6 months ago when I didn't know about my potential...
Summer 2016
Too much party, alcohol and cigars...
At the end of the summer I reach my skinniest shape
It was the perfect moment for a change
Don't forget the cardio..
After long workouts and hard work...
What yesterday was a sacrifice, tomorrow will be an achievement
For more infomation >> 6 months FULL-NATTY BODY TRANSFORMATION // FK fitness - Duration: 6:14.-------------------------------------------
Sugar Man - NERUX - Duration: 3:48.
Sugar man, won't you hurry Cause i´m tired of this scenes
For a blue coin won't you bring back All those colors to my dreams
Silver magic ships you carry Jumpers, coke, sweet Mary Jane
Sugar man met a false friend On a lonely dusty road
Lost my heart when i found it It had turned to dead black coal
Silver magic ships you carry Jumpers, coke, sweet Mary Jane
Sugar man you're the answer That makes my questions disappear
Sugar man cause I'm weary Of those double games l hear
Cause I'm weary Cause i´m tired of this scenes
Sugar man you're the answer That makes my questions disappear
Cause I'm weary Cause i´m tired
Silver magic ships you carry Jumpers, coke, sweet Mary Jane
Sugar man, won't you hurry Cause i´m tired of this scenes
For a blue coin won't you bring back All those colors to my dreams
Silver magic ships you carry Jumpers, coke, sweet Mary Jane
Sugar man you're the answer That makes my questions disappear
Sugar man you're the answer That makes my questions disappear
Silver magic ships you carry Jumpers, coke, sweet Mary Jane
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Ideas Ridículas. Pero es que hay gente inteligente que cree en Dios - Duration: 7:10.
For more infomation >> Ideas Ridículas. Pero es que hay gente inteligente que cree en Dios - Duration: 7:10. -------------------------------------------
Si Tu Novio Te Deja Sola J. Balvin ft. Bad Bunny Letra Video Lyric - Duration: 4:06.
For more infomation >> Si Tu Novio Te Deja Sola J. Balvin ft. Bad Bunny Letra Video Lyric - Duration: 4:06. -------------------------------------------
Where in the hell is the Moon? And what size is it? - Duration: 5:45.
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(Sub. Español) «PENTAGON MAKER» Wooseok le juega bromas a los hyungs | Individual Round | EP3 - Duration: 2:39.
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OPENING RECEPTION FOR MY MOM | vlog - Duration: 10:03.
do you have anything you wanna say about this exhibition?
... what should i say?
you should think about it! lol why are you asking me?!
*speaks english* wait no *switches to korean* lol
i've been drawing clouds for a while now
but this time around i've been drawing them with an abstract expressionism style which has allowed me to evolve my style
why are you talking so formal? this is just for my youtube channel
*tries to act cute*
what were you thinking about while creating these pieces?
while i was drawing these...
mom talk like you're just talking to me lol it's not like this is a real interview
so these paintings were born from anger. not from a family member but someone I know
so because of that anger i used these paintings as way to just let it go
i wanted to let go of that anger and find inner peace
i just held the brush, blended and before i knew it i was done creating these series
since when did you become this ugly??
uh nooo i'm cuteeee *tries to be cute yet again*
i'm so happy
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3 Bad men (1926) - Duration: 1:31:46.
For more infomation >> 3 Bad men (1926) - Duration: 1:31:46. -------------------------------------------
Ghost in the Shell
For more infomation >> Ghost in the Shell-------------------------------------------
KHUDA FARMAYA, khuda farmaya mehbooba, Rab frmaya, Rab farmaya mehbooba, malik ameen - Duration: 5:39.
bigray sary kam bnanda
ban k jogan madinay no jawan gi
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Bulova Men's 97B110 Longwood Quartz Rose Gold Case Brown Leather Strap Watch - Duration: 1:21.
For more info and purchase click on the link down
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Where in the hell is the Moon? And what size is it? - Duration: 5:45. For more infomation >> Where in the hell is the Moon? And what size is it? - Duration: 5:45. -------------------------------------------
Ghost in the Shell For more infomation >> Ghost in the Shell-------------------------------------------
Heat Transfer: Internal Flow Convection, Part I (22 of 25) - Duration: 1:00:00.
Okay. We wrapped up chapter seven last time. That was convection heat transfer outside
of tubes or flat plates, called external flow. This is chapter eight we start today, convection
heat transfer. How do we handle internal flows? All right. Let's look, first of all, I'll
go back and put on chapter seven. Just a quick look at that. So chapter seven had flow over
flat plate, maybe laminar and turbulent called [inaudible] flow maybe. We measured x in that
direction, then we had flow over as cylinder. This was u infinite. Flow over cylinder. The
flow approached the cylinder with a velocity u infinity. And this was a tube of diameter
d. These were external flow. This was chapter seven. This was a tube, flow over a tube,
normal to the axis. This is flow chapter eight inside of a tube. So now we kind of shift
gears. Chapter seven we had flow over the outside of a tube. Chapter eight, we have
flow on the inside of a tube. Same thing with chapter seven. Before you do the heat transfer,
you have to understand a lot of the fluid mechanics, okay? There is some magic Reynolds
number. This is 500,000. The transition from laminar to turbulent, 5 times 10 to the 5th,
500,000. This Reynolds number was based on the distance, x, u infinity x over new. This
Reynolds number was based on the tube diameter. If we have flow inside of a tube, revisiting
me311, we have the Reynolds number. u m times the diameter over new. u m is called the mean
fluid velocity. Of course, in the real world, this d and that d are not the dame thing.
This is the outside diameter of a tube, and that's the inside diameter of the tube. But
we won't worry about that now. As long as you know that chapter eight, it's the id.
Chapter seven, it's the od of a tube. If somebody says the mean velocity -- if somebody says
the velocity of the fluid in that tube is 10 feet per second, and let's say it's laminar
flow. There's the velocity profile. It's parabolic for laminar flow in a tube. And if somebody
says that velocity in the tube is 10 feet per second, well, they sure don't mean the
center line velocity is 10 feet per second. They don't mean the velocity at the tube's
surface is 10 feet per second, zero, no slip condition. What do they mean? They mean that
this would be 10 right there. So, that's the mean fluid velocity. Do you just average it,
10 + 0 divided by whatever, 2? No. No. For instance, if this velocity on the center line
-- If that center velocity is 12 feet per second,
is the mean fluid velocity 12 divided by 2? Uh-huh. No, no. Uh-huh. No, because the cross-section
looks like a circle, and there's a lot more area out here than there is in the middle.
So, it's called a weighted average. It's a weighted average. You just don't take the
center line velocity. It's not like this. Now, I'm not going to draw it, okay? Go back
to math. What's the average value of y, from 0 to 2? Oh, it's 5. 10 divided by 2. It's
5. I guarantee it's 5. No, it won't work here. Won't work here. This is not a linear profile
and it's not a one-dimensional profile. Okay, so anyway, that's what the word mean is. That's
why they don't use the word average. Sometimes, that confuses people. They think average,
oh, take this, divide it by that and that's the average. Half of that value. No, that's
not the average. And you did that in me311 so I'm not going to revisit that. Okay. Anyway,
so here's what happens. We assume we've got the tube. There is an approaching fluid stream
whose velocity is u m, the subscript i means inlet. So, i means inlet, m means mean. So,
this is the mean velocity at the inlet. When it hits the tube at x = 0, a boundary layer
starts to build up around the perimeter of the tube, a boundary layer. That boundary
layer develops from all around the perimeter. All around the perimeter it develops. When
the boundary layers meet at the center line, that's a special region called the entrance
region. That's where the entrance region ends, and that distance is x fully developed. x
f v is the fully developed distance. Let's just assume it's laminar. Let's talk about
-- In a tube, me311, if the mineral's number is less than 2300, we're going to assume it's
laminar flow. Different textbooks sometimes use different numbers. One textbook uses 2100.
Our textbook uses 2300. There's no one universally accepted value. So, our book uses 2300, so
for this class we'll use 2300. If it's greater than that, of course, it's turbulent. Okay,
so for right now we'll just assume laminar flow, make it easy on ourselves. If it's laminar
flow in a tube, we know from fluid mechanics that the velocity profile is parabolic. Parabolic.
Fully developed means if I go down a ways and look at it again, it's the same shaped
parabola. It didn't change. This is the velocity u as a function of r. The profiles don't change.
That's why that's called the fully developed region. Okay. The distance it takes to become
fully developed. For laminar flow, 0.05 Reynolds d. If it's turbulent flow --
The book says, "We're going to use 10." It's typically accepted between somewhere from
10 to 60, that that's how you'd fine x fully developed. Our textbook says, to be conservative,
"We'll say 10." Okay, so that's the two equations you use to find this distance, x f d. So,
how do you find x f d? Okay, fluid mechanics. There they are. Now --
Let's say the Reynolds number is 2000. So, I'll say it's laminar flow. x fully developed
equal the 0.05 times the diameter times the Reynolds number based on d. Let's see what
I assumed here for a diameter. Okay, I said -- let's let it be a 1-inch diameter too.
If d is 1 inch then x fully developed, from this equation right here, x fully developed
is 100 inches, which is on the order of 8 feet. So, here's 1 inch from there to there.
That's a little more than 1 inch. Okay. There's a 1 inch tube. And those boundary layers build
up from the entrances over there. Where do these two dash lines meet the center line
of the 1-inch tube? Oh, boy. 3, 6, 7, 8. Right here. So, it would take that flow this long,
a distance, before finally the boundary layers meet at the center line of the tube. Oh, it's
a long, long way. A long, long way. Should we engineers be worried about what happens
in the entrance region of a tube? Oh, you better, because, you know, a 1-inch tube with
a Reynolds number of 2000 has to be 8 foot long before you get out of the entrance region.
Before you get out of the entrance region and into the fully developed region. So, oh
yeah. Take turbulent flow. Take a Reynolds number based on d. I think I took 20,000.
2 times 10 to the 4th. x is x fully developed. d times 10. What's d 1-inch? A 1-inch tube.
10 inches. Wow. Wow. For turbulent flow, those profiles developed very fast and meet at the
center line very short distance. 10 inches. Compared to laminar flow, 100 inches long?
Oh, yeah. Oh, yeah. It's a big difference in laminar and turbulent flow. Where do you
worry about that? Oh, I'll just give you one idea. Your automotive radiator. Is there tubes
in that thing? Oh, of course there is. They're vertical. What do they carry? Hot water. How
do you cool them? Blow air over them with fins. Is the flow in those tubes laminar or
turbulent? Oh, I suspect it's turbulent. You know, it's hard to get laminar flow in anything.
I've got a real good intuitive guess, an engineering intuitive guess. It's turbulent. Okay. What's
those diameters of those tubes? I don't know. Maybe that big. Maybe a quarter-inch, three-eighths
of an inch. I don't know. 10 times a quarter-inch, 2-and-a-half inches. Oh, they develop pretty
quick, don't they? The flow that comes in the tubes in the radiator developed pretty
quick, I think. They're fully developed. Because you might have 12 inches or 14 inches of the
radiator [inaudible] and they develop in 2 and 2-and-a-half inches maybe. So, anyway,
that's the kind of decisions you've got to make to see what's going on in your automotive
radiator or your trans oil cooler or your oil cooler. How quick does the -- do the boundary
layers build up to where you have fully developed flow? Or is most of your tube in the entrance
region? If this is laminar flow and my tube is 2 feet long, chop it off here, it's all
in the entrance region. It's all at the entrance region. There is no fully developed for a
tube that long. 1-inch tube, 2 feet in length? No. It's all in laminar flow. It's all going
to be in the developing region. So, that's why it's important to know what's going on
in these regions. This is a fluid mechanic's case. Now, we do the temperature. Same kind
of picture. Here's the tube, diameter, d. Okay. But now we're looking at the thermal
situation which is, what's approaching the fluid -- the tube? The fluid is at a temperature
t mean n. Let's go back to chapter seven one more time. What's approaching the flat plate?
u infinity. What's coming into the tube? Don't say u infinity. There's no such thing as a
freestream temperature in a tube. u m i. Flat plate, external flow over a tube. What's the
approaching temperature? t infinity, the freestream temperature. There is no freestream temperature
in a tube. We call it the inlet temperature of the tube, yeah, t m i, inlet temperature
of the tube. When, at profile, it hits the tube, a boundary layer starts to develop,
a temperature boundary layer. And eventually that boundary layer meets at the center line.
The distance from the tube entrance to the center line is called x fully developed. Sometimes
they put t on there for temperature. If there's no subscript, they mean velocity. And this
is the entrance region. And this is the fully developed region. Okay. Now, there's different
conditions with the temperature. Let's draw a profile here where the tube surface temperature
is constant. This is t s, tube surface temperature. And we'll call that constant. Let's say the
fluid that comes in is cooler, a colder fluid. You're heating the fluid. So, here's the temperature
profile. Looks like that. You go down a ways. The tube suface temperatures are constant.
Constant. Constant. Go down a ways. Constant, constant, constant. t s here. t s here. Constant,
constant, constant. The fluid in the tube starts to get hotter. You're heating it. Comes
in cold. Tube surface temperature hot. You're heating the fluid. This is how it looks. Go
down a ways further. This is how it looks. Well, you can see how it's changing. It's
getting flatter and flatter across the middle. All of the fluid in there is approaching the
tube surface temperature, t s. All the fluid temperature is approaching t s, if you go
down far enough. That's the fully developed region for temperature. Here's the fully developed
region for velocity. Okay. Okay, here we go again. How do we find this x fully developed
temperature? Okay. x fully developed temperature for laminar flow. For turbulent flow. Same
as velocity, 10 diameters. Turbulent flow is so mixed up that it doesn't change between
these two pictures. But laminar flow, or but the x fully developed laminar flow does vary.
All you do is you tag on a Prandtl number after the Reynolds number here. We did that
in chapter seven. A lot of our equations in chapter seven had the Prandtl number tagged
on to the right-hand side of the equation. It's characteristic of thermal analysis. Okay.
Let's box these guys in. All right. So, now we have that. There's several objectives of
looking at a tube like this. Number one is you'd like to find the temperature at any
distance along the tube, obviously. Find the temperature of the fluid anywhere down the
tube. Number two, you want to find the heat transfer. Yeah, uh-huh. That's heat transfer.
I mean, 415, find the heat transfer. And you probably want to find h, because h is important.
Convection heat transfer coefficient. So, probably three things you want to look at.
How do I find the temperature as a function of x? Okay. How do I find the heat that's
been transferred to the fluid from the tube? And then how do I find the convection coefficient
h? Okay. All right. Now, this is constant tube surface temperature. I'm going to start
over here now. There's different kinds of boundary conditions on the tube surface. Number
one is you can have constant tube surface temperature. Number two is you can have constant
surface heat flux. So, this'll be constant surface heat flux. q s double prime. Double
prime means watts per square meter. s means on the surface. Okay, so in this particular
tube case -- You have a constant q s double prime. In that
case, you have a constant surface temperature. So, that picture I'll put over here. Looks
like this. No matter what the x-value is, it's the same surface temperature. This is
-- these are the two cases that our textbook looks at. There are other cases, more complicated
cases and so on and so forth. These are the two simplest cases. These are the two cases
we focus on in chapter eight. Do they occur in the real world? Yeah. They're out there.
Let's take one at a time. Let's take the constant surface heat flux. Constant surface heat flux,
this is a tube carrying water, for instance. I take a little electric heating sheet. You
can buy them. They have little resistance wires in them, back and forth, like your toaster
inside. Plus and minus. Plug into the wall. The thing heats up. It puts out so many watts
per square inch, square centimeter. I take this little blanket, I wrap it around the
tube, and now I've got constant surface heat flux. That's one way. Okay. It's not quite
the same, but in a boiler, you have these tubes carrying water and they're vertical
on the walls. And the wall is adiabatic. It's insulated. And the tubes go up the wall, hundreds
of tubes. There's a big flame out here. You're burning natural gas. That natural gas provides
a flame. It's radiation and part convection, but it's so many watts per square meter. Well,
that radiation hits those tubes, but just the front side in a case like that. So it's
a modification of that. But that's how you get constant surface heat flux. You know,
you've got a solar collector, a parabolic trough, and the idea is, here comes a solar
radiation. It hits here and it hits here and it hits here. Well, look at that. You're approaching
this, you're approaching that. So, yeah, it does occur in the real world. Okay, so this
guy over here. Where does this one occur? Well, this is in the condenser of the power
plant. This was the boiler I told you, partially modeled that way. But now this is a condenser.
You've got tubes in the condenser. That's the Redondo Beach Power Plant. Carrying Pacific
Ocean cold water in these tubes, and then into this condenser comes the exhaust team
from the turban. And that steam, hot steam, sees the cold tubes. It condenses on the cold
tubes. At what temperature? The saturation temperature at the pressure in the condenser.
Okay. Every drop of steam that condenses, no matter where it condenses on that tube,
condenses at what temperature? The saturation temperature at the pressure in the condenser.
Right. Every one of these drops has the same temperature, so that's a good approximation
for our t s equal constant. So that's just two example of how these guys work. Okay.
All right. Back to here. We want to ask the question first, how much energy crosses that
line? So, that location, x, how much energy crosses that line? Okay, so to do that, we're
going to go back to thermo, and that's equal to the integral over the cross-sectional area
of the tube, row u c sub p t d a. Here's where it came from. We know from thermo that energy
being transported is m dot c sub p t. The c sub p sometimes stands for the [inaudible]
p, c sub p t. What's the mass flow rate? The mass flow rate is row a v. What's the velocity?
u, there's the density, row. Where's the area? There it is, d a. So, this guy, this guy,
and this guy all are m dot row a v. That's the energy crossing the dash line. All right.
We defined this as m dot c sub p t mean. This defines t mean. So, this equation defines
t mean. So, if you want to find the mean temperature of the fluid, what you do is you solve this
guy. t mean -- So. If somebody says, "What's the mean fluid temperature?" That's the official
integral way of finding the mean fluid temperature. But you've got to know how t varies with r,
you've got to know how u varies with r. It's not easy. Both u and t vary with r. And what's
d a? d a is 2 pi r d r. The little donut shaped area. 2 pi r d r is the differential area
d a. Okay, so -- and we did that in me311 for u, the average velocity, the mean velocity
in a tube. It's very similar. Okay. This t m, why is t m important? Well, this t m is
used in r q h a t s minus t m. So, that's Newton's law of cooling chapter one for a
tube. Chapter one. What's the right temperatures to use? The surface temperature. The surface
temperature over here, r over here. Doesn't matter. The surface temperature minus the
mean fluid temperature. Okay. Now, to see how that temperature varies, we take a little
differential control volume. The distance is d x. Take a little differential control
volume and run an energy balance on the little differential control volume. For this guy,
what does the energy balance says? Energy balance says all of the energy that comes
into the fluid goes into raising this temperature. Okay. What energy comes into the fluid? Oh,
there's a constant surface heat source. There it is right there. That's what comes in. q
s double prime. That comes in multiplied by the area. Okay. And what does it do? It goes
into raising the temperature of the fluid, okay? So, that's our m dot c sub p d t m.
All the energy that comes from the heat source goes into raising the temperature of the fluid,
okay? What's d a? All right, b a, don't forget. This is the -- d a is that lined area. It's
a circle. Perimeter, pi times d. Perimeter times d x, perimeter times d x. So, d a is
p d x. Separate the variables, d t m d x. So, this is q s double prime times the perimeter
divided by m dot c sub p. The right-hand side is a constant, okay? So, integrate this guy
to get t m as a function of x.
And use the boundary condition when x equals 0, t mean equal t mean i. Notice that that
looks like a linear variation. So, if I want to plot that, here's 0. Here's x and I'll
just say, this is the length of the plate, l, and this is the temperature of the fluid,
t mean. It comes in at t mean m. It's linear with x. It's a straight line. So, here's t
mean as a function of x. Now, we're not going to prove this now, but I'll just show you
where the surface temperature goes. If this is x fully developed for temperature -- Then
the surface temperature looks like this. And the distance between these, or these two lines
have the same slope. They have the same slope, okay? But we're interested in the fluid temperature.
So, there's no equation for t s. You won't have an equation for t s. Just, I'm just showing
you graphically what happens. Okay. Now, I think that's -- well, yeah, okay. Let's get
q. How do we find q? Okay, q. The heat transfer to the fluid, m dot c sub p t m out minus
t m in. So, for the constant wall surface heat flux, we have two important equations.
One gives you the temperature at any x value for that tube. The other equation gives you
how much heat has been transferred to the fluid. Okay. Now, second case. t s equal to
constant, okay? We can do it somewhat the same way. Here's our little differential fluid
element. The distance is d x. We run an energy balance on that little fluid element. Okay,
here, right here. What comes into the fluid? Okay. It's not a constant surface heat flux.
It's now a constant surface temperature. So, it's convection. So what comes in is convection,
h. Okay. Times the differential area times t s minus t mean. Differential area is perimeter
times d x. This is convection in. And what does that energy do? It goes into increasing
the temperature of the fluid, which is what? m dot c sub p d t r t m. d t m. And now, what
you can do is you change variables, because that's t m and that's t s minus t m. So you
change variables and you go ahead and solve this guy. It's going to be -- you're going
to have d t m d x. You're going to solve that, okay? And you end up getting this equation.
You want to get these two guys to be the same, so you let t s minus t m equal delta t. So,
that's a delta t there. I'll show you. h p delta t d x equal minus m dot c sub p d delta
t. d t m equal d delta t. Take the differential of both sides. Don't forget that the surface
temperature's constant. The differential is zero. Minus d t m equal d delta t. You want
to separate these guys, d delta t over delta t is equal to minus sign h p over m dot c
sub p d x. That's all the gory details. Go ahead and integrate both sides. Integrate
d x over x. What do you get? Natural log. Take the inverse of natural log. What do you
get? Exponential function. There's where it came from, okay? What'd we do? All we did
was change the variable to make the differential equation look neater and cleaner there. Okay.
Now, let's look at that, all right? Now, we're going to get q. r q. Let's draw the graph,
first of all. This is the mean temperature of the fluid. This is x. The tube is l long.
There's l. Here's zero. The stuff comes in at t mean n. The tube surface is kept constant
at t s, it's kept constant. The fluid temperature increases exponentially. Exponential increase.
Don't forget constant tube heat flux linear variation of temperature. This one, exponential.
Here is the surface temperature of the tube. The stuff that comes in is cold, for instance.
It heats up. If it's long enough, if the tube's long enough, eventually the fluid in the tube
will get to the same temperature as the tube's surface. If it's not that long, stop right
here. It comes out at that temperature. That's t mean out. There's t mean out. Over here,
here is t mean out. Okay. Pretty different. I mean, one is linear. Other one's exponential.
This is like the tube surface temperature. It's constant. This is like I said, condenser.
Do you have to worry about anything too much here? No. The hottest the fluid can get is
the tube surface temperature. The hottest the fluid can get is the tube surface temperature.
Over here, oh you better be careful. This could be a boiler, and maybe there'd be a
tremendous boiler explosion because something bad happened. What can be bad? Well, maybe
you're changing, as this increases, maybe you reach a point where the liquid water suddenly
vaporizes and turns into super used steam and gets so hot you have a boiler rupture.
Explosion. And also maybe the tube surface gets so hot the material fails. Tube rupture.
Because these guys, I'll tell you, these guys never do stop. They don't approach anything
asymptotically. They don't stop. Okay, you better be aware then. This guy could be danger.
But, of course, you do want to, in a boiler, you do want to get superheated. You know,
so it's good to a point, but you've got to be careful. That tube service temperature
gets too hot and things could fail. The tube could break open, rupture. Okay. So, again,
different things going on here. Now, let's take a look at how we get q over here. q equal
h a delta t. t s minus t t mean. t surface is hot, t means cold. Okay. If I want to get
my little d q right here. Okay. d q in that little differential area is equal to h t s
minus t m times my differential area. And my differential area there is circumference,
pi d times the length, x. So, d a is pi d x. Do you think this guy, when I integrate
both sides now, you think I can pull him outside the integral side? Uh-uh. Over here, in the
fully developed region, could I pull out the t s minus t mean fluid? Yeah, because that
is the same, no matter what x you're at, that is the same amount, t s minus t m. It can
come outside the integral sign. Here it can't do it. Can't do it. So, what do you have to
do? See that t s right there minus t m? See that t s minus t m? Yeah, that's what you've
got to do. You put this guy into here and you carry it out all the gory details of integration.
And when you integrate the exponential function, natural log. Natural log. So, what comes out
is going to be a natural log. Here's what it amounts to. q equal h bar the average h,
surface area of the tube a s times delta t with the subscript lowercase l m, where delta
t lowercase l m equal this. Delta t out minus delta t in divided by -- there's a natural
log now, when you integrated. Natural log, delta t out over delta t in. That is called
the log rhythmic mean temperature difference, or just the log mean temperature difference.
It comes out of the integration. Okay, that's where it came from. And where do you put it?
You put it down here in the equation to get q.
What's delta t? The o stands for outlet, the i stands for inlet. What's delta t inlet?
Okay, it's right here. That's delta t inlet. And where's outlet? That's from here to here.
That's delta t outlet. There's how you find those two guys. All the stuff leads into heat
exchanger analysis too. It's like a heat exchanger. Obviously, a boiler or a condenser. Okay.
It's more complicated than this guy, constant surface heat flux. There's this guy, m [inaudible]
delta t. Of course, if you want to, you could also say q equal m dot c sub p t mean out
minus t mean in. Because that equation works for all these guys. It's here. It's here.
Thermo, m dot delta h n [inaudible] p m dot c sub p delta t. So, now we've got three main
[inaudible] equations. Let's look at them. For constant surface heat flux, how do you
find the temperature anywhere on the tube? Here it is. How do you find the heat transfer
that's occurred or the heat added to the liquid, the fluid? Here it is. Constant tube surface
temperature. How do you find the temperature at any x value? Here it is. How do you find
the heat transfer? Either this equation or this equation. Over here, I'm going to find
the temperature at the end of the tube, x equal l, and the heat transfer from 0 to l.
Do I need to know the convection coefficient? Look for h. No. Look for h. No. I don't need
h. Constant tube surface temperature. I want to find the temperature at the end of the
tube. Look for h. Oh, yeah. The heat transfer. Look for h. Oh, yeah. You get the difference.
You get the difference. You've got to find the h to find this temperature here. You don't
need h to find q because you've got a choice. Okay. So just be aware of that. We're going
to find h no matter what. We'll find h for both cases next time, but for right now, just
so you know, you don't need h for this guy to find q and t. Over here, you do need h
to find this guy for the temperature. Okay, now, we're -- I'm going to go over homework,
so we're going to pick this up next time and we're going to find the h's next time. So,
this is pretty much where we are in chapter eight right now, okay? So, let's shift gears
and go to homework. If you came in late and didn't pick up your homework, it's up here
in front. Okay, and we turned homework in today too. Number 12. All right. Just so you
know, let's see, I guess I looked at -- I graded 612. Let me see what I've got here.
Yeah, 612. They gave a picture -- no. Okay. Yeah. Let me just read it again here. Oh,
yeah. There it is. Okay. All right. They gave a temperature profile, so let's look at 612.
All right. This is a flat plate -- yeah. Flat plate flow, like this. And we have the approaching
fluid stream, and we have 30 degrees. Okay. t -- oh, t s. t infinity is 30, t s is 90.
So t s is 90. t infinity is 30. Okay. He tells us that the temperature in the boundary layer
t is 20 plus 70. e to the minus 600 x y. Okay. So, temperature is a function of x and y.
We're measuring x from here. We're measuring y from here. Okay, I think that's okay. I'll
just read it. It says, "Obstacles are placed in the flow, which intensifies the mixing
with increased distance [inaudible] from the leading edge." Somehow, he put something on
that plate which causes more mixing. I don't know what they are. Little bumps on it or
something. So, the further down you go, the more mixing occurs. So, he's artificially
done something to the surface. Okay. Determine and plot the manner in which the local convection
coefficient h varies with x. Then evaluate the average coefficient over the whole plate.
Okay. So, find h x. Now, you can go through all that again if you want, but the equation
in the textbook -- oh, well, look at it here. Equation 6 5. He says that h x equal minus
k partial t with respect to y and y equals 0 divided by t s minus t infinity. Yeah. Okay,
that's part A done. I think we have to find this guy. So, there's this guy. Partial of
t with respect to y. Constant zero. 70 minus 600 times x times 70. e to the minus 600 x
y. Now, to assess. Partial t with respect to y at y equals zero. 600 times 70 times
x times e to the minus 600 x y, but this says where y equals 0. y equals 0. e to the 0 is
1, so d t d y at y equals 0 is equal to 42 times, three 0s, time x. Okay. What I'm saying
is, don't get sloppy in your math. It comes back and bites you. I saw a lot of people
that said d t d y is 42,000 x. Oh, no, it's not. d t d y is this whole long thing. This
thing says once you get d t d y, but get d t d y first, then once you've done that, then
you put y equal to 0. You can take shortcuts, but you better be careful, because d t d y
is not 42,000 x. Okay, not I plot it. h x versus x, 0. Here it is right here. We start
x equals 0. It's 0. Oh, and by the way, where'd that minus sign go? Well, you know, I didn't
do it right. Now it's right. Okay. Minus times minus. That's plus. There it is. Now he says
this plate is 5 meters long. So, 42,000 times 5. Let's see what we've got here. 5 meters
long. Yeah. Okay. h bar. The easy way to do it -- that's why I had you plot it. Once you
plot this guy, once you plot this guy, then here's 5 meters, where's the average value?
And 2-and-a-half. If you want to do it the harder way, then you have h bar equal 1 over
l, integral 0 to l, h x d x. Go ahead and put this guy right here, this d t d y times
k, okay? Put this h x in here. This guy goes up here by the way. Okay, put that h x in
here and integrate it. You can do that. You get the right answer. But what I'm just saying
is, because you know it's linear, linear with x, this is an x up here, it's linear with
x, that -- just take the middle value. Make life easy for yourself on a timed exam situation.
Don't integrate if you don't have to. That'll waste time and increase the chance for a mistake.
Okay. But it only works if it's a linear function. Okay, so just a little long story, but that's
what I was looking for in that problem. All right, we'll stop for today, then pick it
up on --
-------------------------------------------
Heat Transfer: Convection Over Cylinders, Part I (20 of 25) - Duration: 52:15.
Okay. As I had mentioned before, this is the radiation heat transfer numerical problem
out of Chapter 13. It's a rectangular box. The dimensions are given. I've identified
the front surface as A3, the top as A2, the right hand side's A5, and the other surfaces
are defined there on the sheet. Give you the emissivities of all six surfaces, give you
the temperature of five surfaces and surface six is reradiating, and I've calculated the
F's for you for three different ones, F12, F13, F15. Okay. So here's what you do. The
first thing you do is verify those three F values I gave you by getting whatever you
need, X over Y, X over Z, go to graph number so and so, and show me that that number is
correct. Okay. So verify those three F values. Okay. Then, we start with the A, B, C answers.
There are five unknown J values. Okay. It says -- it says write an equation for each
of the nodes for which J is unknown. There are five nodes where J is unknown. Down below,
it says, hint, for part A, use equations 13-21 and 13-22 of the textbook. Equation -- we
had both those equations in our -- in our notes. Okay. 13-21 is the equation you -- you
use where the temperature of the node is known. Equation 13-22 is the nodal equation where
the heat flux is known at the node. So depending what's given, if the temperature node's given,
use equation 13-21. If the heat flux in the node's given, use equation 13-22. So write
those equations out. There'll be, in terms of J1 through J5, the unknowns of those five
equations will be J1 through J5. Solve those by whatever means you want -- what you did
last time for the first one maybe, maybe MatLab, maybe Excel. It's going to be pretty simple,
divide by five matrix. TI89, TI92, whatever it might be. Put on the -- on your -- on your
homework what you used to solve those equations. If you use Excel or MatLab, give me a hard
copy printout of the results -- attach it to the back of this. So give me a -- a hard
copy printout of that. Solve for the five unknown J's, then put the J's in for the equations
to get what part C to get Q4, Q35, and the temperature of the adiabatic surface, surface
six, the temperature of the adiabatic surface. Okay. So that is then due a week from today.
Any questions on that right now? Okay. Now, let's go ahead and take a look at where we
left off last time. We're in Chapter 7. Okay. Last time, we were looking at how we get H
for a flat plate. So the flat plate like this -- it might be part laminar, it might be part
turbulent. There's a critical X value where transition may occur. The Reynolds Number
for that critical transition is 500 thousand -- five times ten to the fifth. That's external
flow over the simplest possible geometry, which is a flat plate. Now we take the next
most popular geometry. Obviously, we engineers use a lot of tubes and pipes. So now we want
to know, how do we find the H value over pipes and tubes? What it amounts to is a circular
cylinder. So this is a circular cylinder. Okay. Its dimension into the blackboard is
L, so it's like a pipe -- a pipe of length L. The diameter of the pipe -- the outside
diameter is capital D, outside diameter. Now we have to go back and revisit ME312 a little
bit. Not much, just a little bit. In ME312, we analyzed the flow over a right circular
cylinder from a fluid mechanic's point of view. Here's what we kind of said. Approaching
flow stream, free stream velocity U infinity. The streamline here, the dash line ends up
at this big black dot. That's called the stagnation point at the front of the cylinder. Stagnation
point means that the velocity there is zero. Okay. Then, of course, the flow goes around
the cylinder like this. It speeds up as it goes around the cylinder. Because the velocity
is zero at the leading edge or the -- the frontal point on the cylinder, a boundary
layer builds up -- a laminar boundary layer builds up. So we have a laminar boundary layer
build up around the cylinder. It gets bigger and bigger and bigger. Eventually, it's -- what
happens is -- we call it the separation point -- it separates from the cylinder and goes
off like that. So these are the flow streamlines. And again, this is our boundary layer, it's
a laminar boundary layer. On the backside of the cylinder, it breaks off and goes like
this, and behind the cylinder is a region called the wake region. Turbulent eddies form
in the wake region like little circular patterns of velocity. You can get a really good view
of that if you go to a stream -- a fast moving stream and there's a rock in the middle of
the stream about the size of a watermelon or something. And -- and -- and the water
goes around that rock, on the backside of that rock, there'll be little circular eddies
and there'll be leaves and bugs floating back there in circles. Boy they're just going in
circles behind there. Yeah, that's the wake region behind a rock in a stream. But it happens
whether it's air or water or whatever. There's a wake region typically behind -- behind here.
It depends on the Reynolds number. If the Reynolds number is really low, okay, then
the -- this point, by the way, is called the separation point. It's where the streamline
separates. It's caused by a pressure gradient. But that was -- that was ME312, we're not
going to revisit that in detail. What happens at -- at this particular case -- low Reynolds
number, the separation point is way back on the backside of the cylinder. As the Reynolds
number increases, the separation point moves towards the front side of the cylinder, eventually
ending up about here. At that point -- at that Reynolds number, something dramatic happens
-- the flow transists to turbulent. There's a turbulent part. It's laminar for part of
the way and then it goes turbulent at -- like this, so the dash line is the turbulent part.
Just like over here, it starts out laminar and at a certain Reynolds number, it transists
to a turbulent boundary layer. The same thing around a circular cylinder. It starts off
as a laminar boundary layer. As the Reynolds number gets higher, eventually, the boundary
layer -- this is the laminar boundary layer, this is the turbulent boundary layer, and
then the separation point goes back to the backside because of momentum consideration.
The fluid particles close to the surface, when the flow goes turbulent, pick up momentum.
The momentum causes them to continue following the surface until, again, the pressure difference
builds up and they fly off. All right. That's the fluid mechanics case. But again, you can't
do the heat transfer part until you understand the fluid mechanics part. Okay. So now our
object, though, is to get H in ME415 because we want to find the heat transfer Q. And Q
is equal to H bar AS TS minus T infinity, assuming the surface is hot and the free stream
is cold. So the temperature of the surface, we call that TS. It's the same all the way
around the cylinder. TS is constant all around the cylinder. Okay. So obviously, let -- let
-- let's give -- let's give AS first. What -- what is AS? AS is the surface area. What
is AS? It's the area of the circular cylinder that is in contact with the fluid. Okay. Pi
DL, pi DL, circumference times length, pi DL. Okay. Obviously, ME415, we got to find
that guy. That's what Chapter 7's all about. Over here. What's the challenge? We got to
find these two guys. Need those two guys. Local heat flux or the heat transfer over
the surface. Okay. Over there, a lot of it was mathematical by nature. Over here, not
-- not much mathematical by nature. The way that you get this guy here is typically by
evolving what we call empirical equations. They call them empirical correlations. That
means they're derived from experimental observations. Derived from experimental observations. And
the first one we have is an -- let's call it one. By the way, the bar over H means it's
the average value. The average over what? Well, the answer is the average over the cylinder
surface. In reality, H varies from the front -- theta equals zero, theta equal 45, theta's
90 -- from the front to the back of the cylinder, H will vary. So the bar means averaged overall
angles theta. Okay. So Nusselt D bar C Reynolds DM Prandtl to the one-third. That's the empirical
correlation. Let's put these guys down. Reynolds number based on diameter D, U infinity, D
over new, Nusselt based on D, that's the bar, H bar D over K. So now, we base the Reynolds
and the Nusselt on the outside diameter, D, capital D. Flat plate, we base the Reynolds
and Nusselt on the distance X, the distance from the leading edge of the plate. Okay.
This is called the Hilpert equation. Just so we know -- Let's see, have we got it here?
I don't have the equation number down right now. But it's the first equation you come
to in that part of Chapter 7. Properties at T film, which is T surface plus T infinity,
divide by 2. The values of C and M are constants. And the values are given in Table 7-2. And
Table 7-2 looks something like this. I'll just put one down there. Let's see where Table
7-2 is here. There it is. I'll do 4000 to 40,000. There's different ranges here -- 4,000
to 40,000. I'll put another one down. One of them goes from 40 to 4000. That value,
4000 to 40,000 -- yeah -- .193 and .618. 618. Okay. So that's what you do. Again, here's
the Nusselt number, there's the H bar you want, you solve for the Nusselt number, get
the -- number one -- get the Reynolds number. Is there any magic Reynolds number? No. Over
here, a flat plate. Is there a magic Reynolds number? Yeah. Five times ten to the fifth.
Over here? No. It might be a laminar boundary layer, it might be a combination of laminar
turbulent boundary layer, but there's no magic Reynolds number that you have to always focus
on. So -- put the Reynolds number here. Get all the properties -- what properties? The
Prandtl number, kinematic viscosity, thermal conductivity, at what temperature? The film
temperature -- TF, film temperature. The boundary layer is considered to be a film, or a layer
of fluid, the film temperature. Okay. These guys came from where? Experimental observations.
Okay. There's another possible equation to use. This is two. This one is Nusselt number.
It looks very similar. Reynolds D to the M, but now there's a Prandtl to the nth power
and then a ratio Prandtl number to the one-fourth. Okay. If the Prandtl number greater than or
equal to ten -- greater than ten, N is .36. If Prandtl less than or equal to ten -- that
should be a ten -- then N is .37. Properties at T infinity, except Prandtl S at T surface.
C and M are in Table 7-4 and it's called the Zukauskas equation. Then, the Churchill equation.
Our -- our -- our textbook gives three different equations to find H bar. Most books give you
one. But our -- our textbook -- our author is really complete, so he gives you three
possibilities. This equation -- I'll just put a few things down. Properties at T film,
no table needed. Which is the good part of it, you don't need a table. In all these guys,
you've got to satisfy some Prandtl number restrictions. So you check the restrictions.
The Prandtl number might -- should be greater than something or the Reynolds number should
be greater than something, so you check the restrictions. On this guy right here, there
are no important restrictions. I think the Prandtl greater than .6 is the only one. So
-- but you -- you always check -- always check and see if there are restrictions on these
equations. How did someone get these equations? Because sometimes it's like magic, like, okay.
I'll use it, but I really don't know where it came from. I'm just a user. I -- I don't
worry about where it came from. But some people worry about where it comes from. Like, how'd
that guy get that table right there? Okay. Well, here's one way that -- that -- that
you can do that. If you -- I'm going to -- I'll tell you. It's example 7-3 -- example 7-3.
There's a wind tunnel, and they put in the wind tunnel a circular cylinder. Diameter
of that cylinder is D, it's length is L, into the blackboard -- sticks out blackboard -- L,
and the wind tunnel creates a nice even flow like this. Several years ago, I had a student
in class and after class was over, she came by my office and said, Professor Biddle, I'm
doing a senior -- I'm having a senior project. I was looking at that example 7-3 in the textbook,
she said, and is it possible I can do my senior project based on that example? And I said,
well, yeah. I think you can try. Yeah. Go ahead and give it a try. So what she did -- we
-- we have a small wind tunnel in the fluids lab. It's really belongs to technology department,
but we -- we use -- at -- at that time, we used it. And it was only about, I think, 12
inches this way -- out of the blackboard this way, 12 inches, and maybe this way 10 inches.
And so she was going to use that wind tunnel. And she got a aluminum cylinder, and I think
it was like, it was 12 inches long. Must have been -- yeah, four inches in diameter. Twelve
inches long -- piece of aluminum -- four inches in diameter, solid aluminum. Okay. She drilled
a hole through the aluminum -- axial hole -- through the aluminum, and then she stuck
this cartridge heater -- electric cartridge heater inside of the hole and made a really
tight fit and put some special heater transfer enhancer in there. So this cylinder's in here.
And then you attach this thing to a power supply, a watt meter -- put a watt meter in
the circuit and this is the input power -- in watts of course. Okay. So you heat this cylinder
that way. Solid aluminum, drill a hole through it, insert the cartridge heater, and then
attach it to a power supply and put a watt meter in line. Then -- well, here's what she
needed to do. She needed to get the Reynolds number -- so Reynolds number based on diameter,
U infinity D over new. Okay. Got the diameter, four inches. I'll get the properties later.
U infinity -- go back to ME313 lab -- fluids lab. We have an HVAC duct in that lab. We
have students measure the velocity of the air in that HVAC duct in that lab to get a
velocity profile in that rectangular duct. Very similar. So what did she do? She took
the pitot-static tube that we used in the 313 lab and she put the pitot-static tube
in the duct at the center line, and that gave her U infinity. Okay. Then she inserted a
thermocouple in the line that gave T infinity -- thermocouple -- digital readout. We have
that all throughout -- throughout the fluids lab. Then, she attached -- to the outside
of the cylinder, she attached thermocouples. How many? She took -- she attached four -- one
to the front side, one to the backside, and one 90 degrees -- and that gave her T surface
-- digital meter output thermocouple transducer. Okay. And then she varied the velocity, U
infinity, over a range ten times -- ten different velocities. Gave her ten different Reynolds
numbers. Multiply the velocity from the pitot-static tube by the diameter, divide by kinematic
viscosity at what temperature? The film temperature. Average TS. Why do you put three thermocouples
on? Because the temperature around the cylinder won't be the same. They'll be close, but not
the same. Aluminum's a good conductor of heat. They should be close, but not the same. So
you average those three temperatures. Okay. Now you want to find the Nusselt number by
definition -- Nusselt bar means the average is H bar D over K. Get K at the film temperature
-- got it, for air. Diameter. Okay. Four inches -- four divided by 12. Now, the H bar. How
do you get H bar? Well, you go back to Chapter 1. For our convection heat transfer, Newton's
law of cooling, Q equal H bar AS TS minus T infinity. I measure TS -- thermocouple,
average them. I measure T infinity. Got it. The surface, AS pi D L, got it, got it. I
have the watt meter, tells me the input power, got it. Solve for H bar. Get Nusselt bar.
All right. Now I've got it. So now I've got the Reynolds number and the Nusselt number.
Now, of course -- first of all, the person that did this experimentation, and getting
away from the senior project, now. But who came up with something like this? Well, I'll
tell you who did -- the guy that he probably took ME312. Okay. ME312, we say, you know,
if you run an experimental program and you want to plot the results, you can just be
random and plot anything against anything. I think I'll plot U infinity versus the K
value. Bad choice. I -- I -- I think I'll plot the U infinity versus the diameter. I'll
change the diameter. No. Bad choice. We tell you ME312, there's something called dimensional
analysis. They say, if the heat transfer's a function of these different parameters,
you can put them together in dimensional parameters, and that's a major hint of what you, the experimenter,
should do in a laboratory environment to plot your data -- your results. Okay. If you do
that with -- with all these parameters, you take H and -- and D and the properties K and
new and U infinity -- forget this guy. This guy is not serious. Forget him right now.
Then, what pops out? The important dimensional parameters are the Nusselt and Reynolds numbers.
Okay. What does that tell me? If you make a plot from your experimental data, the first
thing you should try and do is plot Nusselt versus Reynolds. Okay. That's why engineers
know that that's called the form of the equation I expect. It's called a power law variation
-- power law. So I would plot -- and she did for her senior project, she plotted on here,
Nusselt bar and the Reynolds number and she had ten different velocities, so she had ten
different Reynolds numbers. I'll just show you a few of them here. I'll just say that's
the range and I'll just make it up based on that 40. Here's 40. Here's 4000. And by the
way, if you're going to try and do a correlation -- a power law, the best thing you want to
do is plot that data on log-log paper because if you plot it on log-log paper and it correlates,
you're going to get a -- you're going to get a straight line -- a straight line. If it's
a power law, you'll get a straight line. Look at that data. You say, I don't think that's
a straight line. I don't think that's a power law variation. I guess my results are all
really miserable. I feel bad my senior project failed. I'm going to go home and cry. Yeah,
right. No. No. Not exactly. You say to yourself, you know what? If I want to be real tricky,
those points there almost form a straight line. Look at them. And those points right
there almost form a straight line. Look at them. So, what do you do? So you know what?
I'll fit that curve piecemeal to a bunch of straight lines and then I'll tell you, the
user, what to choose for C and M for that equation. That's what they do. For instance,
4000 to 40,000. Now we tell our freshman and early classes -- we have them do log-log plots
some times. We say, okay. If you want to find the value of C, go to that graph with the
Reynolds number one. Okay. Put one in there for Reynolds. Get the Prandtl number now.
Reynolds one. Raise it to any power you want. I don't care. Raise one to any power you want,
what do you get? One. One. What's the value of C? The value of the Nusselt number where
the Reynolds is equal to one. Okay. You go over here, between 4000 and 40,000. Go back
to where the -- on your log-log graph where the Reynolds is one. Oh, there's the value
of C -- .193. Got it. And then, what's M? M is the slope. Take a ruler out if you want.
You can take a ruler out. Centimeters. Measure the slope of that line. That slope would come
out to be -- with a ruler, for instance, make it really easy on yourself -- .618. So that's
what these guys do who put together these empirical equations. They get a hint on what
to plot from dimensional analysis, then they make their plot and try to fit it into a power
law if they can -- if they can. You know. So -- and it's nothing new. And now, let me
tell you something, okay. If she would have repeated this with a different diameter -- let's
say she doubled the diameter to eight -- eight inches, here's her data points. She says,
you know what? I'm going to put this thing in a water channel down in the fluids lab,
down there -- the civil engineering water channel. I'll put it in there and I'm going
to measure with water now, not air, water. You know. Guess what? Conclusion. It doesn't
matter what the fluid is, it doesn't matter what the diameter is, it doesn't matter what
the temperature is within bounds, all my data falls on the same line. Oh, you know that
from ME312. That's what we begin [inaudible] ME312. It doesn't matter how you change these
things. If you've got the right parameters from your dimensional analysis, they're going
to all plot on the same line. I'll tell you something else. Here's a Reynolds number,
here's a friction factor, here's 2000. Get the Reynolds number. This is for water. This
is for air. This is for oil. You know what? It doesn't matter what the fluid is. It doesn't
matter what the -- what the diameter of the pipe is. I get all my data points on the same
line. Wow, is that amazing? Yeah. But not really. It -- it comes from dimensional analysis.
What are the important dimensional parameters in the Moody chart? This guy's dimension is
F, this guy's dimension is Reynolds number, this guy's dimension, Nusselt, this guy's
dimension is Reynolds number. The power of dimensional analysis for engineers. It is
phenomenal. Phenomenal. Is there a special Moody chart for water, one for air, one for
oil? No. No. No. No. The same chart, one piece of paper. One piece of paper for everything
in the world. Wow! Power. You got it, man. Power. Same thing here. We end up with a plot.
So -- just so you know. Sometimes people say, I'll use it, but I don't know where it came
from. There's where it came from. Okay. And we had a senior project that did this. Now,
her answers were accurate to these numbers here within 25 percent. Pretty phenomenal
for Cal Poly versus Cal -- Cal Tech or Stanford. Okay. I mean, that's -- that's pretty good,
so. Twenty-five percent, I thought -- good job. You know, you did a good job on that
senior project. But, yeah. She took an idea out of a textbook and based her senior project
on that idea. Okay. Now, let's talk a little bit more -- anything about that right now?
Okay. Let's talk a little bit more about these equations. Now, you say, you know, it looks
kind of strange there. If I use equations one and three --
Properties of T film. But be careful. Be real careful. That guy right there. Properties
at T infinity. Shift gears. Big note on your -- no, not on your equation sheet, the exam.
Because on the exam, only one you're going to use -- that's why I boxed it. The only
one you're going to use on -- in this course for an exam situation is that boxed equation.
Okay. That way you don't have to worry about that. Well, but why are they different? How
come you shift gears in the middle? Well, dealer's choice. Dealer's choice. He says,
if you use my equation, who's mister -- who -- who's that? Mr. Zukauskas, Russian scientist.
Okay. If you use my equation, base your properties at T infinity, except where you see that Prandtl
S. That S means at the surface temperature. Why did he do that? Just because he, you know,
doesn't like other people? No. He found his data correlated better when he did that. His
experimental data correlated better, so he said, okay. That boxed equation is based on
properties of T infinity. Dealer's choice. He took the data, he tells you what properties
to use. Okay. Why are there three? I mean, a lot of textbooks only give you one -- one
equation. Our author -- this textbook is so thorough, they give you three -- three equation
here. This one is -- you don't need a table, which is nice for -- for computer code. You
don't need to go into a table. You -- you can -- one equation covers everything. But
it's -- it's a complex equation. So for our homework and -- and exams, no. No. Before
I forget it. Well, I'll go ahead and continue this first. Why are there three? Okay -- 19
-- this, this -- if you check the references at the back of the chapter, this is -- this
was published in 1977. This was published in 1972. This was published in -- really?
Before World War II. My gosh, all mighty. Geeze. You know, '67, '77, five -- 80 -- 82
years ago. Oh, my gosh. They're still in the textbooks? Yeah. Why? Well, it's so simple.
That's why. This has a little more complexity here to it, you know. Now, that was a simple
one. But when that guy took experimental data -- what did they have? I'll tell you one thing,
they didn't have the -- the handheld calculators. They didn't have the laptops. They had slide
rules -- slide rules. They didn't have the sophisticated instrumentation we have today.
So, these numbers here, oh, they're suspicious. You know, they're -- they're suspicious. I
mean, it's risky. You wouldn't want to use that equation in the real world. No. No. These
two guys here. Say, okay. This textbook, this edition, 2011 maybe, I think it is. I checked
the front cover -- 2011. Eleven plus 23, 33, 34 years ago -- 34 years ago! Both these guys,
roughly. Well, where's the equation 2008? No, it's not in the book. How about an equation
for 2001? No, it's not in the book. 1993? Sorry, it's not there. What does that tell
you? I guess, I'll do a search. You know, I'll do a search and see if I find one. But
if I can't find a newer one, I've got to use this guy right here. He's the latest one.
Probably the best instrumentation. Why isn't there a later one? Well, one good reason may
be -- and this is a maybe, okay. In order to do this research program and do a good
one, you need lots of money -- lots of money. You need a couple technicians -- at least
two or three technicians. You need a couple of people to analyze the data and report back
to you. Oh, a staff of about five, plus yourself. You pay them, you pay for lab space. I got
a wind tunnel here. Wow! You lock it up for three weeks -- a wind tunnel. Wow! Maybe -- maybe
millions of dollars. Probably millions of dollars nowadays. Well, what -- what -- what
-- what -- what -- how come they could do it? Well, I tell you something. If you want
to put a man on the moon, you don't want to use a 1933 data instrumentation. I'll put
man on the moon, I want the latest and the greatest. So I better get new H values. And
by the way, there was something called the Cold War then. Oh, it was -- it was in full
blown, man -- it was full blown. Tons of money dumped into who? Our money. DOD. Yes. Tons
of money dumped in the space program. Who? NASA. Us. Yeah. They dumped tons of money
in to get the latest and the greatest. They didn't want to depend on pre-World War II
instrumentation. No. Slide-rule era. Oh my gosh. No. No. Since then, [inaudible] says,
all right, we need -- we need to get some H data on this for something. What are you
going to use? The guy says, well, I'll tell you, boss, either I can use this 1977 data,
that's the last one I found, or I can do a -- a new research program for you for $1.2
million. The boss says, you know what? Let's just use that one. That's okay. Yeah. Unless
you find money, you don't do the work. That's part of the -- the way we work in this world.
If nobody pays you, you don't do the work. So there better be a darn good reason to spend
a lot of money to do the work. Depends on what you want to do, you know. Obviously,
they said that's good enough. That's good enough. And I'll read you what it says in
the book. The reader is cautioned that all these correlations are only valid within 20
percent accuracy. That's a big -- that's a big one right there. They're only valid in
20 percent accuracy. Wow! Wow! Why is that? Well, let's go -- first of all it's experimental.
So you've got experimental uncertainty. Experimental uncertainty. If you minimize that, then what
else is there? Okay. This guy right here. I'll -- I'll just give you for instance. This
guy right here. You know how hard it is to get that thing to be uniform profile? You
do it in a wind tunnel. Do you think you're accurate on the 10 Freeway has that approaching
the -- the grill? I don't think so. You think it's coming straight towards you? I don't
think so. Not most of the time. So very seldom -- very rarely do you have a uniform profile
that looks like that approaching your radiator because your radiator has circular tubes with
air going over them. A heat exchanger has circular tubes with maybe steam going over
them. So right away, is that steam perfectly like that? Oh my gosh, no. Did you see those
heat exchangers? They go like this. Yeah. Yeah. Over the tubes. So, yeah. That's why
that uncertainty's 20 percent. Just so the -- the reader knows. Be cautious because don't
think you're -- don't carry your answers to eight places accuracy on your -- on your TI
1050 model. It's ridiculous. What -- what accuracy better -- should be on your spreadsheet?
How about three significant figures. Nothing more. Nothing more than that. So yeah, be
aware of that. Okay. So the bottom line in our class, we're using this guy. Even though
he's outdated, we're using him. You get the idea how to find the H values. Problem is
for homework, he uses different equations for different problems, so the answers -- if
you use -- pick and choose, you might be off because he used this and you use that, or
whatever. So I'm going to tell you know what you should use to get the answers for homework
so your answers may match his answers. All right. Chapter 7, problem 7-45, 7-45. I'm
sorry, 7-47 -- 7-47. Use Hilpert and you should get his answer. Problem 7-49, he used Churchill
but I don't want you to use Churchill because it's too complicated for what we're doing.
We're going to use Hilpert. So the answer for H bar or whatever you might get, Q, will
not match his answer -- will not match the author's answer -- 7 -- problem 7-49. Use
Hilpert no matter what. Problem 7-53, he used equation 7-44, so we're okay. That's Hilpert.
Problem 7-53, don't do part C. We didn't discuss fin effectiveness. We discussed fin efficiency,
not fin effectiveness, so don't do part C.
Which problem was that?
7-53. That's the only three problems on this stuff. Now -- all right, now, all this leads
up to how about non-circular? Non-circular tubes and pipes? Well, there's a lot of tubes
in the real world that are non-circular. Look at your automotive radiator. They're not round
tubes carrying water. Look at them some time. So to do that, we use Hilpert again. These
are empirical correlations from experimental programs. We use that with Table 7-3. Okay.
Here's Table 7-3. Geometry. Reynolds number C and M. Okay. So it -- first one, non-circular
is a square tube with a pointed part facing forward. This is dimension D. Square tube
with the flat part facing forward. This is dimension D. There's five different pictures
given. I'll show you three. A hexagon-shaped tube --
with the flat pointing forward. And then they give you -- I'll just give you one here. A
Reynolds number range 5000 to 60,000. Then they give you a value of C -- .158 and .66.
And there's two more pictures given there. So you use the Hilpert equation right here,
and if you want the C and the M, you go over here to get the C and the M. It's very straightforward.
It's the only thing you can do. It's the only choice you've got in the textbook is to use
Hilpert with that. This data here was taken much later than Hilpert equation data so this
is more updated data for C and M here. You say well, what if my Reynolds number is 80,000?
[Inaudible] good luck. It's probably out there somewhere. You got to search it. These are
the most popular Reynolds number ranges. Okay. Question back there?
Why don't they, like, update the table?
This one right here?
Yeah.
That's a good -- that's a good point. That's a good point. I -- I suspect that -- that
this one is updated and what they do with this guy here -- I didn't [inaudible] -- this
-- this accounts for property variations. But when they did this one -- when they -- when
they did this correlation, they did use newer instrumentation. So, yeah. I -- I think this
one supersedes that. If -- look at the form, look at that form. They're identical except
for that property variation. And what if it's air? .7 divided by .72 raised to power -- one-fourth
power. Nothing -- close to one. Okay. So I think that's why they -- it has been updated,
but it's been updated and extended to its usefulness. Yeah. Okay. Now, over here, just
so you know, Reynolds number -- and Nusselt number. D obviously does not stand
for diameter. What's the diameter of a hexagon? No. Don't ask a question. There is none. D
does not stand for diameter. It stands for dimension or distance, take your choice. Dimension
or distance. What is D in these pictures of this tube? It's the distance from the upper
most point to the lower most point -- top to bottom. Top to bottom here, top to bottom
here, top to bottom here. That's how they define the Reynolds number and the Nusselt
number. There's nothing magic about that dimension in the Reynolds number. The Reynolds number
is U -- is a velocity, okay. A velocity times some dimension divided by a property. What
dimension? Well, if it's a flat plate, the dimension is X. If it's a circular tube, the
dimension is D, the diameter. If it's a non-circular tube, it's the distance from the top to the
bottom of what the air sees. Here's the air approaching here. What I see in front of me,
this tube here, is that distance, top to bottom. When they do -- I tell my 312 class, when
they do, let's say, drag force studies on a -- on a Nascar or a top fuel dragster or
a funny car, typically, John -- John Force Racing in Orange County, they -- they plot
the drag force as a function of the Reynolds number. If you're -- they -- they put motorcycles
in wind tunnels -- full-sized motorcycles in wind tunnels with a rider on it and change
the speed in the wind tunnel and get different -- different Reynolds numbers and they get
different drag forces on there. Well, when they do that for, let's say, a funny car in
drag racing, what do you think they're going to find D as? The -- the headlight diameter?
No, I don't think so. The wheel diameter? Why? It's got to be something. I don't know.
Maybe the dimensions of John Force's head? I don't think so. You got to -- you -- I don't
know. What should I choose? What should I choose? Well, what they choose. Here it goes.
The distance that the air sees from the bottom to the top of the car. You face the car frontal
and you measure the distance from the wheels on the ground to the top of the funny car,
and that's how they get the Reynolds number. The motorcycle rider. You measure the distance
D -- the distance from the tires on the ground to the top of the guy's helmet on his head.
Metro link train, you measure the distance D from the railroad tracks to the top of the
metro link engine. A tractor trailer truck with the tractor in front and the trailer
behind, look at it head on, and to get the Reynolds number of that truck at 60 miles
an hour on the freeway, you take the distance D from the tires on the ground of the -- of
the tractor to the top of the trailer, top of the trailer. That's the dimension D you
put in the Reynolds number to get the Reynolds number of the truck going 60 miles an hour
on the 10 freeway. So it -- it -- that's the choice you make. What should I -- what should
I put in for this dimension D in the Reynolds number? Whatever makes sense to you. Whatever
makes good common sense to you. Okay. All right. So just -- so you know how you handle
these guys right here, okay. For instance, I can put -- I can put a -- a square tube
like this -- a square -- it's really a fin. There's a fin. I attach a fin to a heated
surface to take heat out. I attach a fin to a heated surface. This could be electronics
package. I want to take heat out. I put 100 fins like that on this thing and blow air
over it. Okay. What do I do? Okay. Right here. I use -- I use that equation in the box. I
use this for D, which is this dimension right here if it's square. I put it in here. I get
H bar. I put the H bar in here. I get Q. That's the heat loss by what? By one fin. Multiply
it by 100. I get the heat loss by 100 fins plus the base area. The heat loss of the base
area here, too. So that's how they use stuff like that. Okay. It -- it can be a fin or
it can be a tube carrying water with steam blowing over it, whatever. These guys right
here are condenser tubes. And they could possibly, I'm just giving example -- condenser tubes.
Steam hits them. Cold water inside. The cold water condenses the steam, the steam drops
off, goes to the hot well. That's how we engineers analyze these things like this. Okay. Good
stopping point. We've finished Chapter 7. Okay. I'll do an example on Friday for you.
But we're through with that right now. And let me go pass out the -- the second exams
for you.
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Healing From The Underworld - Duration: 7:15.
Healing From The Underworld
by Aurora Serrano,
Have you ever wondered why some people are so unlucky?
No matter what they do or how hard they try, they can�t seem to get a break.
Some might believe it�s bad luck, a curse, a spiritual blockage, or a soul contracts
we agreed or created from a previous life time.
However, what if none of this is the reason behind the struggles in our life?
What if something else is holding us from living the life we strive and work so hard
for?
In my spiritual journey, I came across something I never heard of and was dumbfounded at what
I was informed about.
I tried to attain information about this particular subject, but there was limited information.
Intrigue and with the subject, I decided to ask my guides to provide me with knowledge
on this particular topic.
I was very surprised with the information I was provided and how naturally I was able
to implement this particular healing with minimal difficulties.
What I realized was there are energy imprints created by our ancestors through the trauma
they endured in their lives and never even realized it.
Our family not only passes their physical genetic makeup, but they also pass on their
energy /beliefs on how they perceive or interpret their life on to their descendants.
The trauma they endured created a coping skill to prevent any more harm to occur to them
and future descendants, which created an energetic contract with imprints of their perception
and interpretation of the situation they endured.
When this contract was created there were no malicious intent to cause harm or the thought
of leaving generations of descendants bonded and feeling stuck from living their full potential.
In removing the generational imprint, one has to convince/heal the ancestor who crossed
over to release the energy contract they left to their descendant.
Let me give you an example, by using a fictitious character to provide you a clearer picture
of what I am talking about.
Imagine Mary always doing her best in everything she did to get ahead without ever asking for
help, however, no matter what she did or how hard she tried she always struggled financially
in her personal and professional life.
Mary did everything right: college, her own business, saving, investing, and being mindful
about what she spent her money on, but she always seem to fail.
She knew somehow this had to change but could not grasp how too.
She always sensed there was more to her struggle, but could not understand where it was coming
from or how to resolve it.
Until she came across a particular healer who informed her, this was not her fault or
a soul contract she agreed on from previous lifetime, but the bond/ chain was caused by
an imprinting of her ancestor energy through trauma they endured.
To start the healing process one has to journey to the �spiritual underworld�, which is
where many lost souls remains with contracts that ingrained beliefs due to an unfinished
business or traumatic event in their life.
For Mary, what was discovered through the journey of the �underworld� was her grandmother
as a young child seemed guarded and pushed people away from her, especially when they
tried to be nice or offer her help.
Mary�s grandmother grew up from a wealthy family and everything seemed to be defined
by wealth and how much money was accumulated.
Money played a major factor in Mary�s grandmother�s upbringing, her parents were driven by it
and were constantly working and never around her.
Grandmother grew up a majority of her childhood cared for by her nanny and servants.
Mary�s grandmother would constantly beg her parents to stay home and spend time with
her as a child, but the reply was always the same �they can�t�, because they had
to work to provide for the lifestyle she was accustomed to.
One day while working in the �wee hours� of the night, grandmother�s dad passed away
unexpectedly from a heart attack, leaving grandmother heartbroken and feeling guilty.
She struggled to cope with her dad�s death and started to believe she was the reason
her dad passed away and if she wasn�t such a burden her dad would still be alive.
Two beliefs were instilled due to the trauma the grandmother endured, which created an
ancestral energy imprinting to its descendant.
The guilt due to her trauma created a belief that money only brought pain and suffering
so get rid of it as quickly as possible and do everything on your own so you will never
be a burden on anyone.
The subconscious contract that was written was in order to avoid feeling pain or a burden
to someone was to live with very limited amount of money or in poverty and never rely on others
no matter what.
As the grandmother grew up and had her own family, she raised her children different
from her upbringing.
She lived a very simple and humble life and did everything on her own and refused to accept
help from anyone due to the trauma she endured.
To be able to break this genetic imprinting or contract the grandmother had to realize
her father�s death was not her fault and she was never perceived as a burden to her
father.
The grandmother had to understand the coping skills she acquired to deal with her grief
caused more harm to her, her family, and it prevented her granddaughter from living her
potential in life.
When the grandmother was able to grieve properly and feel safe to let go of the belief and
coping skills she created to deal with the trauma, she allowed herself to be free and
move on; which released the energy contract she created.
As for Mary once the generational imprinting was removed it allowed her to feel empowered
and worthy; to seek out advice and help from others to create a successful business that
abundantly flourished without having any emotional or financial stress.
Helping someone who has crossed over an opportunity to heal creates a sense of safety instead
of fear as move on contract free and it also allows family lineage to heal and live life
without blocks or contracts, but freewill.
It also gives us insight the importance of nurturing oneself; especially when something
traumatic happens in our life, because we don�t know what punitive beliefs we create
due to the trauma we might endure or what generational imprints we may leave behind
when we pass.
While we have the chance always remember to not live in fear, but to nurture and love
one�s self each and every day.
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Funniest Pranks 2017 Try Not To Laugh: Funny Fail Compilation 2017 | Top Funny Scary Pranks Videos - Duration: 10:11.
Thanks for watching
Hope you have a great time
Please, like, comment and subscribe for more!!
-------------------------------------------
Yellow Bird Cover (chords in CC) - Duration: 2:15.
[C]Yellow bird up [G]high in banana [C]tree
[C]Yellow bird you [G]sit all alone like [C]me
[F]Did your lady friend [C]leave the nest again [G]that is very sad [C]makes me feel so bad
[F]You can fly away [C]in the sky away [G]you're more lucky than [C]me
[C]I also have a [G]pretty girl she's not with me [C]today
[C]They're all the same, the [F]pretty girls, [G]make them the nest then they fly [C]away
[C]Yellow bird up [G]high in banana [C]tree
[C]yellow bird you [G]sit all alone like [C]me
[F]Better fly away [C]in the sky away [G]picker coming soon [C]pick from night to noon
[F]Black on yellow you [C]like banana too [G]they might pick you [C]someday
[C]Wish that I were a [F]yellow bird [G]I'd fly away with [C]you
[C]But I am not a [F]yellow bird so [G]here I sit nothing else to [C]do
[C]Yellow bird up [G]high in banana [C]tree
[C]Yellow bird you [G]sit all alone like [C]me
-------------------------------------------
Creatine And Diabetics: Can People With Diabetes take Creatine? - Duration: 3:20.
Hey guys, Paul from Ultimate Fat Burner.com here.
Today I'm going to answer a question that's come up a few times over the last couple of weeks
and that is...
Is Creatine Safe for Diabetics?
Can people with diabetes take creatine?
I'll be right back with the answer in just a couple of seconds, stick around, don't you dare go
anywhere.
Alright welcome back and thanks so much for sticking around.
Now before I answer this question, bear with me while I go through a couple of very important
points...
1) I'm talking creatine monohydrate here, not any of the numerous variations of creatine
available on the market today.
2) I'm talk about the plain powdered stuff, not pre-workout supplements that may contain
creatine as part of their formulas, or products like cell tech for example, which combine creatine with
a ton of simple sugars to enhance uptake.
All bets are off the table if you're using that stuff.
we're talking about plain creatine monohydrate in powdered form, mixed
with water - that's it.
3) I'm not a doctor or an endocronologist, and I don't play one on T.V. and I don't play one on YouTube.
You should consider this video as the starting point in your research
and not the final word.
Only your doctor can give you the go ahead on any nutritional supplements and I'm certainly
here to suiggest othwise.
OK. So, with that out of the way, can diabetics take creatine?
Well, to answer that question I went looking for some clinical data verifying that studies had
been performed with creatine on diabetics, and
believe it or not I did find one...
According to a study published in the journal "Medicine and Science in Sports and Exercise"
in 2010...
Creatine supplementation combined with an exercise program improves glycemic control
in type 2 diabetic patients.
This is at a dosage of 5 grams / day.
So based on this preliminary research it certainly appears that creatine is safe for diabetics,
at least for short term use and at a 5 grams per day maintenance dose.
But what about potential kidney issues for diabetics using creatine?
Well, that's been studied as well, and it was found that creatine does not affect kidney
function in people with Type 2 diabetes.
So what now?
Well, I'm going to include a link to these studies in the description below this video - I recommend
you print them off and take them with you the next
time you see your doctor so he or she has all the information needed to make an informed
decision. Only your doctor can tell you if you can take creatine as a diabetic.
Alright guys, that's a wrap - I hope you enjoyed this video.
If you liked it, I'd love it if you gave it a thumbs up, and if you think your
friends would like it, a share would be awesome as well.
If have any questions or comments, or you're a diabetic and have used creatine and want
to share your experience please leave a comment below.
And of course, if you haven't subscribed to this
channel, now would be a perfect time.
It would be really nice to have you aboard.
Youtube will send you a quick note whenever we post new videos so you'll never miss anything.
Thanks so much for watching, and I'll see you really soon.
-------------------------------------------
Leonard Cohen Hallelujah live at the Montreal Jazz Festival 2008 (Captioned) - Duration: 7:13.
I heard there was a secret chord
That David played, and it pleased the Lord
But you don't really care for music
Do you?
It goes like this
the fourth, the fifth
The minor fall, the major lift
The baffled king
composing hallelujah
Hallelujah
Hallelujah
Hallelujah
Hallelujah
Your faith was strong but you needed proof
You saw her bathing on the roof
Her beauty and the moonlight overthrew ya
She tied you to a kitchen chair
She broke your throne
she cut your hair
And from your lips she drew the hallelujah
Hallelujah
Hallelujah
Hallelujah
Hallelujah
Now maybe there's a God above
All I ever learned from love
Is how to shoot at someone who out drew you
But it's not a crime that you're here tonight
It's not some pilgrim who claims to have seen the light
No, it's a cold and it's a very broken Hallelujah
Hallelujah
Hallelujah
Hallelujah
Hallelujah
Hallelujah
Neil Larsen on Hammond B-3
Hallelujah
Hallelujah
Hallelujah
Baby I've been here before
I know this room and I've walked this floor
I used to live alone before I knew you
And I've seen your flag on a marble arch
But listen love
Love is not some kind of victory march
No, it's a cold, and it's a very lonely Hallelujah
Hallelujah
Hallelujah
Hallelujah
Hallelujah
There was a time
That you let me know
What's really going on below
But now you never show it to me
Do you?
I remember when I moved you
And the Holy Dove, she was moving too
And every single breath that we drew was Hallelujah
Hallelujah
Hallelujah
Hallelujah
Hallelujah
I did my best, it wasn't much
I could not feel, so I learned to touch
I've told the truth, I didn't come
to fool you
And even though it all went wrong
I'll stand right here before the lord of song
With nothing on my tongue but hallelujah
Hallelujah
Hallelujah
Hallelujah
Hallelujah
Hallelujah
Hallelujah
Hallelujah
Hallelujah
-------------------------------------------
gnash - suga suga Lyrics Video - Duration: 3:04.
suga suga baby bash & frankie j cover by gnash
-------------------------------------------
OPENING RECEPTION FOR MY MOM | vlog - Duration: 10:03.do you have anything you wanna say about this exhibition?
... what should i say?
you should think about it! lol why are you asking me?!
*speaks english* wait no *switches to korean* lol
i've been drawing clouds for a while now
but this time around i've been drawing them with an abstract expressionism style which has allowed me to evolve my style
why are you talking so formal? this is just for my youtube channel
*tries to act cute*
what were you thinking about while creating these pieces?
while i was drawing these...
mom talk like you're just talking to me lol it's not like this is a real interview
so these paintings were born from anger. not from a family member but someone I know
so because of that anger i used these paintings as way to just let it go
i wanted to let go of that anger and find inner peace
i just held the brush, blended and before i knew it i was done creating these series
since when did you become this ugly??
uh nooo i'm cuteeee *tries to be cute yet again*
i'm so happy
-------------------------------------------
OhPonyBoy - (05) Living In Space [The Stellae Key] LAUNCHPAD - Duration: 4:08.
It's like I've always been living in space,
Running away for a long time now.
It's like I'm living,
Living, always been living,
But your face sent my mind in space.
I should maybe try to kiss, to embrace
The sky inside you,
Please don't let that feeling go.
To kiss, to embrace
the sky inside you,
Please don't let that feeling go.
'Cause your face sent my mind in space.
It's like I've always been lost in space,
Looking away for a place to go.
It's like I'm living,
Living, always been living,
But your face sent my mind in space.
I should really try to kiss, to embrace,
The sky inside you
and let everything go.
To kiss, to embrace the sky inside you
and let everything go.
'Cause your face sent my mind in space.
[RADIO] .0. dr1am 1..
[RADIO] ... thr0ugh0ut ...
[RADIO] ...the g.laxy, ...
[RADIO] ... 24 h0urs a d.y, 7 days a week.
We remind y0u the latest 1nf0rmation that c0mes d1rectly fr0m the s0lar system.
Our White Emperor, Mr. Trustable who currently resides in the Pyramid of the Capital has decided
to maintain the state of emergency 6 more months, extending his legislation power.
He also invites the population to acquire WISBRAND-IDs as quickly as possible,
this security measure is now mandatory throughout the galaxy.
Stay with us until midnight.
-------------------------------------------
Domus Artis: Encarnación, la canción del alma - Teaser - Duration: 1:07.
Participants in the miracle of Life,
souls sing their songs on Earth.
Some of them echo forever.
Those which sing of Love.
A Domus Artis' creation
with music by
Incarnation, the song of the soul
Coming soon
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