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Surface AreaTemperature#15U gllons8-3 Surface AreaAmount of Water t0 storeCapacity Needed cubic FcctConstructio Toul Surfecd Volume Tanks Cost Area (cubic f needed ...

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Surface AreaTemperature#15U gllons8-3 Surface AreaAmount of Water t0 storeCapacity Needed cubic FcctConstructio Toul Surfecd Volume Tanks Cost Area (cubic f needed (sq Ft} 525.00Dia- Circuma Radius Height | McC[ ferenccSurface Arca (Sq Ft)Tank MumherSideTotalRottomCccnano Yomr ari nceds cufc Whici (cell HIDfor tha dry spell Determine the cheupest tank configuration given some constraints Diameter and Height of cach tank bised on the cost per squire foot gwven Cell L Using E convcrsion cunic Toot

Surface Area Temperature #15U gllons 8-3 Surface Area Amount of Water t0 store Capacity Needed cubic Fcct Constructio Toul Surfecd Volume Tanks Cost Area (cubic f needed (sq Ft} 525.00 Dia- Circuma Radius Height | McC[ ferencc Surface Arca (Sq Ft) Tank Mumher Side Total Rottom Cccnano Yomr ari nceds cufc Whici (cell HIDfor tha dry spell Determine the cheupest tank configuration given some constraints Diameter and Height of cach tank bised on the cost per squire foot gwven Cell L Using E convcrsion cunic Toot 7,48 gnllon detecrminc the capacity Dcterminc (nc Nqlus (calunin € ; Tememner thatwo adi On diamclcr Dcle (Colum PIOr column Determine thc Surface Area the Top PI(r^ (Col FI Determine thc Surface Area of the Side (Circumference Height}; Col ( Determine the Total Surface arca one Tank ( Top+Bottom+Sidc;; Col H Deterine tht Volunic ISurtace Arca of To7 Hcight;; Col ! In Column Determine the numnber of tanks needed for the requited capacity in KI CEILING(SKSIG.I" Determine the Total Surface Area for the number of tanks needed H6*J6" (1O. Detennine the cost cach Opuontaccd Thc cuchAcT vcm M Analysis: Nulce esily change the cons{raints investigale difetent Eptions Bused On the required 84.4SQgullons needed, Which cncun : how many do ou necdand tbe cOst? VoU Omit necd 3850 (change 3Su for vour small fan; Which E cheapcst Fll do You necd; what > the CO~["'



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The Environmental Protection Agency is investigating an abandoned chemical plant. A large, closed cylindrical tank contains an unknown liquid. You must determine the liquid's density and the height of the liquid in the tank (the vertical distance from the surface of the liquid to the bottom of the tank). To maintain various values of the gauge pressure in the air that is above the liquid in the tank, you can use compressed air. You make a small hole at the bottom of the side of the tank, which is on a concrete platform$-$so the hole is 50.0 cm above the ground. The table gives your measurements of the horizontal distance $R$ that the initially horizontal stream of liquid pouring out of the tank travels before it strikes the ground and the gauge pressure ${p_g}$ of the air in the tank. (a) Graph ${R^2}$ as a function of ${p_g}$. Explain why the data points fall close to a straight line. Find the slope and intercept of that line. (b) Use the slope and intercept found in part (a) to calculate the height $h$ (in meters) of the liquid in the tank and the density of the liquid (in kg/m$^3$). Use $g$ $=$ 9.80 m/s$^2$. Assume that the liquid is nonviscous and that the hole is small enough compared to the
tank's diameter so that the change in h during the measurements is very small.

The diagram of our tank looks like this and this is on a platform. That is a distance. Why? On the ground crying is 15. Uh huh. Mhm Yeah. Mhm Uh huh. Yeah. And when the water comes out its range it's our now you know that the last time time gives the range are and the body hardly sounds why is keeping by have g key squid. There is no NHL particle velocity two combine these two. He's good is given by rookie four. Why? Oh thank you. That was quick. Now we substitute this into the finally situation. Okay and then so uh huh. Arrow squid. So we are substituting is hoping any place of Yeah the screen now when you saw our square Yeah good. They went around like this expression. Mhm Yeah. Yeah. And if you compare this to the question of straight line they realize that they're slow. Yeah is equal to the expression for right over Well chief, which from the graph we can find to be 25.67 mine. And so making The answer to the subject and plugging in all other values, including why? Which is 50 cm. I was the opening five m we ever but identity of eight two already kilograms. Thank you. Make me that. Similarly. We identify that a slew they intersect the intersect. It was four YH. And from the graph that is 16 0.3 85 And from this we can find mm All right to be 8.2 meters.

In the first part of this problem, we are going to find expressions for I am not and live, uh, Capital de Onda Smalley. So let's start from the question and fi B is equals to l I So from here we can Why this capital is equal switches the indignance and, FYI be you wanted by I We call it the question number one. Now let's define the flux. Has five bees equals toe B s so this can be written as B l hell plus B n is Now we know that this is a b l is equals to Mueller Dance off an I you wanted by W and it is be air is equals to mu times off and I divided by wr It can be written as b a is equals to We're not Times off came, you know, times off capital and I divided by w Now we can avoid these Flood says five b is equals to how we can write me with b s a bill as immune I times off capital and I divided by W into capital D minus small d w plus we can write bs. OK, you know times off Capital and I divided by W. And we can write the area A is W d So we can write this question as five b his equals two Mueller dimes off capital and high, uh, square bits open into capital T minus small D plus candy. Now, by setting this value into equation number one, we can write L s L s equals two. Well, not times off. Capital and Square Square backers opened into capital D minus small d last set. Katie, this can also be written as l not minus a lot small d divided by capital D plus Left. Ah, here we can ride Small d divided by captain D is equals to a lot. Last set, I live minus a lot divided by capital de into Smalley. So for me, we can write the expression for this small d a small these equals two l minus allow divided by LF minus a lot into Gabelli. So this is the expression which interlinked Smalley with capitally and we can write Thio allotted a lot is equals to, um you know, dance off and square Capital de Andi elephant written is physicals too came in not times off and square D in part to be off this problem, we're going to calculate the independence for the human cases. Also, we can write the Indyk tints at any height is a at any height. Is Elise equals two l'm art into want loss. Zion, here we can. Why did you wanted by Capital D. So this is our equation number two. Now let's kill Glendale for different heights for the liquid for the liquid oxygen at these equals to capitally divided by to the value off. All will be Elise equals two single point 63 zero for eight and weak at these equals two small is equals to three capital D divided by four. The value off would be capital is equals to 0.63 07 200. So at small days equals to capital D, the very off all will be equals to capital is equals to 0.63 09 600. Now, in case off mercury, how we can write the value for the values for L s at Smalley is equals to Captain Lee. Divided by four the way off l will be l s equals two zero point 63 000 and we so at small days equals two capital de divided by two while your film will be equals two 0.62 my 99 angry. Similarly, it Smalley is equals to three capitally divided by four. Where you off all will be equals two 0.62 My 99 English just small is equals to capitally. Hell will be equals two 0.62 99 18. The values off in the tents in the case off liquid oxygen arm or detectable than the values often victims in the case off mercury. So the volume gauge for liquid oxygen is better than the William gauge for mercury and off the question. Thank you.

In this problem, we have a cylindrical tank that is vented at the top with an outlet at the bottom for liquid to train through. And we know that the depth of the liquid hft and it's area at the surface, which is represented by this red circle A of H are related by a of H times D H D T is equal to minus K times the square root of age, which follows from Torricelli's law. And in this problem K is equal to 0.25 in part A. We want to find the depth of the water at Time T so to do so, we will need thio find a of H, which is easy because this is a cylindrical container or a cylindrical tank. So that means that that the area at the surface of the liquid will be constant as it drains through this tank. So to determine a of age, we know that the radius of the tank is 1 ft, so that means that the area of the liquid at the surface this pie feet squared. So in part a, we have that pi times D H d t. That's equal to minus 0.25 times the square root of H, And then we can solve this using the method of separation of variables. But this differential equation also comes with the initial condition that each of zero is equal to four because the tank is completely filled, which means that the liquid as a depth of 4 ft at time T equals zero. So from here we get that pie. Times D H over the square root of H is equal to minus 0.25 Do you see? We can integrate both sides to get that two pi times. The square root of age is equal to minus 0.25 plus C that that's equal to minus 0.25 times T plus E, and now we can use our initial condition. So this becomes two pi times. The square root of four is equal to minus 0.25 times zero plus c, which means that four pi is equal to see, so we have that to pie times. The square root of age is equal to four pi, minus 0.25 times T From here we can divide through by two pi We have that The square root of H is equal to two minus zero point 0 to 5 over two pi Times team and 0.2 5/2 pi. That's approximately 0.0 3979 And then from here we can take the square of both sides to get that H is approximately the quantity to minus 0.3 0.3979 times t all squared and then in part B. We want to find the time it takes for the tank to drain. So that means that h of t will be equal to zero. So we have that zero is equal to the quantity. Tu minus 0.3979 times t squared. We can take thes square root of both sides to get that zero is equal to Tu minus 0.39 79 times team, which means that two is equal to 0.0 3979 times t Finally, we can divide through by 0.3979 When we get that T is equal to two over 0.39 79 which is approximately 8.4 minutes. This number is actually in seconds. Um, which is 502.6 seconds. But if you work that out, you get that. That is approximately 8.4 minutes, and that completes the problem.

Okay, so the total magnetic flux can be equal to fire Airbus by and fires you go to be Europe attends air and plus and five equals is equals will be liquid times a local beers the magnetic If you at the airport and Ares is the area airports and Bill liquid is the magnetic few l'equippe are a logo Is the area adequate bar? So, you know, be liquid A liquid can be go to km user on my over w tested up came here is the road safety I'm sorry Relative probability over the liquid Where from the museum Museo is a probability constant And I was the current earned Eastern on returns Yeah w here is the with off the tank and d here is the high off the liquid. So as you can tell, um w can we cancel and this will give us museum on eye candy is able to be liquid a liquid and beer air is good museum on Iow testy minus the SW Since we know air is it was a team honesty, uh has w as you gets out that we can we can sew up and he's with us Beer air is with Museo at theme honesty. So there will have the total magnetic flux people The mu zero I came D plus museum on a D minus t which would give us a museum. Items came D plus capital D minus lower case T. We will have outwards to the inductive is the goto environ by which will eventually give us use your eye square does Kim deep rusty modesty. So if we expend it will have allergies for the museum and square km D plus easier and square times capital D and M minus Build your own square lower case D so that al zero school equals a museum and square capital d Our basic with museum and square km lower case T This will give us how is good at zero minus Algeria. Oh, Lord, is the over capital D last out after lower case t over capital D would you give us the high off the liquid which the lower case t here is? You go to Al Mines Algeria over LF minds out zero times Capital D So for a second question, we know how can we go out zero times one plus x m has. OK, see over a capital D tax em. Here is the magnetic susceptibility off the nigari oxygen. Okay, so we know Al zero is 0.63 Henry and accent is you One point by two constant warning. Three. So there will have allies with Joe 0.63 Henry Test wall plus 1.52 attesting to party three as lower case t over capital D. So we know when de over these you on for we'll have our Is he good with 0.630 point. I'm sorry. 0.630 to 9, Henry. And when the over these would want half have always with 0.6304 a m and when d already is equal to 3/4 hours will be able to on 0.63372 Harry. So when the o. K. C over Capital Diesel, the one who have always will do Joe 10.3096 Harry for next question. So for Mercury, we know how zero sent, which is 0.3 Harry by the magnetic susceptibility is different. So they x m for the mercury is negative. 2.9 tensed into party five you re plugging will have its such unquestionable l. So what the over the years with one? For we'll have our physical, the job 0.6 threes or the zero age. And when d o d 0/2 When I was able to draw a 00.629 and nine Henry. And with the over these will, three or four who have the inductions for the liquid mercury is throw 40.6 to 9 and Henry And when the over the top of the one who has the doctors political mercury, which is out here is you got a 0.6 to 9 a. Henry. So for the last person, while my answer is, uh, poop, it should be oxygen gristle, the liquid oxygen. It's more practical. Okay, It's because there is an easily detectable spread off various for the liquid oxygen. But this is not a case for the mercury. Okay, so there. Well, the answer should be the liquid oxygen is more practical. Okay, And these are the answers for this question.


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