1 00:00:01,133 --> 00:00:03,089 - [Voiceover] Check out this empty box. 2 00:00:03,089 --> 00:00:04,766 Now, check out this lid 3 00:00:04,766 --> 00:00:06,600 that I can put on the empty box. 4 00:00:06,600 --> 00:00:09,300 Let's say there is no resistance 5 00:00:09,300 --> 00:00:11,966 so that if I gave this lid a little nudge, 6 00:00:11,966 --> 00:00:14,340 it just keep moving with the constant speed. 7 00:00:14,340 --> 00:00:15,746 Let's say there's no air resistance. 8 00:00:15,746 --> 00:00:17,566 No resist to forces at all. 9 00:00:17,566 --> 00:00:20,366 Now what I'm gonna do, I'm gonna stick a fluid. 10 00:00:20,366 --> 00:00:21,600 Let's say water. 11 00:00:21,600 --> 00:00:23,035 And I'm gonna fill it to the brim 12 00:00:23,035 --> 00:00:24,035 all the way to the top. 13 00:00:24,035 --> 00:00:25,533 This thing was overflowing. 14 00:00:25,533 --> 00:00:27,500 This goes all the way to the top. 15 00:00:27,500 --> 00:00:30,000 Now what happens is you take this lid, 16 00:00:30,000 --> 00:00:32,299 you go to slide it across again. 17 00:00:32,299 --> 00:00:34,167 You give it a little nudge, it doesn't keep going, 18 00:00:34,167 --> 00:00:35,800 it slows down and stops. 19 00:00:35,800 --> 00:00:37,035 You give it another nudge, 20 00:00:37,035 --> 00:00:39,000 it slows down and stops. 21 00:00:39,000 --> 00:00:40,900 The fact that this fluid's in here now 22 00:00:40,900 --> 00:00:43,933 is resisting the motion that's because it's viscous. 23 00:00:43,933 --> 00:00:44,930 What do I mean by that? 24 00:00:44,930 --> 00:00:48,366 I mean that when this lid was moving across the top, 25 00:00:48,366 --> 00:00:52,100 the fact that this fluid was in contact with the lid 26 00:00:52,100 --> 00:00:54,728 caused this top most layer to start moving 27 00:00:54,728 --> 00:00:57,000 with the same speed as the lid. 28 00:00:57,000 --> 00:01:01,309 There's adhesive forces between this fluid and the lid 29 00:01:01,309 --> 00:01:03,500 on an atomic and molecular level, 30 00:01:03,500 --> 00:01:05,733 this fluid gets pulled with it. 31 00:01:05,733 --> 00:01:08,133 And so it resist the motion but it's worse than that 32 00:01:08,133 --> 00:01:10,934 because if this top most layer gets pulled this way 33 00:01:10,934 --> 00:01:12,566 then the layer right below it 34 00:01:12,566 --> 00:01:14,800 gets pulled by the top most layer 35 00:01:14,800 --> 00:01:17,800 and the second most layer pulls this third most layer 36 00:01:17,800 --> 00:01:19,700 and this keeps going down the line, 37 00:01:19,700 --> 00:01:22,267 and what you get is a velocity gradient 38 00:01:22,267 --> 00:01:24,200 is the fancy name for it. 39 00:01:24,200 --> 00:01:26,579 Which just means that this velocity of this fluid 40 00:01:26,579 --> 00:01:27,933 gets smaller and smaller. 41 00:01:27,933 --> 00:01:29,533 Once you get down to the bottom 42 00:01:29,533 --> 00:01:31,366 well, now the fluid is in contact 43 00:01:31,366 --> 00:01:32,666 with this surface at the bottom 44 00:01:32,666 --> 00:01:34,967 and this surface at the bottom is not moving. 45 00:01:34,967 --> 00:01:38,133 This fluid is at the lowest most point doesn't move at all. 46 00:01:38,133 --> 00:01:40,546 All right, so that's why this lid slowed down 47 00:01:40,546 --> 00:01:41,519 when we gave it a nudge, 48 00:01:41,519 --> 00:01:43,866 it was dragging that fluid along with it. 49 00:01:43,866 --> 00:01:48,000 And if it exerts a force to the right on the fluid, 50 00:01:48,000 --> 00:01:50,000 then the fluid is gonna exert a force 51 00:01:50,000 --> 00:01:54,200 by doing its third law to the left on the lid 52 00:01:54,200 --> 00:01:56,494 and I'm gonna call this a viscous force. 53 00:01:56,494 --> 00:01:58,133 I'm gonna call it Fv. 54 00:01:58,133 --> 00:01:59,301 So, what does this depend on? 55 00:01:59,301 --> 00:02:02,066 What does this viscous force depend on? 56 00:02:02,066 --> 00:02:04,333 One thing it depends on is the area 57 00:02:04,333 --> 00:02:07,533 and not the whole area of the lid. 58 00:02:08,000 --> 00:02:09,667 It's just the area of the lid 59 00:02:09,667 --> 00:02:11,842 that's actually in contact with the fluid. 60 00:02:11,842 --> 00:02:15,900 So if you imagine the dimensions of this box 61 00:02:16,366 --> 00:02:17,576 would only expand here. 62 00:02:17,576 --> 00:02:18,925 So it's only that part of the lid 63 00:02:18,925 --> 00:02:21,938 that's actually in contact with the fluid. 64 00:02:22,400 --> 00:02:25,400 So that area and it's proportional to that area. 65 00:02:25,400 --> 00:02:27,212 The bigger that area, 66 00:02:27,212 --> 00:02:29,679 the more fluid you're gonna be dragging, 67 00:02:29,679 --> 00:02:32,266 the larger the viscous force that makes sense 68 00:02:32,266 --> 00:02:34,333 so it's this area here. 69 00:02:34,702 --> 00:02:36,633 And something else that it depends on 70 00:02:36,633 --> 00:02:39,767 is the speed with which you drag the lid. 71 00:02:39,767 --> 00:02:41,600 So the faster I pull the lid, 72 00:02:41,600 --> 00:02:44,179 well, the faster I'm gonna be pulling this water, 73 00:02:44,179 --> 00:02:45,147 the bigger that force 74 00:02:45,147 --> 00:02:47,133 which means the bigger the viscous force, 75 00:02:47,133 --> 00:02:49,600 which was proportional to the speed as well. 76 00:02:50,153 --> 00:02:54,590 It's inversely proportional to the depth of the fluid. 77 00:02:54,590 --> 00:02:56,300 I'll call that D. 78 00:02:56,300 --> 00:02:58,513 And then it depends on one more thing. 79 00:02:58,513 --> 00:03:00,738 It depends on the viscosity of the fluid. 80 00:03:00,738 --> 00:03:03,233 Maybe the most important factor in this whole discussion. 81 00:03:03,740 --> 00:03:08,233 Eta is gonna be called the viscosity of the fluid 82 00:03:08,233 --> 00:03:11,834 or the coefficient of viscosity. 83 00:03:11,834 --> 00:03:13,367 And what this number tells you 84 00:03:13,367 --> 00:03:15,167 is how viscous, how thick 85 00:03:15,167 --> 00:03:17,133 essentially the fluid is. 86 00:03:17,133 --> 00:03:19,233 How much it resist flow. 87 00:03:19,233 --> 00:03:21,571 And so, coefficient of viscosity. 88 00:03:21,571 --> 00:03:23,667 So to give you an idea honey 89 00:03:23,667 --> 00:03:26,533 or corn syrup would have a large viscosity. 90 00:03:26,533 --> 00:03:29,833 Water would have that smaller viscosity coefficient 91 00:03:29,833 --> 00:03:31,200 and gasses would have a 92 00:03:31,200 --> 00:03:33,533 coefficient of viscosity even less. 93 00:03:33,533 --> 00:03:36,500 So what are the units of this coefficient of viscosity? 94 00:03:36,500 --> 00:03:37,966 Well, if we solved. 95 00:03:37,966 --> 00:03:40,238 If we were to solve for the eta, 96 00:03:40,238 --> 00:03:41,115 what would we get? 97 00:03:41,115 --> 00:03:43,994 We'd get force divided by area. 98 00:03:43,994 --> 00:03:48,994 So this would be force divided by area, 99 00:03:49,233 --> 00:03:53,333 and multiplied by the distance divided by the speed. 100 00:03:53,333 --> 00:03:54,892 What units do these have? 101 00:03:54,892 --> 00:03:58,484 Force is newtons, distance is in meters, 102 00:03:58,484 --> 00:04:01,000 area is in meters squared, 103 00:04:01,000 --> 00:04:03,400 speed is in meters per second. 104 00:04:03,400 --> 00:04:05,000 So I bring that second up top 105 00:04:05,000 --> 00:04:07,166 because it was divided in the denominator. 106 00:04:07,166 --> 00:04:08,243 So it goes up top. 107 00:04:08,243 --> 00:04:09,546 And what am I left with? 108 00:04:09,546 --> 00:04:11,300 Meters cancels meters 109 00:04:11,761 --> 00:04:13,633 and I'm left with the units of viscosity 110 00:04:13,633 --> 00:04:17,666 as being newtons per meter squared times a second, 111 00:04:17,666 --> 00:04:19,899 but a newton per meter squared is a pascal 112 00:04:19,899 --> 00:04:22,666 so this is pascal seconds. 113 00:04:22,666 --> 00:04:24,333 So these units are a little strange 114 00:04:24,333 --> 00:04:27,934 but the units of eta, the coefficient of viscosity 115 00:04:27,934 --> 00:04:31,633 is a pressure times a time, pascal seconds. 116 00:04:32,126 --> 00:04:34,900 But some people use the unit poise 117 00:04:34,900 --> 00:04:37,500 and one poise 118 00:04:39,346 --> 00:04:44,346 is equal to 1/10 of a pascal second. 119 00:04:45,333 --> 00:04:47,666 Or in other words 10 poise 120 00:04:47,666 --> 00:04:50,967 and it's abbreviated capital P is 121 00:04:50,967 --> 00:04:53,250 one pascal second. 122 00:04:53,250 --> 00:04:55,400 And so, you'll often hear this unit poise 123 00:04:55,400 --> 00:04:58,266 as a measure of viscosity. 124 00:04:58,266 --> 00:05:00,976 So what are some real life values for the viscosity? 125 00:05:00,976 --> 00:05:03,133 Well, the viscosity of water 126 00:05:04,151 --> 00:05:07,499 at zero degree Celsius is, 127 00:05:07,499 --> 00:05:08,784 and I'm not talking about ice 128 00:05:08,784 --> 00:05:11,433 but water that's actually at zero degrees 129 00:05:11,433 --> 00:05:14,433 but not frozen yet is about 1.8. 130 00:05:14,433 --> 00:05:18,833 But 1.8 millipascal seconds. 131 00:05:19,425 --> 00:05:20,895 And another way to say that, 132 00:05:20,895 --> 00:05:22,867 look at millipascal seconds, 133 00:05:22,867 --> 00:05:27,200 that would be a centi, a centipoise, cP. 134 00:05:27,561 --> 00:05:31,930 Because a poise is already 1/10 of a pascal second. 135 00:05:31,930 --> 00:05:33,866 Remember one poise is 1/10. 136 00:05:33,866 --> 00:05:38,399 And so a centipoise is really a millipascal second 137 00:05:38,399 --> 00:05:43,300 or water at 20 degrees Celsius is 138 00:05:43,300 --> 00:05:48,099 1.0 millipascal seconds or centipoise. 139 00:05:48,099 --> 00:05:51,766 Now you can see there's a huge dependency on temperature. 140 00:05:52,703 --> 00:05:55,925 The viscosity is highly dependent on temperature. 141 00:05:55,925 --> 00:05:57,433 The colder it gets, 142 00:05:57,433 --> 00:05:59,766 the more viscous a fluid typically gets 143 00:05:59,766 --> 00:06:01,700 which you know, because if you start your car 144 00:06:01,700 --> 00:06:03,233 and it's too cold outside, 145 00:06:03,233 --> 00:06:04,600 that car is not gonna want to start. 146 00:06:04,600 --> 00:06:06,719 That oil inside's gonna be more viscous 147 00:06:06,719 --> 00:06:08,433 than it's prepared for, 148 00:06:08,433 --> 00:06:10,833 and that engine might not start very easily. 149 00:06:11,505 --> 00:06:14,776 Blood typically has a viscosity 150 00:06:14,776 --> 00:06:19,776 between three to four millipascal seconds or centipoise. 151 00:06:21,734 --> 00:06:24,934 And then engine oil can have 152 00:06:24,934 --> 00:06:27,167 viscosities in the hundreds. 153 00:06:27,167 --> 00:06:30,853 Around 200 centipoise. 154 00:06:30,853 --> 00:06:33,481 And then gasses, gasses would have 155 00:06:33,481 --> 00:06:35,442 viscosities that are even less. 156 00:06:35,442 --> 00:06:40,100 Air has a viscosity of around 157 00:06:40,467 --> 00:06:44,400 0.018 centipoise. 158 00:06:45,000 --> 00:06:46,009 Now it's important to note, 159 00:06:46,009 --> 00:06:49,800 if a fluid follows this rule for the viscous force 160 00:06:49,800 --> 00:06:54,492 and the coefficient of viscosity does not depend 161 00:06:55,092 --> 00:06:58,280 on the speed with which this fluid is flowing 162 00:06:58,280 --> 00:07:00,933 or with which you pull this lid over the top 163 00:07:00,933 --> 00:07:02,833 does not depend on that. 164 00:07:02,833 --> 00:07:05,533 Then we call this a Newtonian Fluid. 165 00:07:05,533 --> 00:07:08,467 Then it's a Newtonian Fluid. 166 00:07:08,467 --> 00:07:12,233 But if the coefficient of viscosity 167 00:07:12,233 --> 00:07:14,202 does depend on the speed 168 00:07:14,202 --> 00:07:15,676 with which the fluid is flowing 169 00:07:15,676 --> 00:07:17,700 or the speed with which you pulled this lid, 170 00:07:17,700 --> 00:07:20,333 then it would be a non-Newtonian fluid. 171 00:07:20,333 --> 00:07:22,300 So if this coefficient of viscosity 172 00:07:22,300 --> 00:07:24,800 stays the same regardless of what the speed is, 173 00:07:24,800 --> 00:07:26,100 it's a Newtonian fluid. 174 00:07:26,100 --> 00:07:27,333 If that's not the case, 175 00:07:27,333 --> 00:07:28,984 it would be a non-Newtonian fluid. 176 00:07:28,984 --> 00:07:30,467 Now, you might be thinking 177 00:07:30,467 --> 00:07:31,766 well, this is kind of stupid. 178 00:07:31,766 --> 00:07:32,962 I mean, how many cases are we gonna have 179 00:07:32,962 --> 00:07:35,512 where you're trying to pull a lid over a box, 180 00:07:35,512 --> 00:07:37,833 you've probably never tried to do that in real life. 181 00:07:37,833 --> 00:07:40,233 But this is just a handy way 182 00:07:40,233 --> 00:07:41,566 to determine the viscosity. 183 00:07:41,566 --> 00:07:42,871 Once you know the viscosity 184 00:07:42,871 --> 00:07:44,242 you can apply this number. 185 00:07:44,242 --> 00:07:47,133 This is a constant of the fluid. 186 00:07:47,133 --> 00:07:49,533 Now, anywhere that this fluid is flowing 187 00:07:49,533 --> 00:07:51,074 now that you measured it carefully, 188 00:07:51,074 --> 00:07:54,100 you could determine what kind of flow rate you would get. 189 00:07:54,100 --> 00:07:57,566 So imagine, let's get rid of all these stuff here. 190 00:07:57,566 --> 00:08:00,066 So you had a stationary tube or a pipe 191 00:08:00,066 --> 00:08:01,533 and there was a fluid flowing through it, 192 00:08:01,533 --> 00:08:03,000 maybe it's a vein or a vessel 193 00:08:03,000 --> 00:08:05,200 and it's blood flowing through it. 194 00:08:05,200 --> 00:08:07,100 Anyways, now it's stationary though. 195 00:08:07,100 --> 00:08:09,066 Both the top and the bottom are stationary 196 00:08:09,066 --> 00:08:10,766 so that means the fluid near the top 197 00:08:10,766 --> 00:08:13,033 and the fluid near the bottom aren't really moving 198 00:08:13,033 --> 00:08:14,866 but it's the fluid in the middle 199 00:08:14,866 --> 00:08:16,534 that's moving fastest 200 00:08:16,534 --> 00:08:18,333 and then slightly less fast, 201 00:08:18,333 --> 00:08:21,828 and you get this somewhat parabolic type 202 00:08:21,828 --> 00:08:24,846 velocity gradient where it gets bigger and bigger 203 00:08:24,846 --> 00:08:26,866 and then it gets smaller and smaller, 204 00:08:26,866 --> 00:08:28,966 and so, the velocity profile 205 00:08:28,966 --> 00:08:30,682 might look something like this. 206 00:08:30,682 --> 00:08:35,466 And, if we wanted to know how much volume 207 00:08:35,466 --> 00:08:38,332 of fluid, how many meters cube of fluid 208 00:08:38,332 --> 00:08:40,960 passed by a certain point per time, 209 00:08:40,961 --> 00:08:42,366 we can figure that out. 210 00:08:42,366 --> 00:08:44,433 There's a formula for this. 211 00:08:44,433 --> 00:08:47,601 The volume per time, the meters cube per time. 212 00:08:47,601 --> 00:08:50,239 Now the formula is called Poiseuille's Law. 213 00:08:50,239 --> 00:08:51,333 And it says this. 214 00:08:51,333 --> 00:08:53,695 It says the volume that will flow per time 215 00:08:53,695 --> 00:08:58,100 is dependent on delta P 216 00:08:58,533 --> 00:09:01,930 times pi, times R to the fourth, 217 00:09:01,930 --> 00:09:06,142 divided by eight eta, times L. 218 00:09:06,142 --> 00:09:07,548 Now this is a crazy equation. 219 00:09:07,548 --> 00:09:09,146 Let's break this thing down 220 00:09:09,146 --> 00:09:10,900 and see what it's really talking about. 221 00:09:10,900 --> 00:09:12,833 So here's Poiseuille's Law. 222 00:09:12,833 --> 00:09:16,200 So, this delta P is referring to the pressure differential. 223 00:09:16,200 --> 00:09:17,658 So it will be pressure on this side. 224 00:09:17,658 --> 00:09:19,433 We'll call it P one. 225 00:09:19,433 --> 00:09:21,233 There'll be pressure on this side, P two. 226 00:09:21,233 --> 00:09:22,433 If those were the same, 227 00:09:22,433 --> 00:09:24,567 this fluid's not gonna be flowing very long. 228 00:09:24,567 --> 00:09:25,800 There's gonna be a difference. 229 00:09:25,800 --> 00:09:27,500 If we want the fluid to flow to the right, 230 00:09:27,500 --> 00:09:30,361 P one has to be bigger than P two, 231 00:09:30,361 --> 00:09:32,600 and the greater the difference, 232 00:09:33,133 --> 00:09:36,902 the greater this difference P one minus P two, 233 00:09:36,902 --> 00:09:39,126 the more volume that's gonna flow per time 234 00:09:39,126 --> 00:09:40,633 and that makes sense. 235 00:09:40,633 --> 00:09:42,800 And then pi is a geometric factor. 236 00:09:42,800 --> 00:09:44,667 R to the fourth. 237 00:09:44,667 --> 00:09:47,894 This R is referring to the raise of the tube. 238 00:09:47,894 --> 00:09:49,546 So that's R. 239 00:09:50,100 --> 00:09:52,467 And then eight and eta we know. 240 00:09:52,467 --> 00:09:55,128 Eta is the viscosity. 241 00:09:55,128 --> 00:09:57,533 So this is the viscosity of the fluid. 242 00:09:57,533 --> 00:09:58,676 And the volume flow rate's 243 00:09:58,676 --> 00:10:00,853 inversely proportional to the viscosity 244 00:10:00,853 --> 00:10:03,133 because the more viscous the fluid, 245 00:10:03,133 --> 00:10:04,842 the more it resists flowing, 246 00:10:04,842 --> 00:10:07,802 and the less meters cube you'll get per second. 247 00:10:07,802 --> 00:10:09,927 And it's inversely proportional also 248 00:10:09,927 --> 00:10:11,352 to the length of the tube. 249 00:10:11,352 --> 00:10:13,967 The more tube this fluid's got to flow through, 250 00:10:13,967 --> 00:10:15,752 the smaller the volume flow rate. 251 00:10:15,752 --> 00:10:18,233 So this is called Poiseuille's Law. 252 00:10:18,233 --> 00:10:19,968 It's useful on a lot of medical 253 00:10:19,968 --> 00:10:21,576 and engineering applications. 254 00:10:21,576 --> 00:10:23,000 For whenever you want to determine 255 00:10:23,000 --> 00:10:24,700 the volume flow rate, 256 00:10:24,700 --> 00:10:26,600 now you've got to be careful. 257 00:10:26,600 --> 00:10:29,000 We're assuming this is a Newtonian fluid, 258 00:10:29,000 --> 00:10:32,404 that means eta's not a function of the speed of the fluid. 259 00:10:32,404 --> 00:10:33,633 We're also assuming you have 260 00:10:33,633 --> 00:10:36,867 nice streamlined laminar flow. 261 00:10:36,867 --> 00:10:39,569 So laminar flow means 262 00:10:39,569 --> 00:10:42,961 these layers of fluid stay in their lane basically. 263 00:10:42,961 --> 00:10:45,453 They do not crossover. 264 00:10:45,453 --> 00:10:47,067 Once you start getting this, 265 00:10:47,067 --> 00:10:48,351 you'll start getting turbulence 266 00:10:48,351 --> 00:10:50,067 and once you get turbulence, 267 00:10:50,067 --> 00:10:52,400 you'll need a much more complicated 268 00:10:52,400 --> 00:10:54,800 equation to describe the dynamics of this. 269 00:10:54,800 --> 00:10:56,766 So we're assuming no turbulence 270 00:10:56,766 --> 00:10:58,533 and a nice Newtonian fluid. 271 00:10:58,533 --> 00:10:59,766 And if that's the case, 272 00:10:59,766 --> 00:11:02,400 Poiseuille's law gives you the volume 273 00:11:02,400 --> 00:00:00,000 that flows through a pipe per time.