>> Start at chapter 11. And we'll just cover certain sections of it, it's on your course syllabus. But we'll start off looking at centrifugal pumps. A very common type of pump. Swimming pool pumps, spa pumps, all kinds of pumps. Quite a few of them are centrifugal pumps. Who in here has had the fluid mechanics lab, MA313? How about being in there now? Okay, okay, good. I thought so. Okay, sometime this quarter, I don't think this early, you're going to run a test on a centrifugal pump in the fluids lab. And from that test you're going to put together some performance curves for our centrifugal pump. So, this is how we test a centrifugal pump. I'll go through the procedure that we use in our fluids lab. We have a pump in a circuit with water in it, from a big reservoir. The water is pumped through here, it goes around, back into the big reservoir. We have flow meters in the test setup so we know what the flow rate Q is. We have pressure gauges at points one and two. A centrifugal pump is a radial type of a pump. There's an impeller blade in there. The impeller blade is rotating. It spins the water outward radially, centrifugal pumps, centrifugal. The purpose in life of a pump is to increase the pressure. So P2 is bigger than P1 of course. That's what it's doing. It's increasing the pressure of the fluid, water. We can write the energy equation. By the way, this is called a suction side where the water enters suction side. This is a discharge side of the pump. Suction side, discharge side. We can write the energy equation from point one to point two, right at the pump. A matter of fact, in the lab when you run the experiment, you'll see there's pressure taps in the piping. And those pressure taps are hooked up to differential pressure gauges. There's also, the pump is driven by a motor. Between the motor and the pump there's a coupling. In the coupling there is a tachometer built in. So we can get the speed of the pump, the shaft that drives the pump. The speed. There's also a torque meter in that coupling. So we can get the torque on the shaft between the motor and the pump. So, we can get the torque, we can get the pump speed, we can get the pressure rise across the pump. We can get the flow rate Q. We write the energy equation from point one suction side to point two, discharge side. Here's the equation. There's no straight pipe, there's straight pipe, minimal straight pipe. Maybe a few inches at the most. Forget about that. So, P1 over gamma. B1 squared over 2G, Z1, HP head of the pump. This equation is in feeder meters. P2 gamma. B2 squared divided by 2G, Z2. Usually this difference in elevation, Z1 to Z2, in minimal, in the matter of inches. So, we usually neglect that delta Z. And usually the difference in the velocity head between one and two, is negligible so we can usually neglect that. So we're left with the pressure rise across the pump divided by gamma, equal the head developed by the head for the pump. Of course continuity tells us Q1 has to equal Q2. Okay, that's a given. [clears throat] Okay, so that's our equation. So, what you do in the lab and the way that engineers test pumps is you run at a constant speed. Then you run different flow rates through the pump. And you get a pump performance curve. Which the pump head is plotted on the y-axis and the flow rate Q on the x-axis. And typical shape of the head curve comes off relatively constant and then drops off like that as the flow rate increases. So the pump head is constant for a while and then drops off pretty rapidly because of losses in the pump at the higher flow rates. Drops off rapidly. So that's the pump head curve. Now, besides the pump head curve, there is other curves that you can plot. Let's write these guys down. Let's take first of all, the power into the pump. W dot M . It's either in kilowatts or horsepower. Okay, that comes from where? The motor. There's a shaft from the motor to the pump. So this is the shaft power. It's torque times omega. Torque times the pump speed omega. Radiance per second. Pump speed. And that can give us kilowatts, or we can convert it, put pounds per second into horsepower. Okay. In a laboratory environment as I told you, the shaft has a coupling on it between the pump and the motor and the coupling has a torque meter built into it and a tachometer. So we get both these guys, we read them off. And we can then on this graph show, I'm going to change this because there's -- well, that's okay. This is HP, this curve is for HP. Somewhat fairly linear for a while. This is the power in. And now we can also define the pump efficiency. Pump efficiency, what comes out from the pump divided by what comes into the pump, the power. There is the power in right there. Okay. So, obviously it's dimensionless. W dot out is gamma QHP divided by the power in. So, with our laboratory data we take, we also in our fluids lab, we also draw the pump efficiency curve. And typical pump efficiency curve might look something like this. The key is, it goes through a maximum typically, at a certain flow rate. And it drops off at lower flow rates and higher flow rates. So, there's typically an optimum range of flow rates for a pump. And this point here, the peak on here is like the best efficiency point. So that's just a typical graph of a pump characteristics. A centrifugal pump. And typically for that we'd say that this is at a constant speed. Omega. And then what we do in the lab is we change the speed of the pump and the curves all change. So we get different curves for different pump speeds. Now, when you buy a pump you don't always get that graph with you. When we bought our pump for our fluids lab we had to ask the manufacturer for their graph, because we wanted to compare the pump when it was new to when you run the pump in our lab. Our pump is eight or ten years old by now. I'm sure that impeller blades aren't smooth like they were originally. They're rough now. We expect the performance to degrade. The efficiency to go down. Yeah. So, yeah, we expect that and we get that. But, manufacturers run these curves themselves of course. And then they present you with a graph of their results. Before I pass that out, let me just mention something else here. Sometimes you'll -- these pump mostly pump water, okay. People call this guy here, the numerator, the power out, the water horsepower. That's the water horsepower. This is the shaft horsepower that comes in. They call that the water horsepower. Okay. That's just historically what it's been called. The numerator gamma QHP. This is a graph, I don't think it -- no, it's not from our textbook. Of a manufacturers curves similar to that. Okay. Do you want one? Do you want one of those. Maybe that might be good. I'm not going to put it on the board. Well, I'll put part on the board. So wait and see how it looks. We'll see. One more? >> Yeah. >> Okay, there we go. >> Thank you. >> Mmm-hmm. >> Okay. So, you can see here that this is a manufacturers curve. It shows a picture of the pump, okay? And I'll just draw this for you so you kind of see what's going on here. Let's see, I think I'll do it. Okay. Let's take the top graph. Okay. Here is the pump head. It's labeled HP graph. This is labeled the flow rate Q. It just doesn't really matter for what we're doing. Just so you know the terminology. This is called a shut off head. If there's no flow through the pump, if you close, there's typically a valve here in the line. If you close that valve with the pump on, there's no flow. But the pump still develops this head. H sub P. It's called the shut off head. Okay. So, back here again. Now, there are -- this one, I'm going to take this as an example. It says here, 260. That's the impeller diameter inside the pump. They take that one pump. They can take it apart and put in slightly different sized impellers. The top curve is 260, then there's 240, 230, 206 millimeters. That's the size impellers you can get from the manufacturer and put in that pump. Okay. Take the pump casing apart, put the new impeller in there. Reassemble it. Of course the bigger the impeller diameter, the bigger the head the pump develops. But here's the difference. Now they've got a number of curves that look like this. Those curves are the efficiency curves, 75% for instance. 70%, 65% Okay. So they show the efficiency that way, not the way we've got it here. This is typical of manufacturers data. Sometimes called a pump performance map, pump performance map. I'm not going to show them all but there are other lines here, below here, for smaller impeller diameters. The 240, the 220, the 205. They're very similar lines. Okay. Alright, now, below that there's a graph. And this graph is the W dot M. And again, there's a 260 line. There's also a line just below it, 240, 230, 205. There's four lines here. Okay. And below that, is something we'll talk about in just a minute. It's just for right now NPSH. It's stands for Net Positive Suction Head. But, again, there are four curves there. There's a 240 line, the 205, the 240, there's a 260 in there. Alright, so we'll take the 260 again. The 260 is the bottom line, it looks like this. So these are -- this is typically the way a lot of pump manufacturers present their data to you when you buy their pump. Okay. Not quite as simple as this maybe in a way, because this one picture here shows the pump head and the pump efficiency. This graph gives you the power in, this graph gives you something called the net positive suction head. Okay. Now, let's just mention what the net -- since we've got this graph in our hands, what the net positive suction head is, NPSH. The equation is at the bottom of the page there, this is what it is. Okay. Now, let's draw a picture here. Well, the pictures up at the top, but I'll redraw it again here, okay. So you've got a reservoir. You're taking water out of the reservoir, into the pump. Out like this. Okay. This is your flow rate Q. Okay. This is our point one, this is our point two. Okay. So, this is, I'm sorry, this is point two here. It's on the suction side. Alright. This is P1, this is P2. Okay. P1, P2. Yeah? >> Is PV an actual [inaudible] >> Yeah. It is. I'm going to mention that in just a minute, but it is. You'll find it. Yeah, it is. I'll mention what it is too, I haven't mentioned what it is even. You probably know though. [clears throat] Okay. So we've got all that in there, we need. Okay, so if you look at the bottom of the page. Okay. Here's the problem. I'll read the problem. Determine the elevation that a 240 millimeter diameter pump, okay. Those lines are on this figure. Determine the elevation that a 240 millimeter diameter pump can be situated above the water surface of the suction reservoir, without experiencing cavitation. You draw water from the reservoir. The pump is above the reservoir surface. How high can you put the pump before some bad things really start to happen? Well, what's a bad thing? Well, as you get the pump higher and higher in the flow rate, that pressure is going to start drop. And if that pressure drops enough, if it dropped to the vapor pressure of water, PV, vapor pressure of water. You know what happens then. Little vapor bubbles form. And if little vapor bubbles form at the entrance to the pump, they're going to go through the impeller blade. So now it's not water being pumped, it's a mixture of water and vapor bubbles. Water vapor bibles. And as the vapor goes through the pump, what does the pressure do in a pump? It increases. And as it increases those little vapor bubbles start to collapse. [ Clapping ] They're collapsing in the pump impeller. Matter of fact, one of my students came back several years after he took the class and said, "I'm now working for a company where I am in charge of going in field with pump problems." And he said, "I can walk out there and I can tell when a pump is not working right" he said. "Because I'll hear a bunch of like clunking noises in the pump. And know what that is. It's cavitation." Yeah, you can hear it. Well, so what? Well the so what part is when that bubble collapses the water suddenly hits the impeller blade. [clapping] After 10 million times [clapping] it wears the impeller blade. It makes it rough. It wears it away. The efficiency goes down, the pump fails. That's the serious problem. Its cavitation can cause serious pump problems, because of the impeller surface being pitted by the collapsing vapor bubbles. Okay, so, the question is how high can I put that pump above the water? Swimming pool pump in your backyard. Swimming pool is down there, pump is three foot above it. Is that okay? Somebody better check that. You don't want that cavitation there. How high can you put the pump above the reservoir of water? There it is right there. That's the distance. Elevation. Okay. So we keep reading here now. [clears throat] Say, okay the water temperatures 15 degrees C. I go to the back of the book, it's in a table in the back of the book. At 15 degrees C water temperature, PV in the back of the book. Vapor pressure. He tells us right there. 1666 kPa. He says, absolute. Okay. So, now you're question. Is that guy PV absolute? Yeah. Why? Because in the back of the book in the table it gives you the absolute pressure. Does that mean P atmosphere must be absolute? Of course it does. It's not zero gauge. Both of these pressures have to be in absolute. So you'll southeast down there in the equation, P atmosphere 101 thousand. 101 thousand. That's 101 kPa. The vapor pressure of water at 15 degrees C, oh is it really low, 1666 pascals. Okay. Now, we go to the graph, NPSH over there. Alright? And he tells us what the flow rate is, 250 cubic meters per hour. 250 meters per hour. Of course you always divide that by 3,600, we want cubic meters per second everywhere. We go across horizontally. And we get the NPSH value he tells us here, is 7.4. Okay. So, delta Z is equal to 101 minus PV, divided by our gamma. 9800 minus from the graph, from the graph, from the manufacturers, 7.4. H sub L. If there's any losses in the piping, H sub L. FL over D. He said neglect the losses. Neglect the losses in the pipe. Okay. So delta Z he says is 2.74 meters. Alright, so what does NPSH do for us? Well, it tells us how far above the free water surface we can put a pump before you expect to have cavitation begin. If the pump is any higher above that water surface, we've got some problems. That pumps going to be in trouble. Okay. Because of cavitation. Okay. NPSH, that's what the manufacturer gives you. Alright. I've got to save him. Do I want to save him? I don't think so. Okay. Alright. What kind of pump should you the engineer select? Okay. Pump selection. Use the pump specific speed. Okay. Pump specific speed is given by the symbol NS. I'll write it down. These guys, Q and H, at the best efficiency point. So you've got to go to the highest efficiency point and find out what the pump head is and what Q is at that pump. So the pump specific speed is identified at the best efficiency point. Now, there are two equations. Okay. So, this guy here has to have all the correct units in it. Okay. Like if it's SI or English engineering, okay, this pumps speed radiance per second. Q cubic meters per second, et cetera, et cetera. Most engineers who work with pumps in the English system, they don't like that. They say, you know what? Give me an equation where I can put the pump speed in RPM, how many gallons per minute and the pump head in feet. That makes more sense to me. I don't want to go through all those conversion factors. Because when I work with pumps, I talk about GPM. I talk at RPM. So I want an equation where I can use those units in. Okay. That's fine. Then use this one. But here's what it says in your textbook, see figure 11.11. Okay. And based on that then you can kind of figure out what you've got. I'll just mention real quick here if I can find it. So well go to pump specific speed, chapter 11. Okay, chapter 10. Here we go. Alright. Okay. Alright, so we've got our pump specific speed, figure 11.11. He tells us there in figure 11.11 that if you calculate that and you get between 500 and 4,000 Select a centrifugal pump. So if somebody tells you, alright, I've got a pump operating at 1750 RPM, I want to pump 500 gallons per minutes and I want to pump it to a pump head of 50 feet. Okay. Put that stuff in there. Make sure that the Q and the H, that's going to be at the best efficiency point. If I get a number out of here of 1,000 I say, "Okay, pick a centrifugal pump". If I'm between 4,000 and 10,000 Mixed flow pump. If I'm between or above 10,000 axial flow pump. Mmm-hmm? >> In the bottom, N equation. Is there supposed to be a -- what happened at like the G? Is that gravity? >> The engineers say, I'm going to operate the pump on the surface of the earth. I don't care if it's Pomona or Santa Monica, G is the same. So they say, don't even put G in the equation. Okay. [laughs] It's a good question though, thank you. Good question. You know, don't take the pump to the moon, then all bets are off. Okay. But no, they say, pretty much lump G in here somewhere, 32.2 or 9.81. Okay now, what kind of pumps are these? This is a centrifugal pump. It throws water radially. It throws water in a radial direction. This is an axial pump. It throws water in an axial direction, motor pump. So, that's an axial pump. It throws water like a propeller blade down the pipe. Centrifugal pump throws water in a radial direction. Guess what a max flow pump does? A little of each, a little of each. There's pictures in a textbook. I'm not that good of a sketcher of those. But there's pictures in the textbook on figure 11.11. And then, if you want to do it this way. If NS prime is less than one radial flow. We use radial flow and centrifugal in the same, it means the same thing. If NS prime is between one and four, axial flow pump. If it's greater than four, that was a mixed, excuse me. Use the axial flow. Okay. Okay, so that's how that helps engineers select the right kind of pumps for specific application. Uh-huh. >> I'm sorry, I have a question. Do have to use Q and H in [inaudible] >> Which one now? >> For Q and H [inaudible] >> Q and? >> At H, you use them at the [inaudible] >> Q and H are at the best efficiency point. So Where's the best efficiency point? Right there. What's H? Right there. What's Q? Right there. That's where they are. Mmm-hmm. Looking for the best efficiency point. Okay, now, that's just all about pumps. Not a lot about it, but anyway, that gets you started. We are interested in putting a pump in a pipe network and seeing what the pump will do. So now, we put a pump in a pipe network. So we'll look at this picture. This will be a centrifugal pump. So, here's the lower reservoir. We're going to be pumping water up to a higher reservoir. There's the pump. Difference in elevation. Delta Z. Of course the reservoirs are open to atmosphere. Mmm-hmm, that's fine. Okay, now let's see if I want to draw this thing about right here. Yep. That's good. The difference, I'm going to take an example here and we'll see if we can calculate this guy. Okay. I'm going to take the example and the difference in the elevation is 150 feet. Okay. The pipe. There is 1,000 feet of one foot diameter pipe with an F value of 0.015, F is given. Okay, the flow rate from the lower reservoir to the upper reservoir is Q. I'm going [laughs] I shouldn't keep changing this on you, but I will. I'm going to say, I'm going to take a pump from that manufacturer I gave you. I'm going to take a pump and it's going to have a 205 millimeter diameter of pillar. Okay. And I want to know what flow rate that pumps going to cause between these two reservoirs. Okay. So I know what pump I've got. I've got this guy right here, there he is. Now, this is going to be an English problem, feet meters. Gallons per minute. Maybe cubic feet per second. And on the graph, the manufacturer has the pump head in meters and the flow rate, it tells you right there. Cubic meters per hour. I don't -- I wish I had that in English engineering. It would make life a lot easier. Look at the graph. Oh my gosh, thank you very much. Thank you. It's on there. The top axis, Q. Cubic feet, GPM right? Yeah, GPM. Q GPM. Right side, oh thank you very much, pump head in feet. Yeah you can use this graph whether you're in English or SI units. But it's not quite as easy to read in the English units because the little tick marks on the axis' are hard to read, but you can read it. Okay. So here's what I did then, here's Q. And this is going to be our GPM. And here's our pump head. And that's going to be in feet. And I did to the best of my ability replot that. Okay. So, I have my plot. It starts out as best I can see right around one, I think I took 150 something or other. There it is. Yeah, no, it's 170, uh 175. That's what it was, 175. Okay. And I just, I went to 100 GPM and I went to 1,000 -- I'm sorry, 500 GPM 1,000 GPM. 500 GPM 1,000 GPM, zero. I took the points off of here. I took one point off of here. I took one point up here at 500. I took one point off of here at 1,000. I've plotted those three points over here. Let's see here, here's 1,50. I'll need that in a minute. And it kind of went down like this. At 1,000 it's down to 140. Okay. So it looks like this. There's a pump head curve, replotted from a manufacturers curve. Now, okay, there we are. Okay. Now we have to add here. Let's just start over here. I need that. We don't need this guy. We don't need NPSH. We're going to need that power in. Okay. Energy from one to two. Well, we better throw Moyer [phonetic] losses in there. Okay, there's energy one to two. There's a pump in there so you throw in the HP term, left hand side. I'm going to put the pump on one side, the equal sign. And the pipe network on the other side of the equal sign. I put the pump on the left hand side. I put the pipe network on the right hand side. Okay, I get that. I say, you know what? P1 zero gauge. P2 zero gauge. Got it, gone. I say, you know what? V1 is zero. You know what? V2 is zero, on the free surface of a large reservoir. Got it. I say, you know what. 2 minus Z1, 150. Okay. HP equal 150 plus, there's a start pipe, right there. There it is. Okay. FL over D, V squared over 2G, plus minor losses. In this particular problem the minor losses were 1.85. There was a valve in the problem and the entrance to the pipe network from the reservoir and the exit. You sum all those together and the minor loss is 1.85. The friction factors known, right here, .015. The diameters known, 1. The length is known, 1,000. Put the numbers in there, no problem. I don't want V in the problem. I don't want V because I've got Q on the graph. So I change it to Q. So, HP, equal delta Z, 150. [clears throat] Plus, if you do all the mathematics that's what you get. 0.43Q squared. All I did of course was replace the V Q equal to V over A. So, replace the V with Q times A. Diameters one. So wherever you see a V you put pi divided by 4 times Q. And you get that guy up there. Couple lines missing. Okay. This side of the equation is the pump head curve. This side of the equation is called the system head curve. We call that H system. We call that H pump. I'm going to plot the right hand side on this graph. When Q equals zero, the system head, the right hand side of the equation, when Q equals zero. I'll make a table for you. System head curve. And that's in GPM -- or three feet per second. Pardon me. Cubic feet per second. Okay. Let's do the complete thing here, I've got it all on here. Here's Q and GPM. Convert it to cubic feet per second. And then H system in feet. Okay. Zero, zero, 150. The first data point I plot is Q equal zero, H system equal 150. Right there. Now I randomly choose another point on this curve. This is what it shows here. Take any point you want. Okay. Now this is -- I chose 500 next to it I think. Yep. I'm going to take 500, convert that to cubic feet per second. Put that in the equation on the right hand side, the system head curve. Put that in 1.114. Get H system. I get 150.5. Okay. At 500, 150.5 right there. I say, okay, I'm going to take another Q. I'm going to take a Q of 1,000 GPM. I randomly pick some points on the graph. Q 2.228. H system, 152.1. I go over here, at 1,000. I plot 152.1. Now I connect the dots. Where the two curves cross, the left hand side HP equals the right hand side H system. That's what I do. I plot the pump head versus Q here. I plot the system head versus Q here. Where they cross, then they're equal. That's called the operating point. There's the operating point, OP. Here's the flow rate. When I plotted it, 880 gallons. So, Q operating equal 880 GPM. The pump head, is over here. The pump head about 152. So, where the two curves cross, that's called the operating point. Okay. Now somebody asked me the question, okay, okay, got it. But I want to know how much power has to come in from the motor to drive the pump at the operating point. How much power has to come into the pump from the motor to drive the pump to make that flow rate 880. Go back to the manufacturers curve. Go up here to 880. Go straight down here to W dot N curve. Okay. Go horizontally across and I get the power N is about 30 kilowatts. So W dot pump, about 30 kilowatts. Convert that to horsepower, about 40.2 horsepower. We'll do a lot of SI here just so you know the difference. Some books will call that pump head this. I don't like that. Why? Because look at this guy. What's that say? Lowercase hp. What's that one say? Lowercase a subscript p. No, it's too confusing. Make that a big H. That way you don't get confused. I always use the big H for a pump or a turbine head. Because, in English you don't want to confuse that guy, horsepower. Because, the abbreviation for horsepower is lowercase h times p. Okay, anyway. There it is. Now someone says, "Yeah, but I really want to know what the pump efficiency is. I'm worried about the pump efficiency." Okay, I got you. Let's go back to the manufacturers curve. What's our flow rate? 880. Where's the pump head? 205, right there. 880. There's where it's operating, right there. What's the efficiency right here? 70% What's the efficiency right here? 75%. Take your best guess. I'm guessing 72%. Got it. Good guess. Pump efficiency, 72%. Now we've got everything. We've got everything. You put that pump from that manufacturer from this curve, from the manufacturer, in this system carrying water from here to here, 150 feet, in this pipe. The flow rate you're going to get is 880 GPM. The pump head will develop to be 152 feet. The power into the pump is 40.2 horsepower. The pump efficiency is 72%. Do you want the water horsepower? Okay. You can get the water horsepower. Gamma Q HP equal the pump efficiency times a power that comes in. There's the pump efficiency, .72. Okay. There's the power that comes in, 40.2. You take .72 times 40.2 and that tells you the water horsepower. So now you've got everything you need. You want the NPSH, you got it. You want the power in, you got it. You want the power out to the water, you got it. You want the efficiency, you got it. You want the flow rate, you got it. You want the head, you got it. You can't get anymore than that. That's it. But, you know, now you play the game. You say, you know what, what if I make that pipe smaller? A half a foot in diameter. You know what's going to happen, I mean, from the first fluids course. There's going to be a lot more friction in there. You make that D half the size, that makes this guy twice as big for the same F. Oh yeah, this guy goes up. He's big now. This guy goes up. He's big now. Guess what happens. Do you always start there? Yeah. When the flow rates zero, I always start at 150. But now this coefficient's bigger. There's the new curve, with a smaller pipe. Where's the operating point now? Right there. What did the flow rate do? Well look at it. The flow rate went down, big surprise. You put a smaller pipe between those two reservoirs with the same pump at the same speed, of course the flow rate goes down. Say yeah, but now I'm going to put a pipe in which is two feet in diameter. This was for one foot. Two feet in diameter. Oh, there will be less friction, okay. Be less friction. This is twice now, D is two, compared to one. This number goes down. It might be .01, .15. Start at 150. There it is! For a two foot pipe. What did the flow rate do? It went up a little bit. Of course it did, the pipes bigger now. It makes common sense, less resistance in the pipe. So by changing either the minor losses or the pipe sizes or length or pipe material, you're going to change this system curve over here. This guy comes from the manufacturers graph. This side comes from the picture right here, that's the difference, okay. Ones called the system curve, ones called the pump curve. But there is a difference in those two. Okay. Any question on that right now? That's a big long story, but it's a very complete story. Okay, now. The next topic, oh let's just go over -- well, before I forget it, let me go over the homework. Okay. What we passed back today. Now from now on the homework's going to be on McGraw Hill connect. Okay. But the first set was there. Just so you know, on this particular homework problem, I'll just give you the kind of answers in a way. They can be slightly different because of reading the moody chart, whatever. But what we had was, in this particular problem, we had a reservoir with three different pipes. Pipe A, pipe B, pipe C. Or pipe one, pipe two, pipe three. Whatever you want to do with it. You can call this point A if you want. You can call this point B if you want. And you were supposed to find delta Z if the flow rate through the pipes was 12.5 cubic meters per hour. Okay, it's a series problem. And again, there's no iteration since you know Q, you know the velocity, you know the Reynold's number, you know the relative roughness, you go to the moody chart you get the F 1, 2 and 3. No guessing. .028 F2, .026 F3, .031. If you didn't geet those see me and I'll try go walk you through how you use the. Or if you want to use the curve fit equations, that's okay. You can put it there. I don't care, okay. And when you put those guys in there from A to B and solve for delta Z you should end up with delta Z somewhere around 29.8 meters. Around 30, you know good, that's fine. Okay. So that's the answers to the homework problem. Okay, I think we're at a good stopping point now. So I'm going to stop today because we're a little bit ahead of the game. So we'll pick it up then -- Monday's a holiday, so a week from today we'll see you next time. Get started on that Connect homework though. Yeah.
