We come to lecture 5 point three today.
Last time we finished the general fourier,
and then today we come to the
perfect guess with losses.
The main difference between them,
it's the last time we don't have losses,
but this time we have losses.
Think about when we have losses,
or what happened.
Now we understand the general
effect of area change in a
flow system is developed
some working relationship,
working equations on the
case of perfect guess.
Working equations indicate the relationship.
What we want to get is let all the
parameters how they change with my number
specific ratio and a loss indicator.
For example,
Delta si we want to find all kinds
of parameter change,
pressure change, density change,
closely change, temperature change,
how it's related to mach number,
m one and m two points.
Specific here ratio.
And Delta si losses
for power guess,
is we also have the assumptions.
It's, in principle,
the same steady one dimensional flow,
antibiotic, no sharp work.
But today we assume that it's
a perfect guess with losses.
Last time it's without losses,
we also negro and potential feed the
all assumptions into our fundamental
concepts and the fundamental equations,
state equation, continuity equation,
and energy equation,
put all these assumptions into
these three equations.
And then you will see some interesting
conclusion.
First, in the state equation,
for perfect guess,
we have the state equation,
p equals to rho rt pressure density.
This is a uh parameter.
It's a constant, and then temperature.
Continuity equation tells us low one,
v a one, a low,
AV for the incoming rho equals to rho two,
a two,
v two 4.2.
Let's our continuity equation.
Continuity equation.
Put the area ratio into the left inside.
You have the density and velocity on the
right hand side.
Then from the state equation,
p equals to rho rt rho equals to p
over rt this is rho one.
Here is one over rho two less than.
The second term, and then you have,
whereas the in goes to my
number times sound speed.
So here you find the ratio of my number,
temperature, pressure.
You have pressure, rice ratio,
temperature, rice ratio,my number,songsby,
1234.
You have four groups of ratios,
and then here's area change.
First thing, we tried to put the sun speed,
the sun speed can be converted into
temperature,
into temperature.
A two over a one can be indicated by t two,
t one.
Then just now,
we also have another temperature here,
combine them.
This is a temperature rise ratio.
Now you have pressure, my number.
What you want to do is let finally find the
relationship of area change to my number.
So try to convert pressure rise ratio,
temperature rise ratio
of them into my number.
How to do that?
We start from our energy equation.
Let's our energy equation,
total entropy plus he transfer
into the equals to the
total and so people into plus sharp work.
From our assumption, no heat transfer,
no sharp work,
ht one equals to ht two.
The total entropy is a constant.
It also means total
temperature is a constant.
And then we, from the introduction,
I when we defined total temperature,
that it's a function of static
temperature and mach number,
when total temperature is a constant,
you can find a relationship
between static temperature.
It's a function of a number.
It's a function of my number.
That's our relationship of temperature,
rise ratio.
For the same.
I understanding you can also
find a pressurized ratio,
because here,
total pressure, when there are no losses,
total pressure, is a constant,
when there are some losses,
you can define the losses.
You can define the losses.
And then from the total pressure,
you get a steady pressure relationship.
Here comes the result.
We divine the losses by Delta si
entropy change,
total pressure.
Here is our entropy change, our losses.
We call this as total pressure recovery.
Let's how much of total pressure is lost.
It's a function here,
pressure,
my number.
By putting this one into the right hand
side,
you have the pressure ratio.
It's also a function of my number.
And here be careful.
This is positive.
Now, it's becomes positive.
Here is negative, but here is positive.
Now let's the overturn of our losses.
Anyway,
you find a pressure ratio also
to my number in the loss.
So area change from continuity equation,
it's a function of pressure ratio,
mach number ratio, and the,temperature ratio.
Now,
pressure ratio is a function of my number.
Temperature rise ratio is a function of my
number.
The right hand side is completely a
very complicated equation of my number.
That's what we get here.
A two over a one.
It's such a equation.
I let's pressure ratio,
temperature ratio, my number,
and then made some calculation.
You get this one.
Let's now or we get area for perfect guess.
Think about loss.
It's a function of my number, m one,m two,
specifically ratio gamma,
and loss Delta si only area
change can be indicated by m one,
m two, gamma,
and Delta si if you have area change I
you can have all the other terms.
Total temperature is a constant.
You have total pressure, indicate losses.
You have less one temperature ratio,
pressure ratio,
density ratio.
All of them, I+8 area ratio of the
property change now becomes a function of
mach
number,
specifically ratio for losses only.
That's what we want to do.
If you get this relationship,
now you can calculate 2 points how
their properties change with the other.
Let's highly related by the my number,
specifically ratio and losses.
I think that's all for today.
Thank you.