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, ME313? 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 a centrifugal pump so this is how we test a centrifugal pump I'll go through 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 pump 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 pump, centrifugal.
The purpose in life of a pump is to increase the pressure. So P2 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 the 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 1 to point 2 right at the pump. 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 can get the flow rate Q. We write the energy equation from 0.1 suction side to 0.2 discharge side. Here's the equation.
There's no straight pipe, there's no straight pipe, minimal straight pipe, maybe a few inches at the most. Forget about that. So P1 over gamma V1 squared over 2G Z1 HP head of the pump This equation is in feet or meters P2 or gamma V2 squared divided by 2g Z2 Usually, this difference in elevation, Z1 and Z2 is minimal in the matter of inches. So we usually neglect that Delta Z. Usually, the difference in the velocity head between 1 and 2 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 Okay, so that's that's our equation so what you do in the lab and The way that engineers test pumps is you run different flow you run 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 is comes off relatively constant Then drops off like that as the flow rate increases so the pump head is constant for a while and then drop Off pretty rapidly because of losses in the pump at the higher flow rates drops off rapidly so that's the that's the pump head curve now besides the Pump head curve.
There's 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 in It's either in kilowatts or horsepower. 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. Radians per second, pump speed and that can give us kilowatts or we can convert it foot pounds per second into horsepower.
Okay. In a laboratory environment, we have, 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. The pump efficiency, what comes out from the pump divided by what comes into the pump, the power. There's 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 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. This point here, the peak on here is like the best efficiency point.
So that's just a typical graph of a pump characteristic, a centrifugal pump. And typically for that, we'd say that this is at a constant speed, omega. 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 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 and the pump is I don't know not Eight ten years old by now I'm sure that the impeller blades aren't smooth like they were originally.
They're rougher now. We expect the performance to degrade, the efficiency to go down. Yeah. So, yeah, we expect that.
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 pumps mostly pump water. People call this guy here the numerator, power out the water horsepower. That's the water horsepower. This is the shaft horsepower that comes in.
They call that the water horsepower. That's just historically what's been called the numerator, Gamma, Q, HP. This is a graph. I don't think it, no, it's not from our textbook.
of a manufacturer's curves similar to that. Okay Bang you want one Maybe that might be good. I'm not gonna put on the board. Well, I'll put part of the board So wait and see how it looks. We'll see One more.
Okay. There we go. Okay, so You can see here that this is a manufacturer's curve.
He shows a picture of the pump. 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. 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 the shutoff 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 a pump on, there's no flow. But the pump still develops this head, H sub p, it's called the shutoff 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 size impellers The top curve is 260 then there's 240 230 205 millimeters That's the size and pillars you can get from the manufacturer and put in that pump.
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 a 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 manufacturer's data, sometimes called a pump performance map, pump performance map. 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 All right now below that There's a graph and this graph Is the W dot in 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 stands for net positive suction head. But again, there are four curves there. There's a 240 line, the 205, the 240, the two, there's a 260 in there.
Right, so we'll take the 260 again. The 260 is the bottom line. Looks like this. So 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 give you something called the net positive suction head. Okay, now let's just mention what the net, since we 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. Now let's draw a picture here.
Well there's a picture up at the top but I'll redraw it again here. 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. All right, this is P1, this is P2, okay, P1, P2.
Yeah? Yeah, it is. I'm going to mention that in just a minute, but it is, you'll find out.
Yeah, it is. I'll mention what it is too. I haven't mentioned what it is even. You probably know though.
We've got all that in there. Now we need, yeah, we got that we need. If you look at the bottom of the page, here's the problem. I'll read the problem. Determine the elevation that a 240 millimeter diameter pump.
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 to drop. And if that pressure drops enough, if it drops 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 bubbles. 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. 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 to the field with pump problems. And he said, I can walk out there now, he said, and I can tell when a pump is not working right, he said, because I'll hear. a bunch of clunky noises in the pump. I 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. After 10 million times, It wears that impeller blade it makes it rough it wears it away the efficiency goes down the pump fails That's that's the that's the serious problem is 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 pools 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 a distance elevation.
So we keep reading here now. Say okay the water temperature is 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 your 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 these pressures have to be in absolute So you'll see down there in the equation P atmosphere 101,000.
That's 101 kPa. The vapor pressure of water at 15 degrees C was it really low 1666 pascals Okay Now we go to the graph NPSH over there all right and He tells us what the flow rate is 250 cubic meters per hour 250 cubic 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. So delta z.
is equal to 101 minus PV divided by our gamma, 9800 minus from the graph, from the manufacturer, 7.4. H sub L, if there's any losses in the piping, H sub L, F L over D. He said neglect losses.
Neglect losses in the pipe. Okay, so delta z he says is 2.74 meters. All right, 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 than that above that water surface We've got some problems that pumps gonna be in trouble. Okay because of cavitation Okay NPS H that's what the manufacturer gives you All right I've got to save him.
Do I want to save him? I don't think so. What kind of pump should you, the engineer, select?
Pump selection. Use the pump specific speed. 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 point. So the pump specific speed is identified at the best efficiency point.
Now, there are two. equations. So this guy here has to have all the correct units in it.
Like if it's SI or English engineering, this pump speed radians per second, Q cubic meters per second, etc. 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 and 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 about RPM. So I want an equation that 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 you can kind of figure out what you've got.
I'll just mention real quick here if I can find it So we'll go to pump specific speed chapter 11, okay chapter 10, here we go. Alright, so we've got our pump specific speed figure 1111. He tells us there in figure 1111 that if you calculate that and you get between 500 and 4000, select a centrifugal pump. So if somebody tells you, all right, I got a pump operating at 1750 RPM.
I want to pump 500 gallons per minute, 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 above 10,000, axial flow pump. The engineer say, don't, 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. It's a good question though, thank you.
Good question. No. This is not going to be, don't take the pump to the moon.
Then all bets are off. But no, they say pretty much lump G is in here somewhere, 32.2 or 9.81. 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 fan. 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 Mexflow pump does? A little of each.
There's pictures in the textbook. I'm not that good of a sketcher of those, but there's pictures in the textbook on figure 11.11. Then if you want to do it this way, if Ns prime is less than one, you can do it with radio 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 Mexican, excuse me, use the axial flow.
Okay. So that's how that helps engineers select the right kind of pumps for a specific application. Uh-huh.
Q and H. Which one now? For Q and H, I think P is at first. Q and?
And H. And H. 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. Look at for the best efficiency point. Okay, now that's just all about pumps not a lot about it, but anyway that gets you started now 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. Um, mm-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.
the flow rate from the lower reservoir to the upper reservoir is Q. 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 impeller Okay, and I want to know What flow rate that pumps going to cause between these two reservoirs, and this is water Okay So I know what pump I've got I've got this guy right here there 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 he tells you right there cubic meters per hour I Don't I wish I had that in English engineering 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 and feet. Yeah, you can use this graph whether you're in English RSI units, which it's not quite as easy to read in the English units because the little tick marks on the axes are a little hard to read, but you can read it. Okay, so here's what I did then. And 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, let's see, I think I took 150 something or other. There it is. Yeah, no, it's 170, 175, 175. That's what it was, 175. Okay.
And then I just I went to a hundred GPM and I went to a thousand I'm sorry 500 GPM a thousand GPM 500 GPM a thousand GPM zero I Took the points off of here. I took one point off of here. I took one point up up here at 500 I took one point off of here at a thousand. I plotted those three points over here. Let's see here's 150. I'll need that in a minute.
It kind of went down like this At a thousandth down to 140 Okay, so it looks like this There's the pump head curve replotted from the manufacturers curve now Okay, there we are. Okay. Now we have to add here.
Let's just start over here. Need that. I 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 minor 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 equal sign and the pipe network on the other side 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 z1 z2 my z150, okay HP equal 150 plus There's straight pipe right there.
There it is. Okay FL over D V squared over 2 G 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 no one right here point 0 1 5 the diameter is known one the length is known a thousand 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 plus, if you do all the mathematics, that's what you get, 0.43 Q squared. All I did of course was replace the V, Q equal to V over A. So replace the V with Q times A. Diameter is one. So wherever you see a v, you put a pi divided by four times q, and you get that guy up there.
A couple of lines missing. This side of the equation is the pump head curve. This side 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 equation. When q equals zero, well, I'll make a table for you.
System head curve. That's in cubic feet per second. Okay.
Let's do the complete thing here. I've got it all on here. Here's q in GPM, convert it to cubic feet per second, and then h system in feet. Okay. Zero.
0 150 The first data point I plot is Q equals 0 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 that this is I chose 500 next I think yeah, I said I'm gonna 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. So okay, now I'm going to take another Q. I'm going to take a Q of 1,000 GPM. Okay, 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.
So let's call 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 in 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 that guy. What's that say? Lowercase h p.
What's that one say? Lowercase h subscript p. No, it's too confusing. Make that a big H. That way, you don't get confused.
So I always use the big H for 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, okay, I got you. Let's go back to the manufacturer curve. There it is. What's our flow rate?
Seventy percent. What's the efficiency right here? Seventy-five percent.
Take your best guess. I'm guessing 72 percent. Got it.
it? Good guess. Pump efficiency, 72%. Now we've got everything. We've got everything.
You put that pump from that manufacturer with 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 the power that comes in There is a pump efficiency 0.72.
There's a power that comes in 40.2. You take 0.72 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've got it. You can't get any more than that, that's it. But now you play the game.
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. 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 rate is zero, I always start at 150. But now this coefficient is bigger. There's the new curve with the 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 there which is two feet in diameter. This was for one foot, two feet in diameter. There'll be less friction. Be less friction. This is twice now, d is two compared to one.
Unless this number goes down, it might be 0.15. 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 pipe's 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 the system curve over here. This guy comes from the manufacturer's graph.
This side comes from the picture right here. That's the difference. One's called the system curve, one's 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 very complete story Okay now The next topic oh, let's just go over the well before I forget it let me go the homework, okay, 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 the answers in a way that 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 our pipe one pipe two pipe three What are you going to do with it? You can call this point a if you want you can call this point B if you want 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. Since you again, there's no iteration since you know Q, you know the velocity, you know the Reynolds number, you know the relative roughness, you go to the Moody chart, you get the F, 1, 2, and 3. guessing, 0.028, F2, 0.026, F3, 0.031. If you didn't get those, see me and I'll try and walk you through how you use the Moody chart or if you you want to use the curve fit equations, that's okay.
You can put that in here. 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 gonna stop today because we're a little bit ahead of the game So we'll pick it up then.
She's Monday's a holiday. So a week from today. We'll see you next time Get started on that connect homework though.
Yeah Thank