The container shown in FIGURE EX14.11 is filled with oil. It is open to the atmosphere on the left. b. What is the pressure difference between points 1 and 2? Between points 1 and 3?

Video transcript

Hey, everyone in this problem, a tube filled with seawater, which we're told has a density of 1030 kg per meter cubed is shown below one end is open to the atmosphere. And we're asked to find the difference of pressure between for part one points A and B and for part two points B and C, we have our diagram here in, on the Y axis, we have centimeters, we have the open end of our tube. On the left hand side, the right side is closed. We have point A on the left hand side above point B and then we have point C on the right hand side higher than both points A and B. We have four answer choices A through D and they just differ in what the pressures are for both option one and two in this question. So let's think about what we're trying to find. We're trying to find a difference in pressure. OK. So the difference in pressure, delta P, it's just gonna be P two minus P one or vice versa. This is gonna be equal to negative row multiplied by G multiplied by the difference in height Y two minus Y one or the difference in depth. OK. So we call this equation for the difference in pressure. So what we need and the density we have that we were told that the pro acceleration due to gravity, that's a constant. We know that the only other thing we need is the height of each of these points. OK. So the actual shape of this two we have doesn't matter in this probe. OK. What matters is the difference in height? So let's go ahead and just write out these heights so that we have all of them ready to go. The height of point A is that about 40 centimeters. Our answer choices are in kilo pascals. So what we wanna do is convert to meters so that we can get into that standard unit of pascal. So dividing our centimeters by 100 to take us to meters, we get that the height of A which is 40 centimeters is gonna be 0. m. Point B is right at the bottom of our tube. It has a height of 0 m and point C has a height of about 80 centimeters. Again, converting to meters, dividing by 100 we get 0.8 m. So now we have all of our heights, we can go through and calculate the difference and pressures that we were interested in. So for part one and we're interested in the difference in pressure between point A and point B OK. And so the difference in pressure, I'm just gonna put a subscript A B here is gonna be equal to negative row multiplied by G multiplied by Y A minus YB. Substituting in our values, we have negative 1030 kilograms per meter. Cute multiplied by 9.8 m per second squared multiplied by 0.4 m minus 0 m. And if we work this all out, we get a change of pressure of negative 4037. baskets. We're looking just for the magnitude of this difference. OK. So we don't care about this negative sign. We are going to take the positive value. And so our difference in pressure A B is just gonna be 4037. pascals. We wanna write this in pil pillow pascals to match our answer choices. So we're gonna divide by 1000. We have about 4.0376 Phil A Paska. OK? So that's for P one, for part two, we're gonna do the exact same thing but for points B and C so the change in pressure between points B and C is gonna be negative row multiplied by G multiplied by YB minus YC. This is gonna be equal to negative 1030 kg multiplied by 9.8 m per second squared multiplied by 0 m minus 0.8 m. And if we work all of this out. We forget that this is gonna be equal to about 8075.2 pascal converted to our standard unit. We get that the change in pressure whoops, not between A and B but between B and C. OK? And sorry, not converting to our standard unit, converting to kilo pascals the unit of the answer choices we divide by 1000 and get about 8.0752. So now I wanna compare this to our answer choices. We found that the change in pressure between points A and B is gonna be about 4.04 kg. And the change in pressure between points B and C is gonna be about 8.08 kg pascals. And this is gonna correspond with answer choice. B thanks everyone for watching. I hope this video helped see you in the next one.