean lower pressure? 56 00:02:16,575 --> 00:02:18,253 Well, if we look at the Bernoulli equation, 57 00:02:18,253 --> 00:02:23,253 Bernoulli's equation says P one plus row g h one 58 00:02:24,614 --> 00:02:29,470 plus 1/2 row v one squared 59 00:02:29,470 --> 00:02:34,470 equals P two plus row g h two 60 00:02:34,685 --> 00:02:38,605 plus 1/2 row v two squared. 61 00:02:38,605 --> 00:02:40,710 Oh my goodness this looks frightening, 62 00:02:40,710 --> 00:02:43,718 but look at P one, we just pick some point in the pipe. 63 00:02:43,718 --> 00:02:45,752 Let's just pick this point right here. 64 00:02:45,752 --> 00:02:47,446 We'll call that point one. 65 00:02:47,446 --> 00:02:50,845 So all these ones, this whole side refers to that point. 66 00:02:50,845 --> 00:02:53,637 Let's just pick point two right here. 67 00:02:53,637 --> 00:02:55,277 All this whole side refers to that point. 68 00:02:55,277 --> 00:02:56,077 Now, notice something. 69 00:02:56,077 --> 00:02:59,349 These are basically the same height, 70 00:02:59,909 --> 00:03:02,089 and assume height's not really a big difference here. 71 00:03:02,089 --> 00:03:03,961 So let's cross out the heights, 72 00:03:03,961 --> 00:03:05,097 because they're the same heights. 73 00:03:05,097 --> 00:03:06,624 We don't have to worry about that. 74 00:03:06,624 --> 00:03:10,208 This says that, alright, if there's some pressure at one 75 00:03:10,208 --> 00:03:12,991 and some velocity of the water at one, 76 00:03:12,991 --> 00:03:15,103 you can plug those in here and get this side. 77 00:03:15,103 --> 00:03:15,944 And now look at over here. 78 00:03:15,944 --> 00:03:18,748 We know that the velocity at two is bigger. 79 00:03:18,748 --> 00:03:20,372 We just said that, it has to be because the 80 00:03:20,372 --> 00:03:22,148 volume flow rate's got to stay the same. 81 00:03:22,148 --> 00:03:24,683 So this speeds up in here. 82 00:03:24,683 --> 00:03:27,443 So this is bigger, this quantity here. 83 00:03:27,443 --> 00:03:30,515 But we know the whole thing equals this side. 84 00:03:30,515 --> 00:03:33,756 So if this term increased, that means that the pressure's 85 00:03:33,756 --> 00:03:36,524 got to decrease so that when they add up 86 00:03:36,524 --> 00:03:38,843 they get the same as this side over here. 87 00:03:38,843 --> 00:03:41,129 This is actually called Bernoulli's Principle. 88 00:03:41,129 --> 00:03:43,187 Bernoulli's Principle says that when a fluid 89 00:03:43,187 --> 00:03:45,724 speeds up, it's pressure goes down. 90 00:03:45,724 --> 00:03:47,892 It's totally counter-intuitive. 91 00:03:47,892 --> 00:03:49,600 We always expect the opposite. 92 00:03:49,600 --> 00:03:52,319 We think fast moving fluid, that's gotta 93 00:03:52,319 --> 00:03:55,871 have a lot of pressure, but it's the exact opposite. 94 00:03:55,871 --> 00:03:59,455 Fast moving fluid actually has a smaller pressure 95 00:03:59,455 --> 00:04:01,335 and it's due to Bernoulli's equation. 96 00:04:01,335 --> 00:04:03,631 And this is what causes the Venturi effect. 97 00:04:03,631 --> 00:04:05,887 The Venturi effect refers to the fact that if you 98 00:04:05,887 --> 00:04:08,984 have a tube and you want a smaller pressure region, 99 00:04:08,984 --> 00:04:10,990 you want the pressure to drop for some reason, 100 00:04:10,990 --> 00:04:13,615 which actually comes up in a lot of cases, 101 00:04:13,615 --> 00:04:16,190 just cause a narrow constriction in that tube. 102 00:04:16,190 --> 00:04:19,944 In this narrow constriction, faster moving fluid, 103 00:04:19,945 --> 00:04:21,583 and it'll cause a lower pressure. 104 00:04:21,583 --> 00:04:24,478 This is the idea behind the Venturi effect. 105 00:04:24,478 --> 00:04:26,599 So the Venturi effect basically says for 106 00:04:26,599 --> 00:04:30,246 a constriction in a pipe, you're gonna get a lower pressure. 107 00:04:30,246 --> 00:04:32,239 While we're talking about fluid flow, 108 00:04:32,239 --> 00:04:34,491 we should talk about one more thing. 109 00:04:34,491 --> 00:04:36,811 Let me get rid of this here. 110 00:04:36,811 --> 00:04:38,747 Imagine you just had a brick wall 111 00:04:38,747 --> 00:04:40,587 with fluid flowing towards it. 112 00:04:40,587 --> 00:04:41,779 Maybe it's air here. 113 00:04:41,779 --> 00:04:45,885 So you've got some fluid flowing towards this brick wall. 114 00:04:45,885 --> 00:04:47,906 This seems like a really dumb example of 115 00:04:47,906 --> 00:04:49,851 Bernoulli's principle but I'm going somewhere 116 00:04:49,851 --> 00:04:51,858 with this so stay with me. 117 00:04:51,858 --> 00:04:53,074 This is flowing towards here. 118 00:04:53,074 --> 00:04:54,153 What's going to happen? 119 00:04:54,153 --> 00:04:56,106 Well, it can't go through the wall. 120 00:04:56,106 --> 00:04:57,346 It's gotta go somewhere. 121 00:04:57,346 --> 00:05:00,322 Maybe this just goes up like that 122 00:05:00,322 --> 00:05:02,345 and this, you know, I'm gonna go this way. 123 00:05:02,345 --> 00:05:04,155 It's closer to go that way. 124 00:05:04,155 --> 00:05:05,907 This side maybe just goes down. 125 00:05:05,907 --> 00:05:07,946 This is actually kind of what happens. 126 00:05:07,946 --> 00:05:09,618 But there'll be a portion in the middle 127 00:05:09,618 --> 00:05:11,121 that basically just terminates. 128 00:05:11,121 --> 00:05:14,417 It hits here and kind of just gets stuck. 129 00:05:14,417 --> 00:05:17,167 So there'll be some air right near here in the middle 130 00:05:17,167 --> 00:05:19,221 where it's just not moving. 131 00:05:19,221 --> 00:05:20,638 What if we wanted to know what the pressure 132 00:05:20,638 --> 00:05:24,333 was there, based on the variables involved in this problem? 133 00:05:24,333 --> 00:05:26,882 We could use Bernoulli's equation again. 134 00:05:26,882 --> 00:05:30,109 Pick two points, let's pick this one, point one. 135 00:05:30,109 --> 00:05:32,682 Let's pick this one, point two. 136 00:05:32,682 --> 00:05:35,917 Use Bernoulli's equation, it says this, 137 00:05:35,917 --> 00:05:39,597 and again let's say these are basically the same height 138 00:05:39,597 --> 00:05:41,901 so that height is not a big factor. 139 00:05:41,901 --> 00:05:43,746 And if these terms are the same, 140 00:05:43,746 --> 00:05:45,502 then we can just cross them out because we can 141 00:05:45,502 --> 00:05:48,723 subtract them from both sides, they're identical. 142 00:05:48,723 --> 00:05:50,139 Now, what can we say? 143 00:05:50,139 --> 00:05:52,924 We know the velocity of the air at two. 144 00:05:52,924 --> 00:05:54,724 It's not moving, got stuck here. 145 00:05:54,724 --> 00:05:55,908 It got stagnant. 146 00:05:55,908 --> 00:05:58,436 And so v two is just zero. 147 00:05:58,436 --> 00:06:00,659 And we get this statement that the pressure 148 00:06:00,659 --> 00:06:05,659 at two, which is sometimes called the stagnation pressure, 149 00:06:06,137 --> 00:06:08,714 so I'm gonna call it the stagnation pressure, 150 00:06:08,714 --> 00:06:12,267 because the air right here gets stuck and it's not moving. 151 00:06:12,267 --> 00:06:14,818 You might object, you might say, "Wait, hold on. 152 00:06:14,818 --> 00:06:16,523 "I thought the air had to go somewhere?" 153 00:06:16,523 --> 00:06:17,930 Well, it's all going somewhere. 154 00:06:17,930 --> 00:06:22,378 The point is, there's some air right here that gets stuck. 155 00:06:22,378 --> 00:06:25,442 It get stuck and air starts passing it by. 156 00:06:25,442 --> 00:06:27,354 And so, what's this pressure here? 157 00:06:27,354 --> 00:06:28,714 Well, up here we just read it off. 158 00:06:28,714 --> 00:06:30,226 All these went away. 159 00:06:30,226 --> 00:06:33,306 P two, which is what I'm calling the stagnation pressure, 160 00:06:33,306 --> 00:06:37,913 has gotta equal P one, the pressure over here, 161 00:06:37,913 --> 00:06:42,913 plus 1/2 row v one squared and we get this formula. 162 00:06:45,217 --> 00:06:49,649 You might think, "Why would we care about this? 163 00:06:49,649 --> 00:06:53,505 "Who is regularly shooting air at a brick wall?" 164 00:06:53,505 --> 00:06:55,745 People do it all the time, because you can build 165 00:06:55,745 --> 00:06:59,536 a pretty important instrument with this called a Pitot tube. 166 00:06:59,536 --> 00:07:01,849 And the Pitot tube looks something like this. 167 00:07:01,849 --> 00:07:02,969 Let's get rid of that. 168 00:07:02,969 --> 00:07:05,193 So why would someone use this system? 169 00:07:05,193 --> 00:07:07,226 It's called a Pitot tube. 170 00:07:07,226 --> 00:07:09,360 People use it to measure fluid velocity 171 00:07:09,360 --> 00:07:11,736 or, if you're moving through the fluid, 172 00:07:11,736 --> 00:07:14,649 it's a way to measure your velocity or your speed. 173 00:07:14,649 --> 00:07:16,905 So what happens is you've got this set up. 174 00:07:16,905 --> 00:07:17,952 Let's say you're in an airplane. 175 00:07:17,952 --> 00:07:19,176 You mount this on the airplane. 176 00:07:19,176 --> 00:07:22,128 You're flying through the fluid, which is the air. 177 00:07:22,128 --> 00:07:26,376 So that mean air is rushing towards this section here. 178 00:07:26,376 --> 00:07:28,984 Rushing past you, let's say you're flying to the left. 179 00:07:28,984 --> 00:07:31,752 So you'll notice air flying past you. 180 00:07:31,752 --> 00:07:34,784 A Pitot tube always has this section that's facing 181 00:07:34,784 --> 00:07:37,476 into the wind or into the air. 182 00:07:37,476 --> 00:07:40,413 This air would be directed straight toward this region, 183 00:07:40,413 --> 00:07:43,714 and the key is this is blocked off at the end. 184 00:07:43,714 --> 00:07:47,561 So there's air in here, but it can't be moving. 185 00:07:47,561 --> 00:07:50,185 The air in this section can't be moving all the way 186 00:07:50,185 --> 00:07:53,257 to the front because, I mean, where's it gonna go? 187 00:07:53,257 --> 00:07:56,522 We just said if fluid flows it, fluid's gotta flow out. 188 00:07:56,522 --> 00:07:57,890 There's no out here. 189 00:07:57,890 --> 00:07:59,266 And then there's another region. 190 00:07:59,266 --> 00:08:02,586 Up here you've got a second chamber 191 00:08:02,601 --> 00:08:04,565 where the air flows over the top. 192 00:08:04,565 --> 00:08:08,229 And this is directed at a right angle to that air flow. 193 00:08:08,229 --> 00:08:09,172 You've got another chamber. 194 00:08:09,172 --> 00:08:11,876 And again, in here, fluid's not flowing. 195 00:08:11,876 --> 00:08:14,896 The key is this gives you a way to determine the difference 196 00:08:14,896 --> 00:08:17,906 between the pressure here and the pressure there. 197 00:08:17,906 --> 00:08:20,386 If you had some sort of membrane in here, 198 00:08:20,386 --> 00:08:24,241 something dividing these two sections that could 199 00:08:24,241 --> 00:08:26,225 tell you the pressure differential, right? 200 00:08:26,225 --> 00:08:29,777 If the pressure on this side is a little bigger 201 00:08:29,777 --> 00:08:33,501 than the pressure on this side, and this would bow outward, 202 00:08:33,501 --> 00:08:37,008 one of these is measuring the pressure here 203 00:08:37,009 --> 00:08:40,119 and one of them is measuring the pressure there. 204 00:08:40,119 --> 00:08:40,724 What is the... 205 00:08:40,724 --> 00:08:43,323 Mathematically, what's the relationship? 206 00:08:43,323 --> 00:08:44,595 It's the one we just found. 207 00:08:44,595 --> 00:08:47,539 Right here, this is the stagnation pressure, right? 208 00:08:47,539 --> 00:08:49,988 The air's not moving in here, it flowed straight in. 209 00:08:49,988 --> 00:08:52,227 We know the v is zero right here. 210 00:08:52,227 --> 00:08:57,227 And so the stagnation pressure equals the pressure up here. 211 00:08:59,084 --> 00:09:01,588 Again, I'm assuming there's very little height difference. 212 00:09:01,588 --> 00:09:04,579 Let's say this is a very small device 213 00:09:04,579 --> 00:09:07,002 and it's not like 10 meters tall. 214 00:09:07,002 --> 00:09:09,919 So any height differences are minuscule, 215 00:09:09,919 --> 00:09:11,843 and we would just have our same equation before. 216 00:09:11,843 --> 00:09:16,843 This would just equal the pressure plus 1/2 row v squared. 217 00:09:18,995 --> 00:09:20,754 And this is how you determine the velocity 218 00:09:20,754 --> 00:09:23,826 or the speed, because now we can just solve this for v. 219 00:09:23,826 --> 00:09:28,826 I'd get that v one equals P s, the stagnation pressure, 220 00:09:29,143 --> 00:09:32,942 minus the pressure at one, that whole thing, 221 00:09:32,942 --> 00:09:37,415 times two, divided by the density of the air 222 00:09:37,415 --> 00:09:38,702 and then a square root because you have to 223 00:09:38,702 --> 00:09:40,239 solve for the v one. 224 00:09:40,239 --> 00:09:43,581 So this device lets you determine this 225 00:09:43,581 --> 00:09:46,332 pressure differential right here, check. 226 00:09:46,332 --> 00:09:49,076 You need to know what the density of air is 227 00:09:49,076 --> 00:09:51,079 and this gives you a way to determine the 228 00:09:51,079 --> 00:09:53,671 velocity of the fluid, or in other words, 229 00:09:53,671 --> 00:00:00,000 the velocity of your aircraft flying through the air.