Okay, so the question we left with last time is do you have enough information to determine the mass flow rate of steam through the turbine? So there's a lot of. The short answer is yes of course you do. The longer answer is of course you need to draw your system schematic and show okay. Well, you have one entrance and one exit that's been described. Okay? So we have some mass flow rate that's coming in. And some mass flow rate that's coming out. And remember we, we would look at our conservation of mass. And we would say, [INAUDIBLE], in the most general form, we would have this expression. [SOUND] And you say, oh, look. I know that this is equal to 0, because I've been told that we have a steady state system. I have one inlet and one outlet, so I have m in equals m out, which equals the mass flow rate for the system. And last time we showed you how, in the last segment, the mass flow rate is completely defined in terms of the density of the fluid at the inlet or exit state. The velocity at the inlet or exit state, and the area at the inlet or exit state. So, as long as you have all of this information, either at the inlet or at the outlet, we can define the mass flow rate for the system. So, we look up at the given information, we say okay do I have enough. I'm given the velocity at the entrance. So, I would write down that I have V1, I have P1 and I have T1 on my diagram. And at the exit, we're told that the steam leaves the turbine at a pressure that's known, so I know P2. I also know the diameter at the inlet and the diameter at the exit, so there's D 2, and there's D 1. And if we assume that the diameters are, that we're dealing with circular orifices, circular inlets and outlets. We know that this is going to tell me the area at the entrance, and similarly this information tells me the area at the exit. So, I go through my little checklist, and I say okay, well, at the inlet, I appear to have the area. At the outlet, I appear to have the area. The inlet, I have the velocity. Sorry, that's a velocity here. and I have pressure and temperature at the inlet. I have pressure and I'm told the system leaves as a dry saturated vapor. You need to convert that into some value, into some parameter. Thermodynamic parameter and we know that, that tells us the quality at the exit state is 0. At the entrance state here, we look and we say that's a pretty high pressure, that's a high temperature condition. I'm going to guess, and it's a really good guess, that we're in the super heat region. In which case pressure and temperature are independent and all the state parameters are known. At the exit state I have the quality and the pressure so I know that state is fully defined, those are always unique parameters. So that tells me I have the density, I can get the density from state diagrams. Or from online calculators or from tables at both the entrance and the exit. Now, this is a guess at the entrance that it's a super heat, and that's going to be valid. But, again, that's a good guess. And we'll develop that intuition as we work with these, turbo machinery. And we work with these, these energy transfer devices. So, sure. The short answer is, yes. I can evaluate the flow rate using all the information from the, in, at the inlet condition. I don't have the velocity at the outlet condition, and that in fact is going to be the question I'm going to ask you next. So let's take this information. Let's go ahead and do that calculation. So again, I have velocity, I have area because I have diameter, I need the density or specific volume. So remember, we can always write this as the inverse of the specific volume all at state one. In the tables they typically will list the specific volume instead of the density. So just be again very fluent and capable of moving from one space to the other. So having said that this is a good time for us to introduce the online calculator that we are going to use for this class. Again, I'll provide you with little excerpts of tables. So, we're going to have to use those too. But let's start with just using the easier tool which is the online calculator. Okay, so now you can get to the online calculator through this web address that's shown here, www.steamtablesonline.com. Now, we don't have full access to all the tables, because we're using the free version, but that's going to be plenty for our needs. So we're going to click on Run Calculator for the properties of water and steam. So, what you want to familiarize yourself with is how to use this program. It's a really great and fun tool. General Properties are the first tab the saturation properties are the second. We have steam turbine, flash evaporators. These are getting more complex as we move across the tabs. They have the actual temperature entropy diagrams. We are not going to talk about entropy in this class. It's another thermodynamic parameter. Enthalpy, entropy. So it keeps going and keeps going. So we're really just going to stick with these first couple of tabs in this class. So what we want to do is define, we want the density as the entrance state so we know that we have pressure and temperature. So I know they used lower cased notation here but that's our familiar pressure and temperature here. And we can see that because it tells me pressure in absolute units of bar, temperature again, they're using degrees Celsius which is very common. when we calculate anything with temperature you're going to use Calvin. But when we look up information on these online calculators you're going to use Celsius. Okay so we know from our problem statement that we have inlet pressure of 69 bar. I'm going to make sure I've got that number and we have an inlet temperature of 538 degrees Celcius. And we're going to hit calculate and it propagates this table for us, so again if we come back and we just confirm. Okay, so 69 bar 538 degrees Celsius and you can see we get everything and anything we want to know about that state. It's like It old you. You define two independent and intensive properties and you get every other property you'd ever want. So we can see there's temper, these are input conditions here. Density, specific volume asked, specific enthalpy, anthropy, exergy, internal energy. You name it, it's all here. Heat capacity, we talked about our constant pressure heat capacity. Constant volume heat capacity. But we wanted to come back with whichever one you want. Either the specific volume or the specific enthalpy here. And we're going to use that in our calculation. We'll use the specific volume, the 0.05 0.052 meters cubed per kilogram. Okay. So, we're going to treat that information as known, we have that. while we're here, because we want to expedite our process, we're going to collect information about the saturation state too. So recall that we had, [INAUDIBLE]. we know that we are a saturated vapor. We're told that in the problem statement. So not often you won't know whether or not you're in the saturation region. An so what you would do is, you could determine that you're in the saturation region through the information you have. So, if you didn't have the quality, and let's say you put in two parameters here that put you in the dome. The calculator would say you're out of the range of this, of the, tables. Okay?. So let's go to the saturation properties, 'cuz we know that's where we are. again, notice that we've know changed the input configuration here. Now we have pressure and quality. And again, you can change those. Those are all, you know? Look at all the different forms you have here. You can do pressure, specific volume, temperature, enthalpy. You have a huge array of choices here. So, we're going to put in the pressure at the exit, which was 10 bar, and we had a quality of 100%, because it was a saturated vapor. And we'll do the calculation and what we want to take back with us is the specific volume at this condition is 0.001 meters cubed per kilogram. And be sure you check those oh, I'm sorry, we wanted this, it took me to the, I read the wrong side. That's the saturated liquid result, we want the saturated vapor result. My bad, my apologies, I read the wrong column. So we take 0.194 meters cubed per kilogram. And again, make sure you get the units, that you're always checking your units, because we can be dangerous when we have these tools. And we just use them as a black box. So, we're going to take that number back with us and we're going to go back to do our calculations for the mass flow rate. Okay, here we are back at our calculations for the mass flow rate. So, we went to the steam tables, our online calculator, and we got that density at State One. So, now we can plug in all the information that we have from the problem statement. We have 64 meters per second times the area, which is going to be Pi over 4 times the diameter at the entrance squared,. So that's 0.45 meters squared divided by the specific volume at the entrance state, which we looked up from our calculator and we found it was 0.0518 meters cubed per kilogram. And, we always include our units. And, we look and we say, "Ooh look, meters squared times meters gives me meters cubed," so those cancel. And, if I crunch through on my calculator the math we come up with a number of 196.5 kilograms per second. That's the mass flow rate of, through the turbine. So couple of things. You always want to step back, look at your number. Does it make sense? That's a lot of mass moving through a steam turbine. And that's pretty realistic. Okay. That's a pretty good number. Again, I wouldn't expect you to necessarily have a feel for that unless you work in turbo machinery. But we'll start developing a feel for what numbers make sense. A hundred and ninety-six kilograms per second. We check to make sure our units make sense, and indeed they do. It's a mass flow rate, so it should be mass units per time. We make sure our sines are correct, and, of course, in this system, there's no sine. You know, we don't, we're not differencing anything, so of course it's positive. Cool. So we understand how to do those types of calculations. So we just did the mass flow rate. That calculation, we went through that whole process. What does the velocity, the speed, of the steam at the exit of the turbine? And do we have enough information to determine that? Well, of course we do. That's why I set it up for you. So what is the exit velocity. So what is the 2. Okay. So we go through the same process that we did before. Well we know that the mass flow rate is given by this expression at the inlet outlet. So, if this is what we're looking for, here, we just solve for we solve for the velocity at the exit, and of course we did this in terms of specific volume. So I'll switch to specific volume here And again, A2 is, is already, we know the diameter. We already went to the steam tables and saturation tables and we got the density at the exit state. And so, we just have to, again, turn the crank. And so, we take our previous number of 196.5 kilograms per second. And we, we have area here so we have pi over four, the diameter at the exit again is larger so that's going to be 3.6 meters squared. We multiply that by the density we found not he table, which was, found on the online calculator. Which was .194 meters cubed per kilogram, and we go through and determine that velocity at the exit is 3.5 meters per second. And again the kilograms here will cancel, meters squared canceled with cube, leaving me again these units. So again the system helps me by saying I checked my units. It confirms that that's correct. We look at the number and say, "Does that look reasonable?" and, again, I don't expect you to have a good feel for speeds of [UNKNOWN] at this point in time. But we'll develop those tools as we go through this class. The other thing that's really useful as you go through these types of exercises. Is for us to look at things like, okay well, the mass flow rate we know is proportional to density. It's also proportional to diameter squared and to speed. So if we wanted to like double the diameter we're going to have a quadratic effect on the mass forwarding. So it's good for us to understand these ratios. For us to understand what happens as we change physical dimensions or as we change thermodynamic properties. So those are the types of things that you should always step back at the end of a problem and don't be satisfied with just the number. Look at what you've learned in this ex-, in the whole process. What have you understood in terms of the general features of the system. Okay. So, we've gone through and we've determined the mass flow rate through the steam turbine. We've looked at the velocity, and we've determined quantitatively the velocity at the exit of the steam turbine. We did this by looking up the information we needed in the steam tables. In this case, the steam online calculator. So that introduced us to that tool at the same time. Now what I want you to do is sketch for me what this process looks like as the steam enters the turbine at state 1. An exit the turbine at state 2. So put that on the PV diagram. I want you to include the dome and label states at the inlet is 1 and the exit at state 2 and that's where we start the next unit. Thank you.
