Then divide the gravitational acceleration on both sides. So, here's how we're going to get to that equation, let me draw the tube again here and I'm going to put one liquid here and I'm going to put another liquid over here, I'm doing on a different, I'm flipping the sides here, So, I'm going to call this, I'm going to call this, I'm going to call this h1 right here, and then I'm going to go from the from the interface, I'm going to cross over to the other side and this is going to be h2, okay? So, we've drawn this, we're told that the column of oil is 5 centimeters high, this is the right side, I'm going to call this 2, this is 1. So, it's whatever the atmospheric pressure here at this point is because the pressures are the same you're going to have the same height, okay?
Thus, Now, how did I arrive at this equation here? We cannot solve for So far it appears we have reached a dead end. So, I'm going to be able to write that's the pressure between A and B. Now, we're going to be putting the water up a little bit. So, Delta h is h2 minus h1 absolute value just in case it's negative and h2 is 5, this is 4 so this is 1 centimeter, okay? Now, if you look up here, p A is touching air and PC is touching air therefore they both have atmospheric pressure so they both have the same pressure, okay? So, let's write that equation, Delta h is just the distance between the difference between h1 and h2. So, that's that, different pressures will mean different heights and the open side is always going to be lower, let's write that. So, pressure B, p bottom equals p top plus Rho, g, h, pressure at the bottoms and B PB, pressure to top is going to the PA plus Rho, we're talking about the first liquid so it's Rho1 g and an h, h1 and from here I'm able to write the same equation but instead it's going to be p, let's call it C up here, D over here, p D at the bottom equals p C at the top plus Rho. So, it's open here and it's open here, which means that it's exposed to air on both sides usually air or some other, some other gas, right?
Notice that all my units are standard units, right? The question is, there's two questions here and you assume that the liquid don't mix, this a standard language, if the liquids mix, this is not going to work. Well, you can only have a vacuum if one side is closed, let's close over here, closed, and let's say that on this side the liquid goes up to here, right? In other words h1 is the same as h 2, we're going to call the left side 1 and the right side 2. Problem. Hey guys. Now, what about p A and p C? Let's do an example and see how you might see this in action, so it says that the u-tube shown above has two long sides both open at their ends. The Organic Chemistry Tutor 120,717 views. So, something like that, I was terrible.
So, we want the density of the liquid that's on top of it, that's actually applying the pressure and that's the red liquid which is oil and the density there is 800 kilograms per cubic meter and then you have gravity which is 9.8 meters per second squared and then the height is 5 centimeters. So, instead of being like this they're going to do this, okay? Now, the top points are easy to remember A and B, A and C they're just the top of both columns but how are you going to remember, and D is pretty easy too, D is the interface between the two liquids, it's the interface where the two liquids touch. Now, we have h2 but we don't have h1. And now you have rho1 g, h1 equals rho2 g, h2, you can cancel gravities and that's how you arrive at that equation, okay? So, let's keep going.Practice: Water and oil are poured into a u-shape tube, as shown below. So, you can think of p gauge as p bottom without the p top, that's kind of what it is, okay?
So, this here is 20 centimeters. So, this height here, h1, h1 is 4 centimeters, if this is 4 and this is 5 this has to be 1 centimeter, okay? h2 and you can use this equation right here. Oil is lighter than water, water the density of water is 1,000. Because it moves out, if it moves down by this little bit then this thing has to move up by that same little bit and now the red liquid is up here, let me draw the red liquid and, gotta get your colored pens out, cool? The column of oil, on the right side, is 25 cm tall, and the distance between the top of the two columns is 9 cm.