 Let's solve a question on pressure in fluids. Here we have a manometer which is a device used to measure pressure. Consider an open tube manometer containing a certain fluid. The left end contains a gas at pressure P. We can see that over here. Whereas the right end is open to the atmosphere at atmospheric pressure P a and we can see that we can see that over here and we can see that the height of the fluid in the left column is less than that in the right column. The question is to figure out the relation between P and P a. As always, hit pause and try this one on your own first. All right, hopefully you have given this a shot. Now over here we do need to consider pressure due to fluid, right? There is a fluid. So generally, generally we know that pressure due to fluid, let's say we have this container and there is a fluid up to the height, up to the height h. So if we think about the pressure due to only this fluid at the lowest point, at the lowest point, at this point, that is given by rho gh. Rho is the density of the fluid g into h, the height of the fluid. Now if we look at these two heights h1 and h2, we can say that the pressure due to the fluid at this point, this would be rho gh1 only due to the fluid due to this fluid right here and the pressure due to this fluid through this much fluid, this would be at this point the pressure would be rho gh2. But the total pressure at this point, that would be P plus rho gh1 because there is already a pressure of gas P at this end. So if we think about the total pressure that is pressure due to the gas plus the pressure due to due to the fluid of height h1 and the total pressure due to the fluid of height h2 plus the atmospheric pressure that is PA, PA plus rho gh1. And this fluid is at rest which means that these two points, these two points, this point right here and this point right here, they must be at the same pressure, right? Because if they weren't, if they aren't at the same pressure, then let's say if this part was at a higher pressure than this point, then the fluid would move, it would move in this direction, it would flow towards right. Or if the right point, if this point was at a higher pressure than this point, the fluid would move to the left. So the total pressure at these two points, that's equal. This is equal. Now when we try to work this out, we can take PA to the left-hand side. This becomes P minus PA. This is equal to rho g. This should be, this should be 2, right? rho gh2, rho gh2 minus h1. And we already know that h2 is greater than h1 which means this, this number, this is a positive number. If P minus PA is a positive number, then that means that P, that means that P must be, P must be greater than PA. And we can also try to understand it by looking at the diagram. We see that the fluid is pushed more on the left-hand side compared to the right-hand side. You can see it's, it's below and the fluid over here is, h2 is more, right? So if you say that the area of these two, if these two sides of the tube, if area is the same, then pressure, pressure is really forced divided by area. So if the fluid on the left-hand side, if it's experiencing more force, it should be pushed more down, which is how it is. So it must have a higher pressure on top of it compared to, compared to the right-hand side fluid which is not experiencing that much force, which means the pressure on top of it must be less. And that's why P is greater than PA. You can try more questions from this exercise in the lesson. And if you're watching on YouTube, do check out the exercise link which is added in the description.