>> Okay, just a reminder, next Wednesday is our first midterm, okay? We'll talk about that in about 40, 45, 50 minutes, last part of the class period. So, we'll get to that. We are in chapter 5 of our text. Dimensional analysis and similarity, our similar to studies. Go back and review real quick. We -- this was a problem we looked at as an example. It was a drag force on a smooth sphere. And we said that the drag force was a function of the velocity, the viscosity, the density of the fluid and the diameter of the sphere. There were five variables up there. There were three dimensions, M, L and T. 5 minus 3 is 2. There's two important dimension as parameters. And we identified those by the pi theorem. And the pi theorem said the two important parameters here on the Y axis, here on the X axis, this is called the drag coefficient. FD is a drag force, drag coefficient. This was the Reynolds number. So, no matter what fluid we've got, maybe the squares, what diameter we've got, what velocity we've got, if we take wind tunnel data, for instance, and change those things, all the data points appear to fall on a single line. Actually it comes down, it goes down this way, from upper left to lower right, but that's okay. It falls on a single line. The drag coefficient versus a Reynolds number. As a matter of fact, I'll make it look very similar to one we've had before. So, let me just go ahead and change this guy. Be a drag coefficient comes down. So, we can compare that to another one here. This graph next to it. So, let's draw this guy here, he's like this, okay. I'm not going to put all those symbols on there again, but you get the point. No matter what you would do in the laboratory in the wind tunnel, all your data points fall in a single line. Now, it's not new to you, but you hadn't gone through chapter 5 yet in fluids one. In fluids one there's another set of curves. Looks like this. It's called a Moody chart. And the interesting thing is they're very similar. Now over here in the Moody chart this is laminar and this is fully developed turbulent. And we found out that there's not a Moody chart for air and a Moody chart for water and a Moody chart for oil and there's not a Moody chart for a pipe diameter of 1 inch, 1 foot, 10 feet. No. One Moody chart is good for everything. Wow, are you kidding me. One Moody chart is good for everything? Yeah, sure is. So, no matter velocity in the pipe, no matter what pipe diameter, no matter what the fluid is in the pipe, all the data falls on a single straight line on log log graph paper. F is equal to 64 divided by the Reynolds number. Here's a curve, wave chart, labeled smooth plane. Interesting. There's just one line on a Moody chart. Is there another piece of paper which is valid for air and one for water and one for a 1 inch pipe and one for 10 feet pipe and one for water and one for oil, one for velocity 10, one for velocity 20, one for velocity of 50 feet per second? No. There's only one line. Does that look similar to this? Of course it does. Of course it does. So, no matter if you took data out the lab, you'd find all your data points fell on a single curve like this. Wow, that's pretty impressive. One sheet of paper. A Moody chart for everything we deal with just about. Over here, one sheet of paper. The drag force on a cylinder or a sphere. Wow, that's pretty impressive. How do we do stuff like that? Well, number one is, after we took experimental data, or before, we identified what the important dimension those parameters were? And that gave us a big hint to plot one versus the other. With this guy up here these were two important dimension parameters. Drag coefficient, plot on the Y axis. Reynolds number, plot on the X axis. Moody chart, you didn't know at the time, but you were plotting dimensionless numbers on here. Friction factor dimensionless on the Y axis. Reynolds number dimensions on the X axis. As a matter of fact, carry it further, the pressure drop in a pipe is a function of what's in the pipe row, what's in the pipe mu, the velocity in the pipe, the diameter in the pipe, and, here it comes, the roughness of the pipe. Oh, yeah, roughness. All these curves here are labeled E over D. Guess what E over D is. Oh, I'll tell you. It's a dimensionless parameter. How many important dimensionless parameters are on the Moody chart? Here they come. F is a function of the Reynolds number and the relative roughness. Yep. So, we chart another good example of a dimensionless plot. You can see we engineers -- dimensionless, dimensionless, we like to plot things on dimensionless coordinates, okay. We're good at that. Okay, so now, the next part of chapter 5. Some of those guys have names. I told you drag coefficient, Reynolds number, relative roughness. So, I'm going to take the Reynolds number as a start and look at that. So, the Reynolds number. Row BL over mu. RVL over kinematic viscosity mu. L just stands for a length. I don't care if it's a diameter or the length of a pipe or whatever, L stands for characteristic length. Rewrite this guy. And so I'm going to rewrite it like this. Multiplied by V, divide by V. Multiply by L, divide by L. Take 1 over L, divided by L. I didn't change anything. They all cancel out. When I do that though, numerator becomes row B squared L squared. Denominator becomes mu V over L times L squared. This numerator, row V squared L squared is like a what's called a dynamic pressure. Multiplied by an area. Any time you square something that's an area. If you square a length, that's an area. You might recall from fluids one, dynamic pressure, row V squared divided by 2. So, row V squared is proportionate to the dynamic pressure. And when you multiply a pressure by an area, you know from fluids one, pressure's force over area times area, that's a force. That's called the inertia force. Take the denominator. Mu V over L. Multiplied by L squared. Mu V over L, it kind of looks like... That. Here's a mu, there's a mu. A difference in U, there's a velocity. A difference in Y, there's a length. Yeah, same thing. First parenthesis looks like a shear stress. Okay, that's a stress. Viscous stress. Mu. Second term, L squared looks like an area. Anytime you square a length you get an area. What's a stress? A stress is a force over area. Okay, so force over area times area gives me force. This is the viscous force. Viscous force. So, the Reynolds number could be interpreted as the ratio of two forces. Inertia force. Over viscous forces. Let's take an example of maybe an oil. Oil's are very viscous. They don't always move fast like air in an HVAC duct like that. So, we know the oil has a big viscous force. If the denominator is big, that means the Reynolds number is small. Of course, if the Reynolds number is small with oil, we're probably in the viscous range of the Moody chart. If we've got air going through an HVAC duct and you do this in the fluids lab, you'll find out the Reynolds number is really really big, if you've done it in the lab you know it. If you're in there now, you'll find out on the HVAC duct in our fluids lab. Yeah, because in that duct with the air coming through there there's a high inertia and air is not very viscous. So, if air is not viscous this guy is small. If this guy is small, Reynolds number is big. So, for air in an HVAC duct, we're out here somewhere. Big Reynolds number. Oil in a pipeline, we're down here somewhere. Small Reynolds number. Now, take another dimensionless number. Mock number. You can go through -- by the way, just so we know what mock number is defined as, mock number is defined as V over A. A is the called the local speed of sound. We'll get into that in great detail in our next topic in fluids two, which will be compressible flow. But for right now that's what the mock number is defined as V is the actual velocity of the object, A is the speed of sound at the location where the object's located. That's why it's called local. It means that's the speed of sound at the location you're at. This turns out to be, if you go through the same kind of analysis we go through here, we won't go through it again, but it's inertia forces. Divided by elastic forces. The elastic forces are due to compressibility. That's the mock number interpreted as a ratio of forces. Then -- Through number 3. Not the fruity number. This -- French, you know, the food number. The food, like food, food, Froude. Okay. Froude number. FR. It's equal to the ratio of inertia forces. Divided by gravity forces. And, oh, by the way, it's equal to -- I'll put it up here. Froude is defined as V squared over gravity G times some characteristic length L. Oiler number. EU stands for the oiler number. It's equal to delta P -- it's put down here, delta P over row V squared. Delta P over row V squared. Some pressure difference divided by density, divided by velocity squared. So, the oiler number can be interpreted as a ratio of pressure forces. Divided by inertia forces. The last one we want to look at will be the weber number. Not by the way the drag coefficient is just a takeoff of this guy down here. I'll put it down here. Drag coefficient. They sometimes call capital CD the drag coefficient. Drag coefficient is FD over row B squared, D squared. What's pressure? A force over an area. Right here. So, replace that delta P with a force over an area. There's the force, there's the area. Length squared, diameter squared. So, they're the same thing. But they're dealing with pressure drops or pressure changes. Then it's called the order number. Looking at drag force on object, it's called the drag coefficient. Okay, weber number, weber WE is equal to row V squared L squared over sigma. From fluids one, sigma is the surface tension. And you can interpret the weber number as the ratio of two forces, inertia force. Over the surface tension force. One of the important -- well, different times, different situations. You analyze a situation you have and you say to yourself, "you know what, I think that parameter is important." Pressure drop in a pipe. First thing you do, always, calculate the Reynolds number. Is the flow laminar turbulent? Okay, what's important, the Reynolds number. Flow over a sphere or a long cylinder. First thing you do, calculate the Reynolds number, get the drag force. Okay, Reynolds number. High speed aircraft flying at mach 1.5. This guy's important. Okay? Because at that Mach number the compressibility affects are significant for air and a mach number greater than .3, you better look at the compressibility affects. Less than .3 you can assume it's incompressible, air's incompressible. The magic number for the Mach number, incompressible versus compressible affects. If you've got bubbles and droplets, you could design a new paint sprayer or a can of spray paint. What you don't want when you have this spray can of paint, you're going to paint some sheet here, okay. Psht, psht, psht, psht. You don't want it in big droplets because it's going to run down and droplets on the thing. You don't want it in too fine a mist because it will just blow away and end up on your ceiling or your floor or your arm. No, you got to design that paint sprayer, that little nozzle to spray out just the diameter you want of those paint droplets. Or maybe bubbles. Okay? Bubbles and paint droplets, they all depend on surface tension to make the little spherical bubbles and droplets. So, anything concerning that kind of design you'd say, "I think the weber number's important." Oaky? Order number, yeah, again, the pressure drop across something, a valve, a pressure drop across some kind of a fitting, a Venturi tube, yeah, okay, that's important. Froude number, gravity. You designed a peer for the Pacific Ocean, Redondo Beach. You know that peer is going to be hit by waves and those waves hitting that peer cause the water to go up. So, here's the peer in the water. When the wave hits that peer, the water's going to go up and come back down again. Watch some pictures of waves hitting peers. Well, what's going to happen? That peer pushed water up. What was trying to pull it back down it again? Gravity. Gravity's important. So, yeah, okay, I think if I'm designing that I think maybe the Froude number's important. If I'm designing, let's say, say a barge being pushed by a tugboat, a barge. Barges have a big flat front. The big flat front looks like this on a barge. When the water hits that it goes up and comes back down again. Oh, yeah. That barge had to push that water up against gravity and then it came back down again. Well, what's important? The Froude number. The Reynolds number? Not so important. The Reynolds number will tell us the drag force of friction on the hull. But for most of these objects the big things is you're raising tons of water by feet. What does that? Oh, the engine driving it. Do you want that? Obviously not, you want to go faster. So, what do you do, you test something in a water channel. And what do you try and equate? The Froude number. That's important. So, every one of these has its importance in different parts of our engineering situations. Okay. Table 5:2 in your textbook. There it is. In the white textbook. There's 20 dimensionless parameters there. 20. You think we engineers love dimensionless parameters? You better believe it. You better believe it. We love dimensionless parameters. Wait to you get to heat transfer. You might be in there now. When you get to convection heat transfer, every important equation is written in terms of important dimensionless parameters. Yeah. Friction factor equals 64 over Reynolds number. Yep, there it is, an important equation from fluid [inaudible] fluids one. And there's other ones in fluids two. But especially in convection heat transfer. Anyway, oh, yeah, there's 20 of them listed here. I just put five on the board here. There's tons of them. Why do we use them? For a darn good reason. They make life simple. Look at those graphs. They make life simple for us. Okay, now, all this leads up to what they call similitude. Our similarity studies. So, the last topic in this chapter is similarity studies. And it's nothing new to you. I mean, you can watch commercials and see models maybe of aircraft in a wind tunnel. You might see the model of a car in a wind tunnel or a truck. So, yeah, we do a lot of model studies, model studies. And to do that we got to follow very specific rules. So, let's write down, first of all, what similitude is. Okay. In words. Similitude is the therian art of predicting prototype performance from model observations. Prototype is a thing you're studying, the real thing you're studying. You want to model it in a lab and from that model in a lab you want to predict how the prototype, the real thing is going to perform. It's not just a whole theory, here's the words, theory and art. So, theory gives us some background of that, but sometimes we have to kind of massage that and extend that beyond just theory to see how the prototype will perform from taking model observations. Okay, so, number 1, geometric similarity. I'll write these out in words and we'll talk about them. Okay, you're into constructing models of aircraft, so you go to hobby store and you pick out a model of an F18 plastic model. Look at the box, it says, "172." You say, "Oh, okay, that's a good scale model, I like that. I like that." What that means, of course, you know what it means, but I'll remind you. What it means, of course, is the model is once divided by 72 times as big as the real thing. Put them in inches, in inches. One inch in the model is 72 inches in the real thing, prototypes a real thing. One inch in the model. 72 inches is what? 6 feet? Yeah. 1 inch on your plastic model is equivalent to 6 feet on the real F18. Okay. Everybody knows that. You buy a model you want to know what the scale ratio is. It's on the box. You go to the hobby store, it's on the box. Okay, so you got that. I'm not going to model -- let's say I dropped a sphere in oil, I'm not going to model that in the lab by dropping a cube in oil. No, I'm not that crazy. Model and prototype are the same shape. You want to model a sphere, drop a sphere. Okay, it's got to be the same shape, obviously. Most of these things are fairly obvious, but some aren't. By a constant scale factor, everything in the model is scale 1 to 72. The length of the wings, the height of the aircraft, the diameter of the wheels, everything is scaled by a constant scale factor. But be careful. You say, "Okay, well, I'm going to model this in a wind tunnel." So, if this angle is 30 degrees, I think I'll make the scale one 30 degrees divided by 72. Oh, my gosh, no, you don't change the angles. You don't change the angles. Okay, the rule is them, change -- here it is right here, there's a word, change the linear dimensions, but don't change the angles. Okay, got it, got it. So, that's pretty basic stuff. Let's go on to the more fluid stuff. Number two, kinematic similarity. Kinematic talks about velocities, accelerations. A, velocity is at corresponding points. In the two flows. Model and prototype. Or in the same direction. And are related. By a constant scale factor. In magnitude. B, flow regimes must be the same. You're not going to try and model laminar flow in a pipe, in a real pipe by turbulent flow in your model pipe. That wouldn't make any sense. You're not going to try and model an aircraft going up Mach 1.5 with a Cessna going up Mach .1. No, that wouldn't make any sense. You want the same flow regime. Okay, that makes sense. But the kinematic similarity is you want the velocity at corresponding points, I'll make an example here, here's a small sphere, here's a big sphere. Maybe this is the prototype, maybe this is the model, but just so you know, most people think, oh, the model's always smaller. No, that's because you're used to going to hobby store and seeing the boxes carrying the aircraft at 1 to 72. Sometimes in the real world the model is actually bigger than the prototype. But, okay, that's all right. It can go either way. But this is the model. This is the prototype. Okay. Here are the streamlines. Here's the velocity right here. Velocity model. This right here, here's the velocity of the prototype. Notice where the black dot is compared to where the sphere is. See that there, that distance and that distance? That's got to be this guy right here, okay? That's got to be that guy. If it's a 1/72, this is one inch from the surface, this is 72 from the surface. Because it says, "Corresponding points." What that means is you got to use rule one to figure out if this is where I measure with my pitot tube, the velocity and the wind tunnel on this model, then that's where this velocity VP is going to be this distance for the prototype sphere. And, by the way, of course, these are different numbers. See that constant scale factor? It might be three to one. Maybe it's three to one. That means the velocity of the prototype is three times the velocity of the model at the corresponding point, here and there. Okay. Now, let's do the last one. The last one is number three. Dynamic similarity. Dynamics talks about what? How forces cause accelerations. So, what is dynamic then do for us? Okay, now we talk about forces. What does kinematic tell us? Velocities. Okay, same thing, there's only one rule now. At corresponding points again. Okay, forces, so I'm going to do the same thing again. Here's the model. Here's the prototype. I'm going to say a pressure force. Okay, so, if the flow is moving passed the prototype and the model, there might be a pressure force on the model right here. On the surface of the sphere or long cylinder. Okay, corresponding points. If that's 45 degrees fro0m the front, corresponding point is 45 degrees from the front. Okay, there it is. Keep reading. Identical kinds of forces, pressure forces, are what parallel? Look at this line, look at this line. Yeah, those two lines are parallel. That's what it means. Okay. So, now we've got what we call similitude. Similitude. Between the model and the prototype. Okay, so, let's continue on then with our example. So, I'm going to work the example over here. Going right along with our discussion on the circular cylinder or the sphere, I'm going to say we have a sphere in water. And let's see... Okay. Prototype and model. Prototype. Velocity of the prototype is 5 feet per second. I want to find the force on the prototype from my model studies. The force on the model is measured to be 8 pounds force. I want to find what velocity I should set the air in the model study. Or the water, pardon me. Oh, I'm sorry, it is air, excuse me. So, that is air. The model is in air, prototype is in water. So, let's erase that top thing. Okay. Now we got it. I don't know, maybe I'm going to drag a sphere behind a ship. Instrumentation package. It's spherical in shape. I drag it behind the ship. I want to know if the ship is going 5 feet per second, find out miles per hour, knots, what's the drag force on the ship from towing that sphere? But I'm going to test it in the wind tunnel with air. You can do that, you can change the fluid, you can do that. Okay. So, I say to myself, "Gee, I wonder what's important, what's an important dimensional parameter for a sphere being dragged behind a ship." I was going to say, "You know what, it looks like that picture right there." Yeah, yeah, that's right, it's Reynolds number. Okay. Step one, because you have identified the important dimensions parameter, was it the weber number, was it the Strouhal number, which is a vibrating wire in a windstorm? Was it the Mach number? No, for a ship. Yeah, no, it's a Reynolds number. Okay, so number one step, equate Reynolds number. Reynolds number model equal, Reynolds number prototype. So, we have row B, D over mu model, equal row B, D over mu prototype. These two guys here are testing the same diameter and model prototype sphere. So, the diameter's the same. Diameter, diameter, cancel out. I'm going to go over here to this now. So, I'm trying to find what the velocity of the model, okay, there it is. Velocity of the model. New model over new prototype. Times the velocity of the prototype. The model then, for the model and the model in air 1.64 times 10 to the minus 4, for the viscosity and viscosity. Prototypes in water for water, 0.93 times 10 to the minus 5. The velocity of the prototype is 5 feet per second. So, the model velocity in the wind tunnel, model is in air, wind tunnel, should be set to 88.2 feet per second. Just to give you a measure of that, that's 60 miles an hour. So, you set the wind tunnel to 60 mile an hour and then you measure the force on it. And the force you'll get in your wind tunnel is 8 pounds. Okay, so now I need to know the drag force in the model in the wind tunnel. I say, "Gosh, what do I equate now?" You know. I got to find a parameter that has a drag force in it. Where could that possibly be? There it is right there, drag coefficient. Step two, equate. Step one, equate Reynolds number. Step two, equate drag coefficient. All right, F sub D over row V squared, D squared, for the model. Equal F sub D over row V squared, D squared of the prototype. It's the same size sphere. D is the same. Cancel, cancel. I want the drag force on the real sphere being towed behind the ship. Okay, the drag force on the prototype, which is this guy right there, is equal to row of the prototype over row of the model, multiplied by V of the prototype over V of the model, quantity squared. Multiplied by the force on the drag force on the model. Okay. I go the back of the book and I get the densities of air and water at the ambient temperature. 62.4. And for air, 0.075. Multiply that by the velocity ratio. Velocity of the prototype was 5. Velocity of the model was 88.2. Square that and multiply that by the drag of force on the model times 8. The drag force on the prototype then comes out to be 21.4 pounds force. So, in similarity studies, you're given a problem, you have to figure out where the important dimensionless parameters I should be equating. In this problem there, obviously the Reynolds number. Got it. That gave me one thing. Velocity. Number two, the drag coefficient. Gave me drag force on the prototype. Okay, now, let's try another one. This one -- well, I'll draw the picture first. Okay. This one a one tenth scale model of a hydrofoil. Is tested in a water channel. The model drag force -- Is measured to be -- Eight tenths of a pound. At a speed of 20 feet per second. Find the speed and force for the prototype. It says, "Neglect viscous effects in the problem statement." Okay. You know what a hydrofoil is, okay, it's what an air foil. Air foil operates on air. A hydrofoil operates in water. Hydro, water. Operates in water. So, the hydrofoil is like here. You're skimming on the top of the water. Oh, yeah, they go fast. They go fast. And I don't know, maybe it's an air craft, I don't know what [inaudible] and I don't really care, because that's not part of the problem. There's an aircraft with hydrofoil, okay? Aircraft body, not an aircraft, it's like a ship, okay, so we'll make it like this, okay? Doesn't matter what's up there, we're interested in that guy down there. Okay, let's try and -- we have to equate some things, all right? Let's see, Mach number -- no, I don't think so, no, I don't think so. Weber number -- no, there's no bubble and droplets. No, I don't think so. Let me see. What was that one up there? It had gravity. Oh, yeah, when that hydrofoil hits the water, the water's going to come up on the hydrofoil and it will go back down like that. There's the waterline right there. It pushes the water up in front of it. Okay, that gives it away. Froude number. Here's another clue, another clue. The problem said, the statement of the problem said, "Neglect viscous effects." What's viscous effects? There it is, Reynolds number, Moody chart, X axis, Reynolds number. Why? Viscous effects. Drag coefficient, on a smooth cylinder sphere. Yeah. That's friction. So, yeah, okay, we know now this tells us, this statement tells us neglect the Reynolds number. This one tells us equate the Froude number. By the way, if you don't know what a water channel is, it's a -- we've got one down in the hydraulics, fluids hydraulics lab. There's one in there. It belongs to civil engineering department. It's a long plex in our account poly, it's a long Plexiglas rectangular shaped, about this high, about this wide and water is pumped -- water goes down here, goes into a big tank and it's pumped back to the start again. But what I'm going to say here is, the water only fills part of the tank, up to that height. So, you can test things like that in this water channel in the hydraulics lab. What -- how do you test this model in air? You go to a wind tunnel or you could put it in water too, but you go to a wind tunnel typically. Okay? But in a wind tunnel there's air from top to bottom. In a water channel water fills part of the channel and then you have air up here and the water's down here and you put your little model in here and then you get the drag force on it. That's called a water channel. If you want to look at one, the fluids lab, it's in the civil engineering side of the lab. It's probably from here to that wall there. And it's this wide and it's this high and it carries water down the water channel. Okay, that's just a side light. Okay, so, we go into here now and we said what we're going to do. We're going to equate the Froude number. Step one. Okay, V model over square root, LGL model, equal V prototype over the square root of L prototype G. There's gravity in there. If I'm here in Pomona testing something in our lab, then I'm going to say, "Okay, the hydrofoil's going to operate at a location where G's the same." He chose Pacific Ocean. There's not a lot of difference in G there, sea level, and G here in Pomona at 850 feet above sea level. There's not much difference at all. You can neglect it. Normally then you say, "Okay, I'm going to cancel those guys out." Now, if you're going to test this thing in Denver, Colorado, mile high, you might want to throw in the G in Denver and the G in Pomona. There might be a difference in G, but normally you say the G's are the same for all intents and purposes. Okay, so I get V prototype then. V prototype equals square root of 10 times V model, because 10 is the ratio of the scale model ratio and that comes out to be 63.2 feet per second. Which means the prototype hydrofoil is about 43 miles an hour. 43 miles an hour. And then, number two, of course, to get the drag force we always equate the drag coefficient. So, now we equate the drag coefficient. Okay, F of the model over row V model squared, D model squared, F of the prototype, row of the prototype, V prototype squared, D prototype squared. And we're solving for the force in the prototype. So, force in the prototype is equal to -- are they both in water? Yeah, the hydrofoil operates in water and I've got the water in a water channel. Yep, yep, same fluid, same fluid. Row, row cancels out. So, solve for FP. So, FP is equal to LP over LM cubed times F model. So, that's equal to the prototype is a 10 times a model length. Cubed times F model and F model, he told us, eight tenths of a pound. So, that gives us a drag force of 800 pounds on the hydrofoil. Okay. So, that gives us two examples of how to apply similarity studies. I'm going to work one more next time, but I want to go over a quick review before our midterm next Wednesday. Next Wednesday, okay. So, we'll kind of stop on this now, this is not on the midterm, as you know. I'll go through it in a minute, but this is not on the midterm. So, we'll stop now and we'll pick this up, yeah, after the midterm. Okay. All right, so, let's talk about the midterm. I think, I'm not sure I mentioned it to you, but I'll mention it to you now. The data package that you'll have for the midterm is on Blackboard right now. So, you can go to Blackboard website, you can see what's on the data package, which is what you'll have. I'll give you a data package on the -- at the exam time. You'll put your name on it, you'll use it for the exam, you'll turn it in after the exam, I keep them. The second midterm I pass them back to you, your name's on it, you can mark it up. That's why I do that. You can mark it up. I pass it back to you for the second midterm, you use it for the second midterm, you pass it back to me with your exam, I keep it. On the final I pass the data package back to you, you use it, you pass it back to me with your exam, final exam. Okay, so that data package is online, but don't copy it and bring it here the exam day. I'm going to give you the same data package with your name on it when you come in for the exam. Okay, there is a practice exam, which will be online Blackboard website Friday at 6 pm. Friday at 6 pm, practice exam. That gives you about five days to look at it. You can ask me questions, okay, next Monday that way, office hour next week. So, plenty of time to review that. That was the midterm from the fall, quarter 2017. You'll see what I gave you for the midterm. Okay. There'll be three problems, okay? They'll be from all the material up to dimensional analysis and similarity. So, it -- I'll go through the topics, they're in the course syllabus. That includes pipes and series and parallel. Okay? That includes pump graphs and how you find the operating point of a pump in a system. And that includes -- includes specific speed of pumps, it includes cavitation in pumps. We did problems in class on that and you had homework on that. How you read those pump graphs, typically the pump graphs give you the pump head versus flow rate. The efficiency versus flow rate, the input power versus flow rate and sometimes the net positive suction head versus flow rate. So, of course, know how to use all of that to solve problems. And then we have pumps in series and parallel. Pumps and series, pumps in parallel. If a problem appears to be iterative, if you make a guess on F and you go through the problem one time and you check your F guesses and they don't agree, all you say is, "I would repeat the above calculation with these new F guesses until the F's converged." I would repeat the above calculations with these new F guesses until the F's converged. But don't do any more iteration. Go through it one time. With your next F guess you tell me, my next guess would be F equal .020 for F 1 and F equal .025 for F 2. But don't do anymore work if it's iterative problem. You can bring in one equation sheet, one sheet of paper, 8 and a ? by 11, both sides. Anything you want on there. Obviously, any equations I've boxed on the board are important. Any equations you use for homework or I used for an example problem in class, any equations you used for homework I'd put them on your equation sheet. You can photocopy examples out of the textbook. Homework examples, I don't care, put it on there. You can make things so small they're postage stamp size and bring in a magnifying class, I don't care. Okay? So, you can put anything you want on there. I parked my car in lot C, okay, in case you get a mental block after the exam where you parked your car, you know. So, you know, anything's legal, anything's legal on that sheet of paper. Okay. Both sides, one sheet of paper. Three problems, 60, 70, 80, 90 minutes. That's a lot of time, that's a lot of time. So, you shouldn't be rushed for time, okay, number one. When I taught fluids two last quarter, I was in a 50 minute class. Oh, that's not good. People stress out with that kind of class, because you're always worried. I've only got 47 minutes left, I've got 39 minutes left and, you know. This should be plenty of time to look at your work. My goal is you finish it all and you have time to look it over one time, okay. That's my goal. All right. So, yeah, there should be plenty of time for that. Okay, any questions on that then? Okay, yes, ma'am? >> Any of the tables that you've used in class will give us the information that we need for the problem or should we have those on our sheet? >> When you look at that data package online Blackboard, everything's there. If there's something missing you think's important, put it on your equation sheet. >> Okay. >> I don't think there will be there. I put everything important I use in there, tables, graphs, Moody chart, back of the book, you know, stuff for properties. Yeah, it's all there. Really >> Okay. >> Yeah? >> If we do the practice exam fine will we be okay for the exam? >> Probably not. >> Probably not? >> I'm kidding. If you can do it you're probably ready to walk in that door next Wednesday. Yeah, what I would do is -- that's a good point though. What I would do is don't look at the answers. I got three pages of problems and then the answers. Go over the answers and time yourself. Give yourself -- try it now, because that's a 50 minute exam I gave them. Try for an hour, see what you do. If you don't think, give yourself 15 more minutes and then you'll know how you're doing. Yeah, okay. All right, so we'll see you then next Monday I guess, huh? Right.
