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Chapter 14, Problem 057Your answer partlally correct , Try agaln;cylincrical tank with large diameter filled with water t0 depth D 0,415 m; hole of coss-sectional a...

Question

Chapter 14, Problem 057Your answer partlally correct , Try agaln;cylincrical tank with large diameter filled with water t0 depth D 0,415 m; hole of coss-sectional area 5.31 0mm? in the bottomn of the tank allows water t0 drain out; (a) wnat the rate at whlch water flows out, In cublc meters per seconc? (b} At what distance belovi the bottom of the tank Is the coss-sectlona area of the strean equa to one-half the area of the hole?(2) Numbe 365500Units m^3/5(b) Numbe245Units

Chapter 14, Problem 057 Your answer partlally correct , Try agaln; cylincrical tank with large diameter filled with water t0 depth D 0,415 m; hole of coss-sectional area 5.31 0mm? in the bottomn of the tank allows water t0 drain out; (a) wnat the rate at whlch water flows out, In cublc meters per seconc? (b} At what distance belovi the bottom of the tank Is the coss-sectlona area of the strean equa to one-half the area of the hole? (2) Numbe 365500 Units m^3/5 (b) Numbe 245 Units



Answers

A cylindrical tank with a large diameter is filled with water to a depth $D=0.30 \mathrm{~m} .$ A hole of cross-sectional areac $A=6.5 \mathrm{~cm}^{2}$ in the bottom of the tank allows water to drain out. (a) What is the drainage rate in cubic meters per second? (b) $\mathrm{At}$ what distance below the bottom of the tank is the cross-sectional area of the stream equal to one-half the area of the hole?

And this problem. We have a tank on fluid with a hole in the bottom of it and the fluids draining out. We're told that the tank is your 0.3 meters deep. The area of the cross section, but with a fluid is flowing out, is 6.5 times 10 to the minus fourth meters cube. And what we want to find out is the rate at which the fluid is draining and the distance and the distance We love the whole that the cross section of the fluid flow is 1/2 of the exit hole. So we have Bernoulli's equation. We can use that to look at the difference between our state at zero on one and then also one and two. So we have peanut over row, plus 1/2 be not squared. Plus gee, why not? That equals. We want overwrote those 1/2 me one squared plus g. Why one and and also equals P two row plus 1/2 we two squared plus G. Why, to some of these terms are zero. The velocity at the top of the tank is zero pressure here and the president are those are all equal and atmospheric pressure will measure why from the top of the fluid. So that zero that leaves us with fee. One squared equals minus to t. Why one and why one is minus tease? That's too t d. So everyone is simply square root of two g d. The volumetric flow rate. At one, there's a one times V one, so that's a one time square root of two G p. A. One is 6.5 times said that minus fourth liters. Cube would get the volumetric full rate and put all our numbers in 1.6 times. 10 to the minus, Third mused. He per second. We want to figure out what the distance he is, so we need a supplement. Bernoulli equations with their continuity equation. So RV one is a one time square with two cheapie RV, too, is a two, which is half a one time fee to why, to his minus big D minus Little D continuity then gives us that V two is to be one. Bernoulli's equation says that fee to square it was minus two Gene. Why, too, which is 23 happily plus little d for you two squared is for the one square for you one squared ISS to G D. This is 80 times D. First, we can cancel out G's and two d equals for the minus three equals C Times Capital, G and Capital T is a 0.3 meters so weak it that this is zero point nine meters.

So the question is given that there's a bank a little bit certain death Roboto on the depth of the bank is given by the equation. BT is ik would do by minus point. Don't be. I would swear now this is the equation of the depth of the bank and it is given that at peak where do zero thank is build up to so then that now in the class question is who find bit at dynamic Where does you so if we put equals zero in this equation, we get that by minus I want to go into zero. It was weird that is equal to 25 whether unit will be meeting So this is down. So the perspiration Andi, the second question is we find the time in the time will be empty. So number b, I would be okay. Dying win. Dan will be empty that is giving his son go. So in the question we have DT is a quantified minus point people t was felt So this is the depth of the bank. Now this that's Toby zero. If this deft is equal to zero than the dampening fie empty. So this is equal toe by minus point toe de I was with is equal to zero on this is equal toe 0.2 Easy will do five easy. We're 25 The wanted my point. Oh, that is 500 by 22. That is, it would do to 72.72 seconds on this is equality 2272.72 divided by 60 minute is it will do 37.87 minutes time taken to emptied up dunks. Next question is who find the Domi off. So for this we have five minus points to be is greater than equal to zero are point to do the is greater than equal to fight Minus point of bodies were then able to fight well there he is less than required toe by divided by points to you that is a weird routine less than equal toe to toe 72.7. So the present it buyer straight line We get the value from 2 to 72.72 the words negative infinity. So we can say that the domain of the function The reign of the function is a little minus impunity toe to toe 72.72 This is a manual, though, that function on hints you have bought our second answer that this time taking too big the tank empty. And this is our tournaments that is doing, although there the bank.

All right. So if we want to know how far the water is going to go, we first need to figure out what velocity it exits the hole with. And to find that we want to apply Bernoulli's equation, too. The flow of the water in the hole And in this case, Bernoulli's equation reduces to row G H equals 1/2 row B squared the rose cancel. We solve this for V. We get V is equal to route to G H then were given that the water exits the hole horizontally and the vertical distance the waterfalls before hitting the ground is capital H minus. Lower case H. We said that equal toe one have chiti squared solving for t we get tea is equal to route to capital H minus lowercase H over CI and the distance that the water travels is simply its velocity times the time that it spends in the air, which, if we combine these two expressions, comes out too for H times each minus. H. Kane on part B were asked where we could place another hole, such that the water would travel the same distance. So basically what we need is on DH the argument under the square root toe match. So let's call the new value of of H H primes that each crime is the new candidate position of Cole. So in order for the two distances to be the same, this house to be equal to regular H times, each minus each and if each prime is said to be each minus age capital H minus, lower case each than, um, you can see substituting not in here, that it'll it'll reduce to this right hand side. So this is the other, um, height that we could have put the whole lot. Actually, I should say the other depth that we could have put the whole act because A H is measured from the top.

Hi everyone since liquids at same David having the same pressure as surrender figure so we can write twice of me not to be had two plus at not and to ruin to G. Yeah. So you can realize to pay north by logic minus that you know this is the answer of party no party can technology of the water. It's got to pressure energy or water at that way. So half and B squared. Okay. And P A condo. So where the city you will get okay? Hello it off two mp upon. I'm into rope substituting the value to the pronto. This is mass capture them. Let me correct here also. Right. Yes. So took upon door into peak and pressures be not this G. H. Yes yeah japan minus at not. This is the setup be part no see part okay from giving the questions we can write to peanut rocky. I had to pull -80 not it's called to be not plus row G. X. So X. You will get we're not upon Rajhi plus uh, Cuban minus age. Not that is a stimulus edge. One that his exes. Yeah. At one meeting widow the top. That's all. Thanks for watching it.


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