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The columns 1 S= padeys-n liquids (see figure) Assume that the two liquids glass and 25,0 cm tube with open side of the tube after the barrier is wader oni ISpoosot...

Question

The columns 1 S= padeys-n liquids (see figure) Assume that the two liquids glass and 25,0 cm tube with open side of the tube after the barrier is wader oni ISpoosot sidesn filled with removed. I H with density

the columns 1 S= padeys-n liquids (see figure) Assume that the two liquids glass and 25,0 cm tube with open side of the tube after the barrier is wader oni ISpoosot sidesn filled with removed. I H with density



Answers

A narrow, U-shaped glass tube with open ends is filled with $25.0 \mathrm{~cm}$ of oil (of specific gravity 0.80 and $25.0 \mathrm{~cm}$ of water on opposite sides, with a barrier separating the liquids (Fig. $\mathbf{P 1 2 . 6 2}$ ). (a) Assume that the two liquids do not $\mathrm{mix},$ and find the final heights of the columns of liquid in each side of the tube after the barrier is removed. (b) For the following cases, arrive at your answer by simple physical reasoning, not by calculations: (i) What would be the height on each side if the oil and water had equal densities? (ii) What would the heights be if the oil's density were much less than that of water?

So we have a U shaped tube and we have oil on one side of the tube and water on the other side. So and then there's a barrier separating the two so and the liquids do not mix. So when the barrier is removed, ah, pressure should be equal, which essentially means that the density of the water times the height should equal the density of the oil times the height of the oil. Here we have an initial height of twenty five centimeters, and then the density of the oil was simply equal. These specific gravity of this oil times the density of water. So here we're going to have tio substitute for these and on. Because the density of the water is greater than the density of the oil, the heights of the water will actually decrease while the height of the oil is going to increase. So plugging For this we can say that the density of water times twenty five centimetres minus this some h some height change equals point eight times the density of water times twenty five plus the same height change. So here we can cancel out the density of Warner and we find that H is equaling two point seven seven seven centimeters. The height of the water is decreasing, so this would be twenty five minus two point seven seven seven and this is going to be twenty two point two two three centimetres. For the oil. We have twenty five plus two point seven seven seven and this is going to be twenty seven point seven seven seven centimeters. So, as you can see, because the density of the water is greater, this the height is going to actually decrease. And the and because of this and turn the height of the oil will increase. Now the question is asking if the density of the be one says the density. If the density of the oil we're the same as the density of the water, then of course, the heights of both of these liquids would be equal. And this is on ly because the same pressure pressure is equal on either side. On B two, it's asking if the what how would happen if the density of the oil was much less than the density of the water and we can see in the previous slide in the first workbook. If the density of the soil was much less, that means that the height of the oil would decrease, greatly increase, actually apologize. So if the density of the oil was much less than the water, that means that the water is exerting much as well are. The pressures are equal. On other side, however, the height needs to be. Height is going to be the factor that accounts for this change in death Death city. So if the density is much less than if the density of oil is much less than water, the height of the oil would have to increase greatly in order for it to exert the same amount of pressure as the water is exerting on the other side of the tube. So these would be the answers. The heights would be eaten for B won, the heights would be equal, and then for B to the height of the oil would increase greatly. And that's the end of the solution. Thank you for watching

In this particular case, the great pressure is be miners B A T M Equus row water G times 25 cents 1,000,000,000 minus X Onda. We would have 25 centimeter minus X. It was 20 centimeters plus x. From here we find that X equals 25 Michael 20 divided by two centimeter equals 2.5 sandy weaker. So the height of the fluid in R A is 25 minus X it was 20 do poor and five centimeter and hide up The fluid in R B is 25. Thus X equals 27.5. Sandy winder If the pressure exerted by God, um A is small. In that case, the hiding arm be will be 20 Find us to have born five equal 37.5 centimeter and hide off in our A with the 25 minus two abort five it was to as four and five centimeter

In the first part of this problem, we're going to calculate the first speed at different regions. So it widely in the speed will be we won and let this pretty narrow region is way too. In order to calculate the speed off the fruit, a different regions, we will apply the equation of continuity that can be written as a one we want is equals to every well, this is the cross sectional area and the winds are the speed of the flu. They're different regions. We can wipe this we, as we is equals to elevated by t where this l is the length off portion off the bip and it is that I've been told so we can write his question as one we want is equals to a l divided by t Now we can watch this waiting for we want as we want is equal to Yeah l do wanted by t 0.1. Now we consider this a multiplied by a list for you Eso this question can be written as we want is equals to capital we which is the volume of the flute divided by t 0.1. Now let's put the values into this quiet we can white we want is equals to into 6.0 multi collaborate terrorists for minus tree I'm two per second into U H one divided by a one which is equals to 40 multiplied Waiter and spot minus four meter square. So from here we can wide video for this we want, as we wanted equals two 1.5 kilometers per second. So this is the speed of the flu that white region. Now for the nether region, we can white Uh, we too as we two is equals to our capital with which is the volume of the flu divided by t 0.80 Wanted by two Our soldiers put the violence into this equation. We two is equal to into 6.0 wanted collaborate terrorist part minus three m que per second into one day wanted by a two which is equal to 10.0 Want to fly by tour is about minus four meter square. So from here we can ride the value for this we too as we two is equals to 6.0 We to prosecute in part via this problem we have to calculate the pressure difference between the two regions. What is the difference of the pressure is identity which is equals toe be one minus p two. In order to calculate the difference of the pressure, we will apply the Bolognese equation which is routinized p one plus wonder wanted by two our road We want square where this was the identity of the flute Loss road G H where research is the innovation off the bip But this region is equals to p two plus one divided by two rules We two squared plus wonder wanted by sorry when you wanted to be two squared plus Rajhi Hey, since both portions are at the same elevation so we can write this rodeo here and here too. From here we can write this p one minus p two is equals to one divided by two low into, uh, we two square minus five on square. Let's put the values into discredit. So p one minus p two is equals to one divided by two into row bitches equals toe our terrorist power tree K G part and cube square brackets open in tow Veto which is equals to 6.0 m per second all squared minus into 1.50 m per second. Hold squared square back clause. From here, we can write this defense off the pressure as Data P is equal to P one minus P two is equals to 1.69 multiple away. Turner is par for Pascoe. Our disk in Britain as a Delta P is equals toe 16.9. Hello, pasta in part solve this problem. We have to calculate the difference in height between the balcony columns in the U chef, too. So let the difference or fight is that H? Once again, we will use the bar knowledge equation. To calculate this high, which can be written for this case, is P one loss raw W, which is the identity of the water. G h Z equals toe P two lost a role and which is the density of the Mercury Judge From here, we can write this equation for H S H is equal to be one minus p two divided by rogue M minus raw W in tow. G. Let's put the village into this quiet, which is equal to 1.69 multiple. Narrator is par for Paschal Divide by, uh, Royal, which is equal to 13 point six. Multiply bitterness Bar she K g Parent cube minus at 1.0 multiple laboratories bar three kg, but, um, cube into in 29.81 m per second square. So from here, we can write the video for this H s H equals two 0.1 37 m. It can be written as h is equals to 30.7 centimeter and off the question. Thank you.

So taking the upper mercury level as Statham, the pressure due to Mercury. Did you hide minus the pressure due to water for height? Is he going to a difference of pressure? So the pressure due to Mercury due to hide would be one point 13.6 Into terrorists to power three In two G, which is 10 and height minus we have the water pressure that is 100 into terrorists. To power one, enter terrorist power three tim is the gravity and the height is H and that would equal to 1.69. Enter terrians to power for which is difference of pressure. Mm. Mhm. So when we equate this equation for height, What we get is the height is equal to 0.1368 m And that would be 13 corn seven m.


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