0:00:00.270,0:00:02.070 - [Instructor] We talk about[br]fluid pressure all the time, 0:00:02.070,0:00:05.970 for example, blood pressure[br]or pressure inside our tires, 0:00:05.970,0:00:08.040 but what exactly are these numbers? 0:00:08.040,0:00:09.390 What does 120 mean over here? 0:00:09.390,0:00:11.910 Or what does 40 mean over here? 0:00:11.910,0:00:15.900 So the big question over here[br]is what exactly is pressure? 0:00:15.900,0:00:17.700 That's what we're gonna[br]find out in this video, 0:00:17.700,0:00:18.690 so let's begin. 0:00:18.690,0:00:19.920 To make sense of this, 0:00:19.920,0:00:22.560 let's hang a perfectly cubicle wooden box 0:00:22.560,0:00:24.300 and think about all the forces. 0:00:24.300,0:00:26.430 We know that there's gravitational[br]force acting downwards, 0:00:26.430,0:00:29.160 which is perfectly balanced[br]by the tension force, 0:00:29.160,0:00:32.400 but there is another[br]set of force over here. 0:00:32.400,0:00:34.920 Remember that there are[br]air molecules in our room, 0:00:34.920,0:00:37.650 and so these air molecules[br]are constantly bumping 0:00:37.650,0:00:40.260 and exerting tiny forces. 0:00:40.260,0:00:42.300 But how do we model these forces? 0:00:42.300,0:00:44.880 There are billions of air molecules around 0:00:44.880,0:00:47.490 and they're constantly bumping,[br]so how do we model this? 0:00:47.490,0:00:49.920 Well, we can model them to be continuous, 0:00:49.920,0:00:52.320 that simplifies things,[br]but more importantly, 0:00:52.320,0:00:54.270 if you think about the surface area, 0:00:54.270,0:00:55.650 since this is the perfect cube, 0:00:55.650,0:00:57.780 and the surface areas[br]are exactly the same, 0:00:57.780,0:01:01.110 that means the number of[br]molecules bumping per second 0:01:01.110,0:01:04.230 on each surface is pretty much the same, 0:01:04.230,0:01:06.090 and therefore, we could model these forces 0:01:06.090,0:01:09.480 to be pretty much the same[br]from all the directions, 0:01:09.480,0:01:13.350 and that's why these[br]forces together cancel out 0:01:13.350,0:01:16.470 and they do not accelerate[br]the box or anything like that. 0:01:16.470,0:01:20.520 But these forces, look,[br]are pressing on the box 0:01:20.520,0:01:22.230 from all the direction, 0:01:22.230,0:01:26.220 so it's these forces that[br]are related to pressure. 0:01:26.220,0:01:28.140 But how exactly? 0:01:28.140,0:01:30.690 Well, to answer that question, 0:01:30.690,0:01:32.790 let's think of a bigger box. 0:01:32.790,0:01:35.070 Let's imagine that the[br]surface area over here 0:01:35.070,0:01:39.720 was twice as much as the[br]surface area over here. 0:01:39.720,0:01:43.050 Then what would be the amount of force 0:01:43.050,0:01:44.910 that the air molecules[br]would be putting here 0:01:44.910,0:01:46.470 compared to over here? 0:01:46.470,0:01:49.110 Pause the video and think about this. 0:01:49.110,0:01:52.080 Okay, since we have twice the area, 0:01:52.080,0:01:53.040 if you take any surface, 0:01:53.040,0:01:54.900 if you consider, for[br]example, the top surface, 0:01:54.900,0:01:57.540 the number of molecules bumping per second 0:01:57.540,0:01:59.700 would be twice as much[br]compared to over here, 0:01:59.700,0:02:01.110 because you have twice the area, 0:02:01.110,0:02:03.120 and there are air molecules everywhere. 0:02:03.120,0:02:06.300 So can you see just from that logic, 0:02:06.300,0:02:07.680 the amount of force over here 0:02:07.680,0:02:09.960 must be twice as much as over here. 0:02:09.960,0:02:12.210 If the surface area was[br]three times as much, 0:02:12.210,0:02:14.850 the amount of force[br]must be thrice as much. 0:02:14.850,0:02:16.200 In other words, you can see 0:02:16.200,0:02:19.200 the force that the air molecules[br]are exerting on the box 0:02:19.200,0:02:22.050 is proportional to the surface area. 0:02:22.050,0:02:27.050 Or in other words, the force[br]per area is a constant. 0:02:27.150,0:02:31.320 That is the key characteristics[br]of the force exerted by air 0:02:31.320,0:02:33.153 or, in general, any fluid. 0:02:34.020,0:02:38.100 And that ratio, force per area, 0:02:38.100,0:02:42.330 is what we call, in general, stress, okay? 0:02:42.330,0:02:44.010 But what exactly is pressure? 0:02:44.010,0:02:47.070 Well, in our example, notice that 0:02:47.070,0:02:48.810 the forces are not in[br]some random direction. 0:02:48.810,0:02:52.530 All the forces are perpendicular[br]to the surface area, 0:02:52.530,0:02:54.690 but how can we be so sure, you ask? 0:02:54.690,0:02:57.570 I mean, these are random[br]molecules bumping into it, right? 0:02:57.570,0:03:00.120 Well, if you zoom in, what do you notice? 0:03:00.120,0:03:01.860 You notice that when the molecules bump 0:03:01.860,0:03:03.570 and they sort of collide, 0:03:03.570,0:03:07.590 and they reflect off of the[br]walls of our cubicle box, 0:03:07.590,0:03:09.480 what you notice is the acceleration 0:03:09.480,0:03:11.550 is always perpendicular to the box, 0:03:11.550,0:03:14.250 and therefore, the force that[br]the box is exerting on them 0:03:14.250,0:03:16.650 is also perpendicular to the box. 0:03:16.650,0:03:18.240 And therefore, from Newton's Third Law, 0:03:18.240,0:03:21.450 the force that the molecules[br]are exerting on the box 0:03:21.450,0:03:24.960 will also be equal and opposite[br]perpendicular to the box. 0:03:24.960,0:03:27.810 And that's why the forces over here 0:03:27.810,0:03:29.370 are always perpendicular. 0:03:29.370,0:03:33.150 And so look, there's a special[br]kind of stress over here. 0:03:33.150,0:03:34.560 It's not just any force, 0:03:34.560,0:03:36.270 the force there are always perpendicular, 0:03:36.270,0:03:39.030 and that particular special kind of stress 0:03:39.030,0:03:42.330 where the forces are perpendicular,[br]that is called pressure. 0:03:42.330,0:03:45.180 So you can think of pressure[br]as a special kind of stress 0:03:45.180,0:03:48.090 where the forces are[br]perpendicular to the area. 0:03:48.090,0:03:50.040 But wait, this raises another question. 0:03:50.040,0:03:52.920 Is it possible for fluids to exert forces 0:03:52.920,0:03:55.500 which are paddle to the area as well? 0:03:55.500,0:03:56.910 Yes. 0:03:56.910,0:03:59.820 Consider the air molecules[br]again, they're all moving, 0:03:59.820,0:04:03.210 but they're all moving in[br]random direction, isn't it? 0:04:03.210,0:04:07.050 But now, imagine that[br]there was some kind of wind 0:04:07.050,0:04:09.150 that could happen if the[br]block itself is moving down, 0:04:09.150,0:04:11.580 or there is wind blowing[br]upwards, whatever that is, 0:04:11.580,0:04:14.070 there's some kind of a relative motion. 0:04:14.070,0:04:15.510 Now, if there is a wind, 0:04:15.510,0:04:17.850 let's say the air molecules[br]are moving upwards 0:04:17.850,0:04:18.960 along with the random motion 0:04:18.960,0:04:20.850 that they're doing along with that, 0:04:20.850,0:04:23.880 then because these molecules also interact 0:04:23.880,0:04:25.290 with the molecules of the box, 0:04:25.290,0:04:28.560 they will also exert force on them, 0:04:28.560,0:04:31.200 pulling them upwards. 0:04:31.200,0:04:33.690 This force is called the viscous force, 0:04:33.690,0:04:35.460 and at the heart of it comes from the fact 0:04:35.460,0:04:37.500 that molecules can[br]interact with each other 0:04:37.500,0:04:39.270 and as a result, look, 0:04:39.270,0:04:42.840 this total viscous force is parallel 0:04:42.840,0:04:45.420 to the surface area, 0:04:45.420,0:04:49.230 and this force tends to shear our cube. 0:04:49.230,0:04:50.790 It's kind of like this deck of cards. 0:04:50.790,0:04:52.830 If you press it[br]perpendicular to the surface, 0:04:52.830,0:04:55.050 then the stress is just the pressure. 0:04:55.050,0:04:57.810 But if you press at an angle,[br]then there's a pedal component 0:04:57.810,0:04:59.820 which shears the deck of cards. 0:04:59.820,0:05:02.250 And shearing stresses[br]can be quite complicated, 0:05:02.250,0:05:03.240 but we don't have to worry about it 0:05:03.240,0:05:06.930 because in our model, we[br]are considering ideal fluids 0:05:06.930,0:05:09.750 and ideal fluids do[br]not have any viscosity. 0:05:09.750,0:05:11.400 And we're also going to[br]assume that we are dealing 0:05:11.400,0:05:14.370 with static fluids, which[br]means no viscus forces, 0:05:14.370,0:05:16.530 no relative motion, and therefore, 0:05:16.530,0:05:19.110 we can completely ignore shearing stress. 0:05:19.110,0:05:23.070 And therefore, in our model,[br]we only have pressure. 0:05:23.070,0:05:25.320 Forces will always be only perpendicular 0:05:25.320,0:05:26.670 to the surface area. 0:05:26.670,0:05:28.410 All right, so let's try[br]to understand pressure 0:05:28.410,0:05:29.370 a little bit better. 0:05:29.370,0:05:30.630 What about its units? 0:05:30.630,0:05:32.820 Well, because it's force per area, 0:05:32.820,0:05:33.930 the unit of force is Newtons 0:05:33.930,0:05:36.120 and the unit of area is meters squared, 0:05:36.120,0:05:37.170 so the unit of pressure, 0:05:37.170,0:05:38.220 at least a standard unit of pressure, 0:05:38.220,0:05:39.870 becomes Newtons per meters squared, 0:05:39.870,0:05:42.120 which we also call pascals. 0:05:42.120,0:05:43.680 So over an area of one meter squared, 0:05:43.680,0:05:46.470 if there's one Newton of force[br]acting perpendicular to it, 0:05:46.470,0:05:49.440 then we would say that the[br]pressure is one pascal. 0:05:49.440,0:05:50.910 And that is a very tiny pressure. 0:05:50.910,0:05:52.650 One Newton exerted over one meter squared 0:05:52.650,0:05:54.270 is incredibly tiny. 0:05:54.270,0:05:56.280 So the big question is,[br]what is the pressure 0:05:56.280,0:05:57.840 over here in a room? 0:05:57.840,0:05:59.190 What is the atmospheric pressure? 0:05:59.190,0:06:01.650 Pressure that the air[br]molecules are pushing 0:06:01.650,0:06:03.690 on the sides of this cube with? 0:06:03.690,0:06:05.490 Well, turns out that pressure 0:06:05.490,0:06:08.460 is about 10 to the power of five pascals. 0:06:08.460,0:06:12.120 In other words, that is a 100,000 pascals. 0:06:12.120,0:06:14.760 That is insanely huge. 0:06:14.760,0:06:18.450 A 100,000 Newtons of force is exerted 0:06:18.450,0:06:21.390 by the air molecules per square meter. 0:06:21.390,0:06:24.300 That is insanely high. I[br]wouldn't have expected. 0:06:24.300,0:06:27.300 That is the amount of[br]pressure we are all feeling 0:06:27.300,0:06:28.680 just sitting in our room 0:06:28.680,0:06:30.420 due to the air molecules over there. 0:06:30.420,0:06:32.220 But that was an important question. 0:06:32.220,0:06:35.670 Why don't things get[br]crushed under that pressure? 0:06:35.670,0:06:37.650 I mean, sure, this cube[br]is not getting crushed 0:06:37.650,0:06:40.260 because the internal forces[br]are able to balance that out. 0:06:40.260,0:06:42.720 But what if I take a plastic bag 0:06:42.720,0:06:44.760 and there's nothing inside it, 0:06:44.760,0:06:47.250 then because there's so much air pressure 0:06:47.250,0:06:48.630 over from the outside, 0:06:48.630,0:06:50.700 shouldn't the plastic bag just get crushed 0:06:50.700,0:06:52.230 due to the air pressure? 0:06:52.230,0:06:53.510 Well, the reason it doesn't get crushed 0:06:53.510,0:06:55.470 is because there's air inside as well. 0:06:55.470,0:06:58.530 And that air also has[br]the exact same pressure, 0:06:58.530,0:07:01.050 which means it is able to[br]balance out the pressure 0:07:01.050,0:07:01.950 from the outside. 0:07:01.950,0:07:04.560 But what if you could[br]somehow suck that air out? 0:07:04.560,0:07:06.090 Ooh, then the balance will be lost 0:07:06.090,0:07:07.170 because the pressure drops 0:07:07.170,0:07:11.850 and then we would see the[br]plastic bag collapsing, 0:07:11.850,0:07:14.730 getting crushed under the[br]pressure from the outside. 0:07:14.730,0:07:16.320 That all makes sense, right? 0:07:16.320,0:07:18.060 Okay, before moving forward,[br]let's also quickly talk 0:07:18.060,0:07:19.500 about a couple of other units of pressure 0:07:19.500,0:07:21.270 that we usually use in our daily life. 0:07:21.270,0:07:23.670 For example, when it[br]comes to tire pressure, 0:07:23.670,0:07:28.230 we usually talk in terms[br]of pounds per square inch. 0:07:28.230,0:07:31.020 And just to give some feeling for numbers, 0:07:31.020,0:07:33.060 10 to the power of five[br]pascals happens to be close 0:07:33.060,0:07:36.360 to 14.7 pounds per square inch. 0:07:36.360,0:07:38.130 So that is the atmospheric pressure 0:07:38.130,0:07:39.540 in pounds per square inch. 0:07:39.540,0:07:41.913 Another unit is millimeters of mercury, 0:07:41.913,0:07:44.520 and 10 to the power of five[br]pascals happens to be close 0:07:44.520,0:07:46.560 to 760 millimeters of mercury. 0:07:46.560,0:07:49.680 In other words, the atmospheric[br]pressure can pull up 0:07:49.680,0:07:54.120 the mercury up to 760[br]millimeters in a column. 0:07:54.120,0:07:56.400 Anyways, let's focus on Pascals for now. 0:07:56.400,0:07:59.370 And the big question[br]now, is pressure a scalar 0:07:59.370,0:08:01.890 or a vector quantity, what do you think? 0:08:01.890,0:08:03.540 Well, my intuition says it's vector 0:08:03.540,0:08:06.030 because there's force in one over here, 0:08:06.030,0:08:07.260 but let's think a little[br]bit more about it. 0:08:07.260,0:08:11.970 In fact, think about[br]pressure at a specific point. 0:08:11.970,0:08:13.290 How do we do that? 0:08:13.290,0:08:16.230 Well, one way to do that[br]is you take this box 0:08:16.230,0:08:17.910 and shrink it down. 0:08:17.910,0:08:20.640 Let's say we shrink the size of the box. 0:08:20.640,0:08:23.550 Well, now, the area has[br]become, let's say half, 0:08:23.550,0:08:27.360 but the number of air molecules[br]will also become half, 0:08:27.360,0:08:29.850 and therefore, the[br]force also becomes half, 0:08:29.850,0:08:31.980 making sure force per area stays the same. 0:08:31.980,0:08:33.930 So the pressure stays the same. 0:08:33.930,0:08:35.550 We'll keep shrinking it, keep shrinking, 0:08:35.550,0:08:36.840 and keep shrinking it. 0:08:36.840,0:08:41.190 Now shrink it all the way[br]to an extremely tiny point. 0:08:41.190,0:08:43.350 We call that as an infinitesimal. 0:08:43.350,0:08:45.090 Now, the areas are incredibly tiny, 0:08:45.090,0:08:47.040 the forces are incredibly tiny, 0:08:47.040,0:08:50.040 yet the force per area stays the same. 0:08:50.040,0:08:52.800 That is the pressure[br]at a particular point. 0:08:52.800,0:08:55.770 And now the question is,[br]should we assign a direction 0:08:55.770,0:08:58.440 to this number, to this pressure? 0:08:58.440,0:09:01.590 Well, not really, because[br]all I need is a number, 0:09:01.590,0:09:04.020 because what this number is[br]saying is that if you zoom in 0:09:04.020,0:09:06.090 and if you have any area, 0:09:06.090,0:09:09.360 then there will always be[br]forces perpendicular to the area 0:09:09.360,0:09:12.690 that is exerted by the fluid,[br]and that force per area 0:09:12.690,0:09:14.580 will be 10 to the power of five pascals. 0:09:14.580,0:09:16.500 And that is valid from any direction. 0:09:16.500,0:09:18.540 It doesn't matter how[br]your area is oriented, 0:09:18.540,0:09:21.300 that will always be the case. 0:09:21.300,0:09:24.420 Which means, look, all I need is a number. 0:09:24.420,0:09:26.670 I don't need a direction 0:09:26.670,0:09:28.560 to communicate the idea of pressure, 0:09:28.560,0:09:32.370 and therefore, pressure[br]is a scalar quantity. 0:09:32.370,0:09:33.840 And because the number of air molecules 0:09:33.840,0:09:36.300 bumping per square meter is[br]pretty much the same everywhere 0:09:36.300,0:09:39.030 and their speeds are pretty[br]much the same anywhere you take, 0:09:39.030,0:09:43.440 therefore, the pressure[br]now is the same everywhere. 0:09:43.440,0:09:46.920 But if we zoom out and look[br]at the entire atmosphere, 0:09:46.920,0:09:49.140 for example, that's not the case. 0:09:49.140,0:09:50.910 In fact, that 10 to the[br]power of five we said 0:09:50.910,0:09:53.160 is the pressure close to the sea level, 0:09:53.160,0:09:54.630 but if you were to go[br]a little bit above it, 0:09:54.630,0:09:56.864 say at 10 kilometers, which[br]is the cruising altitude 0:09:56.864,0:09:59.670 of commercial airplanes,[br]you would now find 0:09:59.670,0:10:01.560 that the pressure is about one fourth 0:10:01.560,0:10:03.030 is what we'd find over here. 0:10:03.030,0:10:04.620 Why is the pressure different over here 0:10:04.620,0:10:05.910 compared to over here? 0:10:05.910,0:10:07.440 Well, that's because[br]the molecules over here 0:10:07.440,0:10:09.870 are carrying the weight[br]of the entire atmosphere 0:10:09.870,0:10:10.703 on top of it. 0:10:10.703,0:10:12.780 That entire weight is pushing down, 0:10:12.780,0:10:14.700 pressing the molecules over here. 0:10:14.700,0:10:17.340 However, if you consider[br]the molecules at this level, 0:10:17.340,0:10:18.780 they're not carrying the entire weight, 0:10:18.780,0:10:20.550 they're carrying the[br]weight only on top of them. 0:10:20.550,0:10:22.260 They're not carrying the[br]weight of this amount 0:10:22.260,0:10:23.093 of air molecules. 0:10:23.093,0:10:25.290 And that's why the pressure[br]over here is slightly lower, 0:10:25.290,0:10:27.120 which means the pressure depends 0:10:27.120,0:10:29.070 on the height if you zoom out. 0:10:29.070,0:10:31.500 And so now, the next[br]obvious question would be, 0:10:31.500,0:10:33.750 is there a relationship between[br]the pressure and the height? 0:10:33.750,0:10:35.640 Well, there is, and it's[br]harder to think about that 0:10:35.640,0:10:37.770 for air molecules because air molecules 0:10:37.770,0:10:40.260 are very compressible, so[br]it's a little hard over there. 0:10:40.260,0:10:42.660 But let's consider[br]non-compressible fluids, 0:10:42.660,0:10:45.180 like water, for example. 0:10:45.180,0:10:46.770 So here's a specific question. 0:10:46.770,0:10:49.200 If we know the pressure[br]at some level over here, 0:10:49.200,0:10:53.790 what is the pressure at[br]some depth, say h, below? 0:10:53.790,0:10:55.560 So let's say the pressure at the top is PT 0:10:55.560,0:10:56.860 and the pressure at the bottom is PB. 0:10:56.860,0:10:58.920 Well, we know that the pressure[br]at the bottom is higher 0:10:58.920,0:10:59.760 than the pressure at the top. 0:10:59.760,0:11:00.840 So we could say pressure at the bottom 0:11:00.840,0:11:04.530 equals pressure at the top,[br]plus some additional pressure 0:11:04.530,0:11:06.240 due to this weight of the water. 0:11:06.240,0:11:07.830 But how do we figure that out? 0:11:07.830,0:11:10.830 Well, for that, let's just[br]draw a cuboidal surface, 0:11:10.830,0:11:12.600 having the surface area A. 0:11:12.600,0:11:14.910 Now, the additional pressure[br]that we are getting over here 0:11:14.910,0:11:17.190 is due to the weight of[br]this cuboidal column. 0:11:17.190,0:11:20.700 To be precise, it's going[br]to be the weight per area. 0:11:20.700,0:11:23.550 So this term over here is[br]gonna be weight per area. 0:11:23.550,0:11:26.700 But what exactly is the[br]weight of this cubital column? 0:11:26.700,0:11:28.110 Well, weight is just the force of gravity, 0:11:28.110,0:11:30.900 so it's gonna be MG, where[br]M is the mass of the water 0:11:30.900,0:11:34.290 in this column divided[br]by the area, which is A, 0:11:34.290,0:11:36.060 but how do we figure out what is the mass 0:11:36.060,0:11:38.430 of the column of this water? 0:11:38.430,0:11:41.880 Well, we know that density[br]is mass per volume. 0:11:41.880,0:11:44.670 So mass can written as[br]density times volume, 0:11:44.670,0:11:47.220 and that's because we know[br]the density of a fluid. 0:11:47.220,0:11:51.720 So we can write this as[br]density of the fluid, 0:11:51.720,0:11:53.940 density of water, times[br]the volume of the column 0:11:53.940,0:11:55.710 times GD divided by A. 0:11:55.710,0:11:58.200 But the final question is what[br]is the volume of this column? 0:11:58.200,0:11:59.970 Hey, we know the volume of the column. 0:11:59.970,0:12:01.200 Volume of this cuboidal column 0:12:01.200,0:12:03.540 is just going to be area times the height. 0:12:03.540,0:12:05.970 And so we can plug that in over here, 0:12:05.970,0:12:07.920 and if we cancel out the areas, 0:12:07.920,0:12:10.230 we finally get our expression. 0:12:10.230,0:12:11.640 The pressure at the bottom will equal 0:12:11.640,0:12:15.750 the pressure at the top plus[br]this additional pressure 0:12:15.750,0:12:18.030 due to the weight of this column. 0:12:18.030,0:12:20.100 And this equation will work anywhere 0:12:20.100,0:12:22.590 as long as you're dealing[br]with a non-compressible fluid 0:12:22.590,0:12:25.170 because we are assuming[br]the density to be the same. 0:12:25.170,0:12:27.090 If you consider a[br]compressible fluid, like air, 0:12:27.090,0:12:30.120 the density varies and this[br]calculation becomes harder, 0:12:30.120,0:12:34.350 and so you'll get a considerably[br]different expression. 0:12:34.350,0:12:36.630 But what I find really[br]surprising about this 0:12:36.630,0:12:38.820 is that for a given[br]non-compressible fluid, 0:12:38.820,0:12:40.890 which means it has a specific density, 0:12:40.890,0:12:42.900 the pressure difference between two points 0:12:42.900,0:12:46.440 only depends on their[br]height, nothing else. 0:12:46.440,0:12:48.030 In other words, this means[br]the pressure difference 0:12:48.030,0:12:50.280 between two points, say[br]10 centimeter apart, 0:12:50.280,0:12:52.770 whether you consider that in an ocean 0:12:52.770,0:12:56.220 or a tiny test tube, it's the same. 0:12:56.220,0:12:59.220 It doesn't matter how much[br]water you're dealing with, 0:12:59.220,0:13:02.400 it's just the height that matters. 0:13:02.400,0:13:04.740 Anyways, now we can introduce[br]two kinds of pressure. 0:13:04.740,0:13:07.050 The pressure that we have[br]over here, these two, 0:13:07.050,0:13:09.180 they're called absolute pressures. 0:13:09.180,0:13:11.460 For example, if this was[br]the atmospheric pressure, 0:13:11.460,0:13:13.590 then that is the absolute pressure. 0:13:13.590,0:13:15.870 The absolute pressure of the atmosphere 0:13:15.870,0:13:16.770 close to the sea level 0:13:16.770,0:13:20.280 is about 10 to the power of five pascals. 0:13:20.280,0:13:21.810 But now, look at this term. 0:13:21.810,0:13:23.400 What does that term represent? 0:13:23.400,0:13:26.130 That represents the extra pressure 0:13:26.130,0:13:27.900 that you have at this point 0:13:27.900,0:13:29.910 over and above the atmospheric pressure. 0:13:29.910,0:13:34.110 That extra pressure is what[br]we call the gauge pressure. 0:13:34.110,0:13:36.150 And most of the time when[br]we're talking about pressure 0:13:36.150,0:13:37.290 in our day-today life, 0:13:37.290,0:13:39.360 we are not talking about[br]the absolute pressure, 0:13:39.360,0:13:41.070 we're talking about the gauge pressure. 0:13:41.070,0:13:43.530 So for example, when we talk[br]about the blood pressure, 0:13:43.530,0:13:46.020 we say it's 120 millimeters of mercury. 0:13:46.020,0:13:47.490 What does that even mean? 0:13:47.490,0:13:49.770 Well, remember that the[br]atmospheric pressure 0:13:49.770,0:13:52.800 is 760 millimeters of mercury. 0:13:52.800,0:13:55.530 This is the pressure over and above that. 0:13:55.530,0:13:59.190 So the pressure in the arteries, or veins, 0:13:59.190,0:14:00.750 during a cysto for example, 0:14:00.750,0:14:05.430 is 760 millimeters plus[br]120 millimeters of mercury. 0:14:05.430,0:14:06.480 That's what it really means. 0:14:06.480,0:14:08.400 So this is the additional pressure 0:14:08.400,0:14:10.290 above the atmospheric pressure, 0:14:10.290,0:14:12.090 so this is the gauge pressure. 0:14:12.090,0:14:14.070 The same as the case with our tires. 0:14:14.070,0:14:16.140 For example, if you look at[br]the pressure inside the tire, 0:14:16.140,0:14:19.440 you can see it's about 40 PSI, 0:14:19.440,0:14:21.420 but that is a gauge pressure, 0:14:21.420,0:14:23.460 meaning it's over and above[br]the atmospheric pressure. 0:14:23.460,0:14:26.340 Remember, the atmospheric[br]pressure is 14.7 PSI. 0:14:26.340,0:14:30.150 So the pressure in the tire is 40 PSI 0:14:30.150,0:14:32.400 above the atmospheric pressure. 0:14:32.400,0:14:35.520 So most of the time, we're[br]dealing with gauge pressures. 0:14:35.520,0:14:36.840 Okay, finally. coming back over here, 0:14:36.840,0:14:39.360 suppose we were to draw a[br]graph of the gauge pressure 0:14:39.360,0:14:40.770 versus the depth. 0:14:40.770,0:14:42.630 Okay, what do you think the[br]graph would look like for, 0:14:42.630,0:14:44.820 say, a lake and for the ocean? 0:14:44.820,0:14:46.440 Why don't you pause it and[br]have a think about this? 0:14:46.440,0:14:47.790 Okay, let's consider the lake. 0:14:47.790,0:14:49.860 Right at the surface, the[br]gauge pressure is zero 0:14:49.860,0:14:51.630 because the pressure[br]over there is the same 0:14:51.630,0:14:53.850 as the atmospheric pressure,[br]so we start from zero, 0:14:53.850,0:14:56.460 and then you can see that the[br]gauge pressure is proportional 0:14:56.460,0:14:58.020 to the height, it's proportional to it, 0:14:58.020,0:14:59.280 so we get a straight line. 0:14:59.280,0:15:02.880 And so we'd expect the[br]pressure to increase linearly. 0:15:02.880,0:15:05.580 That's what we would get for[br]the lake. What about the ocean? 0:15:05.580,0:15:08.010 Well, ocean is also water,[br]so it has the same density, 0:15:08.010,0:15:09.060 or does it? 0:15:09.060,0:15:10.890 Remember, ocean has salt water, 0:15:10.890,0:15:12.750 so the density is slightly higher. 0:15:12.750,0:15:14.610 So for the ocean, we expect[br]the line to be steeper, 0:15:14.610,0:15:16.650 having slightly higher slope. 0:15:16.650,0:15:18.330 Finally, before wrapping up the video, 0:15:18.330,0:15:20.460 if you were to submerge[br]a cube inside water, 0:15:20.460,0:15:22.170 earlier, we said that the[br]pressure is gonna be the same 0:15:22.170,0:15:23.490 from all directions, 0:15:23.490,0:15:25.080 but now we know that the[br]pressure on the bottom 0:15:25.080,0:15:27.840 is slightly higher than[br]the pressure on the top, 0:15:27.840,0:15:29.640 which means the forces on the bottom 0:15:29.640,0:15:31.530 would be slightly higher[br]than the force on the top 0:15:31.530,0:15:33.030 because the area is the same. 0:15:33.030,0:15:36.900 So wouldn't that produce[br]a net upward force? 0:15:36.900,0:15:40.290 Yes, it would, and that's[br]called the buoyant force, 0:15:40.290,0:15:43.080 which is responsible for[br]making certain things float. 0:15:43.080,0:15:45.880 And that's something we'll[br]talk about in a future video.