 One specific concept that we are going to be encountering when we consider the effects of pressure is how a pressure in a fluid is affected by the weight of the fluid itself. And for that discussion, let's actually open up a new page here. If you consider a unit cell of fluid that has dimensions delta z, delta y, and delta x, and you wanted to compare the pressure at the top of that cell to the pressure at the bottom, what you would be considering is how the force above the bottom is applied to the bottom. So you could think of that like the force on the bottom is equal to the force exerted on the top of the cell plus the weight of the cell itself. I mean if I had a column of textbooks sitting on a desk and the bottom textbook weighed five pounds and the middle textbook weighed three pounds, the top textbook weighed one pound, then the force exerted by the bottom textbook onto the desk is going to be nine pounds because it is the weight of that textbook plus the weight applied on the top of that textbook. You could also consider that as pressures. So we could describe the pressure on the bottom as the force on the bottom expressed per unit area of the bottom. Similarly, the pressure on the top could be expressed as the force on the top divided by the area on top. If we were to rearrange both of these equations in terms of force, the force on the bottom would be P bottom times area of the bottom. We could write the force on the top as being P top times A top. And while weight of the cell might be useful in circumstances where we know the weight of all the water in a swimming pool or something like that, generally speaking it is more convenient for us to describe intensive properties. So instead of describing the weight of the cell, it would be more useful for me to describe the mass of the cell times gravity and then volume of the cell times density of that fluid times gravity. And then to account for situations where the acceleration acting on the cell isn't just gravity, I mean if we were considering the swimming pool in the back of a pickup truck that was going around a corner or something, it might be generalized as acceleration instead of gravity. So now we're describing weight as the volume of the cell times the density of the fluid times acceleration. Then rearranging and solving would yield P bottom times A bottom is equal to P top times A top plus the volume of the cell times the density of the fluid times the acceleration that fluid cell is experiencing. I know that the area of the bottom and the area of the top and the volume of the cell can all be described in terms of these dimensions of the cell that I have defined. Delta x and delta y are the two dimensions that make up the top and the bottom. Therefore the area of the bottom would be delta x times delta y. The area of the top would be delta x times delta y. And the volume of the cell would be delta x times delta y times delta z. And then I can describe the pressure at the bottom times delta x times delta y is being equal to pressure at the top times delta x times delta y plus delta x times delta y times delta z times the density of the fluid times the acceleration that fluid cell is experiencing. Delta x cancels, delta y cancels, which means that the size of the cell only matters vertically. It doesn't matter at all the width or the front to back dimension of this cell. It could be one square meter, it could be a hundred square meters, it could be half a square meter. When we are just talking about these properties, the height is the only thing that matters. Now I will point out that this breaks down a little bit when you get to very small scales because the capillary effect has a non negligible effect on some of the characteristics of the fluid. But for now in general we can describe the pressure at the bottom as being equal to the pressure at the top plus delta z the height of the fluid times the density of the fluid times the acceleration that fluid is experiencing. I commonly write this as delta p that is the pressure difference between the bottom and the top which means delta p is equal to the density of the fluid times acceleration the fluid is experiencing times the height of the fluid. You will hear me refer to that as the PAH equation because it looks kind of like the word PAH even though that's a Greek letter rho which means that it would be more accurately pronounced raw but PAH is what it's called for my purposes just for quick reference. When I say the PAH equation I'm referring to this thing.