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Data collected by the author for flow coefficient at BEP for 30 different pumps are plotted versus specific speed in Fig. P11.49. Determine if the values of $C_{Q}^...

Question

Data collected by the author for flow coefficient at BEP for 30 different pumps are plotted versus specific speed in Fig. P11.49. Determine if the values of $C_{Q}^{*}$ for the three pumps in Probs. P11.28, P11.35, and P11.38 also fit on this correlation. If so, suggest a curve-fitted formula for the data.

Data collected by the author for flow coefficient at BEP for 30 different pumps are plotted versus specific speed in Fig. P11.49. Determine if the values of $C_{Q}^{*}$ for the three pumps in Probs. P11.28, P11.35, and P11.38 also fit on this correlation. If so, suggest a curve-fitted formula for the data.



Answers

DATA ANALYSIS:
BOTTLED WATER The table shows the per capita consumption of bottled water $y$ (in gallons) in the United States from 2000 through 2007.(Source:
Economic Research Service,
U.S.Department of Agriculture)

(a)
Use the technique demonstrated in Exercises 77-80 in Section 7.3 to create a system of linear equations for the data. Let $t$ represent the year,
with $t = 0$ corresponding to 2000.

(b)
Use Cramer's Rule to solve the system from part (a)and find the least squares regression parabola $y = at^2 + bt + c$.

(c)
Use a graphing utility to graph the parabola from part (b).

(d)
Use the graph from part (c) to estimate when the per capita consumption of bottled water will exceed 35 gallons

So this is talking about different beverages 1.5 for X minus 0.32 Why minus Z is negative? 1.45 and they want us to solve for Z specific type of beverage. So I just add Z and add 1.45 So I have my equation solved for the letter they're asking about. Plus one point for five equals e and they want us to fill in this table. The table goes from 2006 up to 2010 on $60 sound 2008 2009 2010 And then it gives us these X values. The X Y years go 2.32 point two, two point on 1.9 and one point need. So here we have the year. The axe It gives us why Values 3.43 point two, 3.13 point zero in the last value for why is 2.9 and it gives us values for Z. And those e values are 3.93 point 83.53 point 43.3 And so then we're supposed to make 1/5 column to approximate Z and all I'm doing is just plugging in the X and Y numbers into this equation right here. Okay, so just plug in those numbers each into the equation. We get the values for Z Ah, 3.90 3.81 3.54 3.42 and 29. So it's part day right? There is just finishing out that calling. Part B says. Compare them and those numbers are almost identical, so they are very similar. You could probably write that it was almost identical in part. See, the question says, um, to increases or decreases in consumption of two types. What effect does that have on the third time? And you can see that they're all going in the same direction there as Ex gets smaller and why get smaller so dozy? As Ex gets bigger, why gets bigger? So does Z, And so, for part C, I would just say the three actually go to the next line for that. For part C, I would just say the three beverages move in the same direction, and so one way you can write that the same direction one way you could write that is that Yeah, X increases. And why increases? Then Z increases and you can see that from the table. And similarly, if X decreases and why Decreases and Z also decreases So really, all we did was solved Our equation for the letter they're asking about frizzy plugged a bunch of values in. And then I saw that they all changed in the same direction.

Okay, Good dailies and gentlemen. Ah, this is problem number 84 from section 4.5. And what essentially gives us is it gives us some sort of graph. Um, you know, looks something like, I don't know, something like, um maybe like this Basically a start. Sort of. Here it goes down, and then it comes on a little bit. Too many goes down. Sort of looks kind of like a two humped camel, if you will. Sort of comes back kind of threats. Need its initial point. Sorry. And, um, the bottom is inter is intervals from 0 to 24. Um, so this is ours t ah, in hours and then the y axes is, um the rate are of tea or, um r of t, which is the rage at time t, um, and in particular than r of t is equal to d w d t. Um, where I call, um w of tea is the Why what w of keys. The water used at time t So, like I said, it's Ah, it's a graph of D w d t um, And this question, there's not really much to this question. This is sort of just a inspection question, if you will. There's not really much actual calculations or anything to do. Um, but in the first question, I mean the first problem. Um, I noticed, based on my own inspection, it looks like the water as opposed to my graph here, Um, the maximum water rates occur at about nine. 2100. You just look at the graph and see where the graph its maximum occurs. And it looks to me like it's roughly about nine. And you know, 2100 are, um or, ah, nine PM so 9 a.m. and 9 p.m. roughly symmetric thea amounts of water used in a day. Um, all that is now is the inner Groll, Um, from 0 to 24 um, off the d d a d w d ax the ax. So, in other words, you can write This, of course, is just, um, 0 to 24 off our G uh, g g. So it's the same thing. Are tee um yeah. R t, uh, t t t r of two used is there is. There is the function for which is being graft here. Um, and the last question asked roughly, You know, when the least amount of water is being used roughly, I'd say between maybe two and four more. One and three, I don't know. It depends on how you look at it, but roughly between two and four. And you know, you kind of figure that because that's when most people are asleep. Probably the least amount of people are using the water. And really, that's all these questions after it's a It's a very short question. Um, it's pretty much just by inspection. So, uh, you know, hopefully, I mean, kind of the key to this question is to sort of get used to the idea that, um, you know, basically there's a relationship between the graph of the derivative and the function itself, which in this case, is W, um, and its values based on the graph, Um, in this case, it's the integral, um, so they're sort of relationship between it, and so you can see the graph of the you know, the rate function and that that sort of, you know, um summarizes the relationship between the rate and the amount, if you will. So it's just something to sort of It's something to see, I guess. Um Anyhow Ah, that's really it for this problem. Uh, thank you very much.

So here for this we're going to use the results from part A in a problem 65. So we can say that for part A for problems 66 of course, would be. We can say that in this case we have a change of pressure equaling piece of one. And this is gonna be equal to 2.0 atmospheres. And so we considered the velocity would be equal to the square root of two times the change in pressure. This would be divided by the density multiplied by the area divided by the acceleration quantity squared minus one. And so this would be equal to the square root of two times to atmosphere. So two times two times 1.1 times 10 to the fifth Pascal's and then this would be divided. This would be divided by 1000 kilograms per cubic meter and then multiplied by five a divided by a quantity squared minus one, and we find that V is going to be equal to 4.1 meters per second. This would be our answer for part A For part B. We can say that the equation of continuity we're going to use the equation of continuity and we can say that V ah would be equal to a over a cross sectional area divided by the acceleration times V. This would be equal to five a over a times B. This is equaling five V or five, uh, times the velocity and this is equaling 21 meters per second. We can then four part seed, find the flow rate, the floor. It would be the cross sectional area times the velocity. This would be equal to pi over four times the diameter squared 5.0 times times 10 to the negative forth meters squared. And then we're going to multiply this by 4.1. No, my positive meter quantity squared and then we're gonna most players by 4.1 meters per second and we find out the volumetric flow rate we can call it Q. This would be equal to 8.0 times 10 to, uh, to the negative third meters cubed per second. This would be the volumetric flow rate for part C. That is the end of the solution. Thank you for watching

So we have a pint experts into two houses. We have a cause A and we have a host be. And then your tour that r V over R A is equal to 1.5. So we're gonna start using that so forth. Thing is Q is equal to i times Arkady power for be to minus P 1/8. Peter L. Now sensor for both, because is the pressure difference on the viscosity and the length are the same and pie and ate our constant. So we can say that Q is proportional to our power for which means that Q b o ver que es is equal to our B to the power for divided by our aid to the power for which is R V over R a nd power for so we get q B over Q A is equal to 1.5 to the power for so we could keep that in mind for a second as we go to the next life. So we also know that Q is equal to the rig product off area and speed so we can say Q b o ver que es is equal to area off be times the speed and be divided by the area off eight times the speed and pose A. So this side we already know is 1.5 to keep our four and the area off the pipe is given by pi times its read here. So this would be pi r squared VP over pi Times are a squared times me and R B squared over r squared would be with 1.5 square. So we have 1.45 to the power for is equal to 1.5 square The pies get crossed out times be over very gay And when you simplify that for me be over here you would get that to be true to life.


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