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