A barrel contains a 0.120-m layer of oil floating on water that i...

Question

A barrel contains a 0.120-m layer of oil floating on water that is 0.250 m deep. The density of the oil is 600 kg/m^3. (a) What is the gauge pressure at the oil–water interface? (b) What is the gauge pressure at the bottom of the barrel?

Accepted Answer

Hi everyone today, we are going to calculate the gauge pressure at the boundary between oil and water in the drum and the gauge pressure at the very bottom of the drum itself. So from this question, it is given that the oil is going to be 0.8 m and the water is going to be 0.4 m. It is also given that the density of oil is going to be 50 kg per meter cube, which is going to be way less than the density of water, which we know is going to be 1000 kg per meter cube. So because of this, we know that our system will have the oil on the upper layer instead of the water. So I'm just gonna draw our system real quick here. This is going to be our oil which is going to be 8. 0.8 m. And this is going to be our water. We're just going to be 0.4 m just like so okay, now that we know what our system looks like, we can actually start solving this problem. So recall that to solve this sort of problem, the pressure that we have is going to be calculated by using this formula right here, pressure is going to equal to p A T. M. Or atmospheric pressure plus H road G, which is essentially just the effect of the depth of the point. So in calculating gauge pressure in particular were literally calculating the pressure difference. So that is essentially p minus p A T M. The P here is going to be our formula here. So the delta P is going to equal to P A T. M plus H rho G minus P A T M. Again. So the P A T. M will cancel out and the delta P. Or the gauge pressure is just H rho G. Okay, so now we can start by calculating our first condition which is at the boundary. So delta P bound is going to equal through this which is H Ro N G. We know that at the boundary layer here, whatever is above us is pure oil. So this is essentially just the height of the oil, the row of the oil and the G. So we know what those values are, we can just pluck them in. So H oil is 0.8 m row oil is 7 50 kg per meter cube and the G is 9.8 m per second squared. Therefore the delta P bound is going to be 5880 pascal's just like, so, okay, next ah it's going to be our second part of the problem which is the gauge pressure at the bottom. Similar to this part. We know that at the bottom, whatever is above us is the oil that we just calculated here and also the water. So this is going to h oil. Rose oil multiplied by G plus h water. Roll water, multiplied by cheap. The h oil is from this part here which is 5880 pascal's. It's going to be the same which is the gauge pressure off the oil layer and then the gauge pressure of the water layer is going to be calculated with 0.4 m which is H water rho water which is kg per meter cube and G is 9.8 m per second square just like so. And this will come out to be delta P bottom is then going to be 9800 pascal's just like so okay, I'm just gonna highlight it. So we found that the gauge pressure at the boundary is 80 pascal's and the gauge pressure at the bottom is pascal, which corresponds to option C. On our multiple choice. So this is going to be C right here. Okay, if you guys are still confused on this particular topic, please check out our other lesson videos similar to this one and hopefully you guys will gain a better understanding on this particular topic. That will be all for this particular practice problem. And thank you

A barrel contains a 0.120-m layer of oil floating on water that is 0.250 m deep. The density of the oil is 600 kg/m^3. (a) What is the gauge pressure at the oil–water interface? (b) What is the gauge pressure at the bottom of the barrel?

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