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.
