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Top of Bell AnaHatchThe experimenta Jiving Dell shoun abovelcwered (rom (escthe ocean $ surtace and reaches maximum depth 75 M Inicially accelerates dounwaro rate o...

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Top of Bell AnaHatchThe experimenta Jiving Dell shoun abovelcwered (rom (escthe ocean $ surtace and reaches maximum depth 75 M Inicially accelerates dounwaro rate of 0.10 MVs? until reaches speed 0r 2.3 MVs which then pressure Inside the beil remains constant atmoscnete The top of the bell has Joss-sectional arez 8.6 m2 Tne density seawater 1025 kg/m'remains constant Durina the descent(a) Calculate the total :Ime take s the bellrtachTAMImMM7 depth of(D) Calculate the weight che Katerthe top

Top of Bell Ana Hatch The experimenta Jiving Dell shoun above lcwered (rom (esc the ocean $ surtace and reaches maximum depth 75 M Inicially accelerates dounwaro rate of 0.10 MVs? until reaches speed 0r 2.3 MVs which then pressure Inside the beil remains constant atmoscnete The top of the bell has Joss-sectional arez 8.6 m2 Tne density seawater 1025 kg/m' remains constant Durina the descent (a) Calculate the total :Ime take s the bell rtach TAMImMM7 depth of (D) Calculate the weight che Kater the top tne bell Yhen T Is ar the Mazlmum depth (c) Calculaie the absolute pressur the top of the bell atthe maximum depth. On the top of tne bell there Circuia harch raduS (d) Calculate the minimum force necessani Ultt cccn thc hatch ccllat thc Maximum dcpth (e) What coulj You do reduce che (orce necessen open [he hatch this depth? Justily your answer. (Thls may checked Iater Your (eacher'



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A cylindrical diving bell has a radius of $750 \mathrm{~cm}$ and a height of $2.50 \mathrm{~m}$. The bell includes a top compartment that holds an undersea adventurer. A bottom compartment separated from the top by a sturdy grating holds a tank of compressed air with a valve to release air into the bell, a second valve that can release air from the bell into the sea, a third valve that regulates the entry of seawater for ballast, a pump that removes the ballast to increase buoyancy, and an electric heater that maintains a constant temperature of $20.0^{\circ} \mathrm{C}$. The total mass of the bell and all of its apparatuses is $4350 \mathrm{~kg}$. The density of seawater is $1025 \mathrm{~kg} / \mathrm{m}^{3}$. (a) An $80.0 \mathrm{~kg}$ adventurer enters the bell. How many liters of seawater should be moved into the bell so that it is neutrally buoyant? (b) By carefully regulating ballast, the bell is made to descend into the sea at a rate of $1.0 \mathrm{~m} / \mathrm{s}$. Compressed air is released from the tank to raise the pressure in the bell to match the pressure of the seawater outside the bell. As the bell descends, at what rate should air be released through the first valve? (Hint: Derive an expression for the number of moles of air in the bell $n$ as a function of depth $y ;$ then differentiate this to obtain $d n / d t$ as a function of $d y / d t .)$ (c) If the compressed air tank is a fully loaded, specially designed, $600 \mathrm{ft}^{3}$ tank, which means it contains that volume of air at standard temperature and pressure ( $0^{\circ} \mathrm{C}$ and $1 \mathrm{~atm}$ ), how deep can the bell descend?

So Okay, 66. We have been not us Rajhi Age Age is 82.3. Middle, we'll be not. Is the atmospheric pressure Dimes 2.5 middle minus x times A Is the volume It will spin art ties v off the bell Times ratio of the temperature. So from here, you can solve for X which will come out as 2.24 middle on Before the bell it was not. Thus row G times 82.3 Middle on that will be 9.16 atmosphere.

So the question is asking us once the diving bell reaches the bottom of the rather the bottom of the sea to rescue these thirty three people. Um, what's the water level at the in the diving bell? And then it's further asking us. What is the necessary gauge pressure of the of Ah air that could be pumped into the diving bell in order to expel all the water out of the diving bell. So we should first write down our givens. Why you go seventy three meters is how far deep sea diving bell must go, and then we're going to say T's of S, which is the temperature at the surface is going to be twenty seven degrees Celsius and this is going to be three hundred kelvin. You basically, in order to convert to Calvin use at two. Seventy three to the temperature and Celsius and anti sub. Why the T support? I simply means the temperature at a depth of why or why equaling seventy three meters. This is going to equal seven degrees Celsius. So this is going to be two eighty Kelvin. At this point, we can say the density of saltwater is again. Ten, one thousand thirty kilograms per cubic meter and then open and on the diving bell. The height of the diving bell is two point three meters. It's going to be open with top. Closed out the bottom. Sorry, closed at the top, Open at the bottom of my apologies. And we know that the height in the diving bell is going to be proportional two. It's going the height and the diving bell is proportional to the volume. Um, inversely proportional to the pressure. So that will be pees over piece of why this is basically the atmospheric pressure and divided by the the pressure at why the lapse of seventy three meters. So it's going to be so. The height and the bell is proportional to the volume to the volume of the bowel, which means that it is also inversely proportional to the pressure and then directly proportional to the temperature. So then we can say t why t s And actually we're going to redefine these variables. We're not going to say h prime were going to say height of the bell and then height at why the depth So we can then move this over and say H y equals h piece of over peace. Why, as at this point, what would be the pressure at? Why so Pressure sub? Why would be, um, the atmosphere pressure plus the density of saltwater times, gravity times Why? And at that point, we can now solve for H y. So h why would equal two point five and then it would be times P y, which is this so would be one o one three to five Pascal's. This is atmospheric pressure atmosphere, pressure piece of was one opens so and then we can simply dio plus And then it'LL be ten thirty nine point eight seventy three and then times two eighty, the temperature at the depth of seventy three meters, divided by the temperature at the surface, and this is going to be equal to point two eight meters. So the change in height would be equal to two point three minus point two eight. Um, so the changing height rather would be point zero two point two zero two point zero two meters. So that would be your answer right here. And then it's asking us what's the pressure? The necessary gauge pressure that you must of the air that you must inject into the diving bell in order to expel all the water. So the necessary gauge pressure would just be equal to the density of salt water times, gravity times why, and it's going to be again. Ten thirty nine point eight seventy three. And that's going to be equal to seven point three seven times ten to the fifth Pascal's. So this would be the necessary gauge pressure. This would need to be the pressure of the air in order to expel all of the water outside of the diving bell once the diving bell has reached a depth of seventy three meters. And that's the end of the solution. So this would be your answer Part B. And this is part of a and that's the end of the solution. Thank you for watching

Okay, So this problem, we have a question relating pressure and volume. So we have that brasher. The finest initial pressure square hoods off the initial pressure divided. I defined a initial volume divided by the final volume. Sorry, uh, we have we have that just Ivan Bell cannot be less and 8.7. She must be greater. Let's put it this way. His diving bell must be greater then 8.7 the volume and the pressure needs to be lower than 1.5. So we want to test if this diving bell attains to the criteria matter the criteria. So to test this, let's put one of the variables in the maximum. Therefore, let's put the pressure in the maximum and test if, well, if you meet the criteria off the volume. So let's isolate the volume here. First of all, so we can say that he a square If I did, i p zero square going to be cool. The zero divided by V. Therefore, volume is defined us ah p zero divided by p the square multiply by vizier. That's the creation for the volume. That's calculate this. We know that the Fordham should be initial pressure. Just wanted wanted. You must feel square, which is also one the multiplies the initial volume off 17 divided by 1.5 the square. So if regard Klytus, we're going to find that the volume is seven point six meters cubic six, which is less than eight point seven meters cubic that far. We can say that this diving bell do not attend to the criteria establish. Okay, that's the final answer. Thanks for watching.

In this problem, we are told we have a diving bell, which is basically usually it's kind of a jar like thing. Um and it is It's a way for to kind of store oxygen or air down underneath the water for divers. And so we have this diving bell here. We are told that s so Here's the bottom, and this is at 100 m, So H is 100 m above below the surface of the water. Um, we told that the surface appear temperatures 20 degrees C. But down here, it's 10 degrees C. Um, this diving bell is has a length of 3 m, and so we want to figure out what the how much what The height of the water is in here. So obviously, as we push this down, we're going to get down to so that the pressure, the pressure, um, of this air needs to be equated with the pressure at this level of the at this level of the ah of the the fluid pressure. Right. So we know P one V one over t one equals p two V two over t to So again, um P one when it was initially at the top was just at atmospheric pressure. P two. Now we have atmospheric pressure, plus the pressure from the fluid above us, which is a row g h. Again. There's there's there's a little bit of ah, simplification I used here because this should be actually h minus. Why? But h is you know, we know that that why is going to be no larger than three and a check is 100. So I'm basically assuming here that this is just eight. This level here is very close to H to make things a little simpler. Um, so we know the volume. The initial volume of the air was just the control volume of the bell jar. And the final volume is, um, basically is a the cross sectional area times l minus. Why so just whatever's left in here. So when can plug all this stuff into here? And we noticed that AIDS cancel out. And that's good, because we weren't told what that waas and then we can solve for l minus. Why? And so l minus, Why is t two over t one times atmospheric pressure times the, um length of the bell jar divided by atmospheric pressure pressure, atmospheric pressure plus the pressure from the water, the hydra hydrostatic pressure of the water. Now we can again then solve for y. And so that's just l minus this whole quantity here and now if we plug in our values, we get something that is extremely different from what the textbook answer says, um or the again. I've been given the answers, but I don't know how they got the answer. Um, and they got an answer of 26 centimeters, and I'm assuming that's from some solution manual or something. Um, 26 centimeters just doesn't seem right. And I don't know, I haven't really tried to back out what that would be. Maybe they used 10 m. Um, the thing is, is that, you know, at 100 m, um, you and so if you're if you're if you're scuba diver And I used to, um, you gain an atmosphere of pressure every time meters, you go down. So at this that this 100 m down, you know, you're at about 10 atmospheres of pressure, so you know that that's quite a bit of pressure. Eso What? What That says is that you know this. This number here, this number here is going to be very small, right? So, you know, we're got basically one divided by 11. So, you know, this is close toe 1/10 and this close. This is post the one. I mean, the temperature didn't change much. So one minus 1/10 roughly you know is nine. You know, 0.9. And eso, that's, you know, about 2.7 m is why, um and so you know, the volume of the air is, you know, they got 20 0.26 m, which basically says that, you know, you just have a little bit a little bit of water in the bottom of this. In reality, I'm pretty sure you actually have a lot of water in this. Oh, I know what that I just looked at. I just noticed what it is because they asked the wrong question. How high does the water rise in after? See that? That's, uh what? That 26 centimeters is actually the the height of the air in here, right, because it was 3 m and now it's 2.76 m. So the difference is 0.26 m. So we have just that little bit of air in here. That's not the height of the water. Um, So they asked him the question. How high does the water rise in the bell jar? Um, it didn't ask how much air was left, what the height of the air was, anyway. I think that's where the 26 I just realized that I think that's where the 26 centimeters came from again. And then the second part of the question is a compressed air hose from the surface is used to expel all the water from the bill. Uh, and they ask, What does the men on pressure is needed? And again they get about 10 Mega Pascal's, which is, you know, 100 atmospheres. Um, so but there's no way that you need 100 atmosphere. Obviously, 100 atmospheres would work, although you probably wind up just floating this thing back up. Um, well, obviously, I mean, it's gonna want to float up. There's some weight. It needs to be weighted down. Obviously. Um, but yeah, I don't know how they get about 10 mega Pascal's, because basically, if you set y equal to zero. So what you want is you want the pressure of the air to be the same as the pressure of the water. There's level, which is roughly, you know, um, 10 atmospheres, which is roughly, you know, one point, um, one point, you know, one mega pascal. So I don't know how they get a factor of 10. Um, because the temperature again doesn't change that much. Right. Um, And again, though, you could say, Well, there's, you know, the weight of the air because the hose is going down. Well, the weight of the air is very small because, you know, the density of air is, you know, very was about 1000 of that of the water. So, you know, that's going to be a very small effect. So I don't know how they get get 10, roughly attend, make a pass. Guy answered, because again, it should be roughly the pressure that is at the bottom. You know, you need the pressure. You need to get this pressure up to, um, 1.15 mega Pascal's. And so you need, um you know the pressure to get that water down or to get the air down that far you need, you know, about 10 atmospheres. And then, you know, he then need about 10 atmospheres in here in the end to get the thing feel the jar bell jar with era. So I That doesn't make sense to me how you get, um ah, 100 atmospheres. Um, that's just that's a lot of pressure. So, anyway, I believe the answer is roughly 10 atmospheres.


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