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PointsSERCP11 9.7.P.036.My Notesliquid (p 1.65 g/cm flows through horizontal pipe of varying cross section a5 the figure below- In the first section; the cross-sect...

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PointsSERCP11 9.7.P.036.My Notesliquid (p 1.65 g/cm flows through horizontal pipe of varying cross section a5 the figure below- In the first section; the cross-sectional pressure 1.20 105 Pa, In tne second section, cross-sectlona area 50 cm0.C cm? , the flow speed 249 cmls, and theCalculate the smaller section $ flow speed_ (Enter vour answerleast two decimal places )Calculate the smaller section'$ pressureSubmians Ver

points SERCP11 9.7.P.036. My Notes liquid (p 1.65 g/cm flows through horizontal pipe of varying cross section a5 the figure below- In the first section; the cross-sectional pressure 1.20 105 Pa, In tne second section, cross-sectlona area 50 cm 0.C cm? , the flow speed 249 cmls, and the Calculate the smaller section $ flow speed_ (Enter vour answer least two decimal places ) Calculate the smaller section'$ pressure Submians Ver



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A liquid $(\rho=1.65 \mathrm{g} /$ $\mathrm{cm}^{3}$ ) flows through a horizontal pipe of varying cross
section as in Figure $\mathrm{P9} .36$ In the first section, the cross-sectional area is 10.0 $\mathrm{cm}^{2}$ the flow speed is $275 \mathrm{cm} / \mathrm{s},$ and the pressure is $1.20 \times$ $10^{5}$ Pa. In the second section, the cross-sectional area is 2.50 $\mathrm{cm}^{2}$ . Calculate the smaller section's (a) flow speed and (b) pressure.

This problem covers the concept of the continent equation. And for party from the continental question debate. The speed we do equals even upon a two times we even more subscribe the value so we do equals evenness 10 centimetres square And it is 2.5 centimetres square and we witness 2 75 centimetres or second. So the flow speed we do at 2.5 centimeters square cross section is 1100 centimetres four seconds. Or you can also add possess we do equals 11 m for a second. How party using about newly question we can right even plus half of ruby one square at the same level people plus half from even square equals B two plus half row beetles are from this the pressure of we do equals even pless half of rule. We even square minus we to square. I'll substitute the value. So the pressure at the projection to at 2.5 cm square equals even is 1.2 In to Tenders five pastors let's have for that entity After fluid is 1.65 grandpa centimeter to. Or we can write 1.65 into hundreds, three kg for my interview into a one square. That is 2.75 Uh medals, four seconds squared minus 11 majors, four seconds square. So we get the pressure at the Section two B 2 equals 2.64 into tenders full baskets

Aloha in this problem where Shona drawing similar to this where we have pipes of some going into ah, brick building. And we're told that we were just given values for information at the start of this system at street level as well as at the top height of the building. So the height of the building is 16 meters, and the gauge pressure, which is the actual pressure minus the pressure of the atmosphere, is 3.8 atmospheres. That's a standard unit. Um, the in terms of the Earth ends here at sea level and a libelous PG for gauge and this is the in pressure here and started the system at street level. And it has a velocity coming into this system. A 0.78 years for second, says goods. Just write all this given information down in terms of they're ables and systematize ing with labels like in and out, Um, because that's what we're going to be using Bird always equation, which is like an energy conservation equation for the input and the output of this system. Here, the diameter, the larger diameter is here at the beginning of this pipe system. That's five centimeters. Just label it a capital deed emphasizes the bigger one. It's everything. This is the import side, the output side, the diameter smaller. This is the top of the building, 2.8 centimeters. And that's all of the given information on. We want to find the output velocity as well as the output gauge pressure. So this is a top of the building, and we know that we can start by writing Bernoulli's equation. So the input gauge pressure twist roadie. Why zero? Which we could take me. Zero we can, just to find this is y equals zero here and this part Pete White was H plus 1/2 ro arose the density of water. So row with those road water, Mrs Flynn, known constant. So you could find this earlier in chapter 10 in a textbook 1,000 kilograms per meter cubed, um, I'm staying put velocity squared, and we have the sequels and same quantities on the other side of the pipe system. And we're told that the faucet at the top of the building is also open to the atmosphere. So we're looking for the gauge pressure. Um, we know that it's exposed atmosphere. So they're both sides. They're both experiencing atmosphere pressure here. What? You No and we This's going to be useful equation. We have the output pressure and we have the upper velocity. But this is one equation, and we all know that their valuables are known like the impact pressure, the density of the water jesu concert, nature, acceleration due to gravity, input, velocity, the height, age. But one equation with two unknowns isn't enough to solve for those two unknowns. We need another equation, and we can to think more about this problem. And we know that there's going to be We can't play the continuity equation for this fluid flow here. So you know that the area times the velocity will be constant. This is like the volumetric flow rate Be a constant. So we know. Is it a one which is, or maybe a in This is the cross sectional area. The input kinds of influence velocity will be the same as the output area times the output philosophy, especially this pipe is wider. We have the constant input velocity and that is going to shrink down. So we expect that the output velocities speeding up as it's, um, maybe slowing down is it's kind of squeeze into smaller prey. So three well, see, it's well, yeah, I think I should speed up bullets weaken. Just calculate this out. Begin solve for the upper velocity, which is something we want to know So we can plug this into Bernoulli's equation and it just have one equation with one unknown. You can just sell fat algebraic Lee since will give us the outpour velocity and we're not told the areas, but we're told the diameters of these pipes. We know that it's since the dead Amador must be circular and, um, the area's pyre squared. Where are the radius? That's the dam are over too squared. Let me see. They can cancel out the denominator of, um, the two squared. This was the pie separating us. And then we can display in because we have the equation that in parameter, over the output diameter, square times, impulse velocity. So we can Well, you just keep these end terms of centimeters because unit's gonna cancel out. So our final answer for the output velocity should be about 2.5 meters per second. An important lost. He was about we're told was 0.78 So So it is speeding up through this smart pipe and then we want to look back and realize equation to rearrange it. So now we have This is another note apology that would employ him. So you wanted to write this as an equation for the gauge pressure at the top of the building? They labeled out. So on the other side of the equation, he had he pressured street level. Hey way We don't have a potential energy trucks. He set the height there to zero. We have 1/2 throw me in would square And then from the other side of the equation, we said, Scratch Thea, please Velocity term and ro gh that's you, you on their way. But we have to just rearranging that a little bit. And now we can just plug in these numbers all the char given or we just calculated to be out 3.8 atmospheres and we can convert from atmosphere is using to write this in noons per meter squared, which is a pascal What really? You You want to add up all these terms in terms of Pascal's? We could still write the final answer. Auntie Em this convert back look. Yeah, so this is the losses. Grady, when I uses many digits, is you can hear. Just keep that in your calculator on Bennett's Approximate at the end to get the most accurate approximation here. No, just in the final answer. This's the density of water cheese, 9.8 meters per second square. We're told that ages 16 meters, so this will be an answer in terms of noons per meter squared, because here we have velocity squares. That's a meter squared over second square there and a kilogram meters per second, squared over meter square. That's a Newton meter squared because a kilogram meteor per second square that's a noon. It's a unit of acceleration. Mass turns exploration. That's a new end, and you should get about 2.25 times into five means Premier Square, which is a Pascal. And we can convert that then two atmosphere's if we want. Oh, good says that 2.2 atmospheres at the top of this building. So these were the two answers we're looking for. Yeah, with velocity and the outlet gauge pressure

Customer 46. For the first part, we have to find out velocity the two off the water at the top floor. So we do is equal toe from continued education. Even we won upon A to substituting the values everyone is 54 into First diameter is far for cemeteries, 0.5 is quiet and vascular stays zero point 6 m purse, again divided by a second area, which is 554 into second. Dammit terrace 50.0 26 It's quiet Solving this, we will get this again. We'll all stay at the top floor. The two equal to two point to one age me that five seconds. Now, for the second part of the question from the Benali question, we can write the pressure at that off. Lord potato is equal to initiative. Pressure at the street Be one last Uh huh. Raw in tow. We won squired. We'll all stay at that ST minus be to inspire less So it is minus roti at now substituting the values P one is given us 3.8 atmosphere 3.8 atmosphere can be written as three pointed into one point 01 in 2 10 to the power five Paschal's. This is the one value in Paschal's plus half times density off water. They just tend to the power 3 80 per meter, cubed into the velocity oneness can velocity one is 0.6 m per second, so 0.6 c squared minus second lost. We have already calculated 2.2 18 is square minus, then city or water, 10 to the power. The in tow 9.8 and height is 18 m, so multiplied by 18. Solving this, we will get the value of P two equal to 20 five 120 faster and this is also equal to 2.0 t atmosphere.

Applied Bernoulli's equation. We can say piece of one plus the density of water multiplied by the sub one squared, divided by two plus the density of water times G. Why someone This would be equaling two piece of two, plus the density of water. He's a two square divided by two, plus the density of water g wise up to. So we can then say that Visa two squared minus visa of one square is gonna be equaling two times piece of one minus piece of two, divided by the density of water minus G times Weiss of two minus y sub one. And we can then say that Visa two squared minus visa of one squared equally two multiplied by 1.75 minus 1.20 times 10 to the fifth. Pascal's divided by 10 to the third kilograms per cubic meter, minus 9.80 meters per second squared multiplied by 2.50 meters, and this is giving us 61.0 meters squared per second squared. And so, from the equation of continuity, we can say visa to is equaling beasts of one, both supplied by a sub one over a sip too, so this would be equaling to be sub Wanna multiplied by pi r Someone squared divided by pi r sub two squared Cancel out the pies and this is giving us the V sub one multiplied by are some one divided by ourselves to quantity squared. This is giving us visa one multiplied by 3.0 centimeters divided by 1.50 centimeters Multiple rather raise to the second power and so visa to is equaling four times Be someone now you can use this to substitute and so substitute this into our previous equation where we know Visa two squared minus V. Someone squared equals 61.0 meters squared per second squared. So then we can get 16 minus one times visa one squared, equaling 61.0 meters squared per second square or your niece of one equaling approximately 2.2 meters per second. So this would be your answer for part A for part B, then visa to is equaling four times v someone so this would be four times 2.2 This is equally 8.8 meters per second. This would be our answer for part B. And finally, for part C, we can say the volume volumetric Floor it through the pipe is gonna be the flow rate ace of one visa one equaling a sub to visa too. And looking at the lower point, we can say that cue the volumetric flow rate is gonna be equal in chi. Are someone squared v someone so this would be equaling Pi multiplied by 3.0 times 10 to the negative second meters quantity squared multiplied by 2.2 meters per second. This is giving us 5.71 times 10 to the negative third meters cubes per second. So volume per unit time. This would give us our volumetric flow rate for part C. That is the end of the solution. Thank you for watching


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