A large tank of water has a hose connected to it, as shown in Fig. P18.65. The tank is sealed at

A large tank of water has a hose connected to it, as shown...

Key Concepts

Bernoulli’s Principle

This principle states that in an ideal fluid flowing along a streamline, the sum of the pressure energy, kinetic energy, and potential energy per unit volume remains constant. It is used to relate the fluid’s speed, pressure, and height, and is the fundamental tool to determine the velocity of fluid flowing out of a tank through a hose when there are pressure differences due to elevation and other sources.

Isothermal Process

An isothermal process is one in which the temperature remains constant. In the context of the problem, as water leaves the tank, the compressed air above the water expands isothermally. This means that the pressure of the air changes according to the ideal gas law, with the product of pressure and volume remaining constant, which in turn influences the pressure available to drive the water flow.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the force of gravity. It increases with depth according to the relation p = ?gh. In the problem, the water’s height directly impacts the pressure at the hose outlet, making it a key factor in calculating the water’s exit speed.

Torricelli’s Law

Torricelli’s Law is a specific application of Bernoulli’s principle that describes the speed of efflux of a fluid under the influence of gravity. Under ideal conditions it states that the fluid exits the tank at a speed equal to the square root of twice the gravitational acceleration multiplied by the height of the fluid column, although in more complex scenarios the pressure contribution from compressed air must also be taken into account.

Transcript

00:01 So what we have in this question is enlarged ankles, which has the water horse.

00:06 Last thing of boredom that has a host on the tops office is sealed.

00:09 So the air between the tops, office and water is it higher pressure, which gives us the battle.

00:17 Let us know that by me.

00:19 One the questions right.

00:21 Sit as b.

00:21 But i find it easier.

00:23 Prey denoted this is the one.

00:24 So that meeting authority says b one and right.

00:27 The pressure between the water and you're currently easy quick 4.2 into 10 to the power fight bus group.

00:40 And it says that currently the hide off the water is 2.5 and the atmospheric per service i'm supposing she's as peter that is given as tended the park.

00:52 So i passed on one engine bark bypass school that is called the part like bhaskar.

00:58 Now the question is, what is this period? this water pours out of the horse when this height is different.

01:03 Five meter.

01:05 Now, to find out this way, we have to remember the airborne.

01:08 Now this principle that says that the prisoners e the kinetic energy and potential new jersey always remains constant.

01:16 So let me write that in question.

01:18 Here.

01:19 What is this? he comes from the presidency.

01:23 Oh, a rule.

01:26 Be square.

01:26 Were bees the publicity and proving that in city comes from the kind of energy hang row z hedge with g the excellence in gravity and as is the height of the ticket.

01:42 So this comes from the insanity of this regiment constant right inside that frank on the outside of the thing.

01:49 So we will be using this to remand of honesty.

01:52 So using this princess, just write that for inside.

01:56 He is a happy one to wear using this principle.

02:01 Okay, so he's got to be one inside the density of quarter, since it is a very large african neglect of inner city inside.

02:09 Right.

02:10 So we don't need red b inside of the water on certain densities rule.

02:14 Jeez already.

02:16 And i don't.

02:17 The water is was is a region here.

02:20 Okay, you be inside that what? and so the time now this should be called outside the tank.

02:26 The present is too.

02:29 Know how probie square identity says? do you know? he says so? he's quite a city off water.

02:38 Oh sake.

02:39 Thank you didn't sit outside his room.

02:46 Do you see? hightower's had his one, so i don't need to write anything.

02:51 Because heidi, it's one so into one is one.

02:54 So trump is too.

02:56 What we can, right is just that ends that comes here.

03:01 That will give me you want my miss peter.

03:05 Is it quickly? so even minus two plus ruin z times that's minus one is quite good.

03:23 Oh, who these quiet they're from.

03:29 We don't x person for publicity.

03:31 If he goes to look under grew by zero he won minus right less grace deep at minus one.

03:55 So this gives me the express card felicity the hose off water coming out of those if you want.

04:03 And you are right now in this case for the first part of the question that is part of it.

04:10 We we know that that's so far apart.

04:14 He's given that height at physical keeper and fight right now in this room in city of water rule is always i wasn't busy for me.

04:26 You reconsider that here.

04:31 So we have actually have a role.

04:33 We have g disease in 10.8 meters per second squired, and we have the one.

04:43 We have people this plot, all these values in here.

04:47 Then you get the will be quite true 26 point to five meters per second.

04:58 If you're plugging the values off, you want me to neurology and etched in their boat because for me, you get felicity's computer.

05:06 It's explained to meet persons that this is diversity, it reads.

05:10 The water comes out of the horse.

05:12 No second part off the question says that as the water rose out of the tank, that's decreases, and we have to complete the flu when the heidi's three and when the height is, too.

05:22 So it would be easier if we on out a genital carmela and that in years it's and just recon.

05:30 So secure the handoff.

05:31 Getting that from the refinery.

05:33 Now what else changes in this expression for v? so that's ingests zeal, mr scene.

05:40 He took atmospheric elements the same.

05:41 It was very present in city apartments.

05:43 The same soapy want answers in this right.

05:45 So too, did remind the one we use boyle's, not because the change it cost in person, so using boys lot through before and after the decrees off height says that trump was love...

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