# Question about Jet engines (thermodynamics)

• Maximilian Popelier
In summary: I can continueIn summary, the student is trying to solve for the jet engine efficiency but is getting stuck because they made a mistake in the numerator. Once they correct the mistake, they are able to solve for the jet engine efficiency.
Maximilian Popelier
Hi, I need help
I got a project for school about jet engines. They say bysubstitution of equations 5.1, 5.2, 5.5 and 5.6
butI don't know the steps how i get t0 the last formule.

Thank you
Maximilian Popelier

Take eq. (5.7) and replace ##w_a## and ##q_a## by the right-hand side of (5.5) and (5.6), and then further simplify using (5.1) and (5.2).

Tank you very much i will try it tomorrow

hi thank you..
but now I'm stuck here...

You made a mistake in the numerator. After having corrected that mistake, before you use equations (5.1) and (5.2), notice that η is 1 - something, so try to get that 1.

Im sorry I tried it but I am again stuck at the next step...

Maximilian Popelier said:
Im sorry I tried it but I am again stuck at the next step...

My whole Project or just the formule?
Here is the formule:

#### Attachments

• furmule gip.PNG
4.7 KB · Views: 422
You made a mistake in the last equality
$$1 + \frac{-a}{b} = 1 - \frac{a}{b}$$
$$1 + \frac{-a}{b} \neq 1 - \frac{a}{-b}$$

Maximilian Popelier
owww... sorry but I am still stuck

#### Attachments

• fysica.PNG
3.2 KB · Views: 413
You can now take out a factor in front of the fraction.

How if i do it i have do divise the T1 by the Factor

The Bill

i forgot the 1 -

Take a factor out of the numerator only.

oke and then?

Maximilian Popelier said:
oke and then?
Then you should get eq. (5.8). You can write what you got in post #13 such that you get the same term in ##T_1## and ##T_3## in the numerator and the denominator.

Maximilian Popelier
sorry i don't get it but i got this

Maximilian Popelier said:
sorry i don't get it but i got thisView attachment 109348
Compare what is in the parenthesis with the denominator.

I now see you also made a mistake when changing ##T_4## to ##T_3## in the numerator.

Nice i got it!
Ty very much

Oh i didn't get it i got a "-" wrong i will take a picture

$$T_4 = T_3 \left( \frac{p_2}{p_1} \right)^{-\left(1 - \frac{1}{k} \right)}$$ so you should get the right factor in front.

Can you please write it all out and take a picture. It will save us a lot of time

\begin{align*} \eta_{\mathrm{th}} &= 1 - \frac{T_4 - T_1}{T_3 - T_2} \\ &= 1 - \frac{T_3 \left( \frac{p_2}{p_1} \right)^{-\left(1 - \frac{1}{k} \right)} - T_1}{T_3 - T_1 \left( \frac{p_2}{p_1} \right)^{\left(1 - \frac{1}{k} \right)}} \\ &= 1 - \left( \frac{p_2}{p_1} \right)^{-\left(1 - \frac{1}{k} \right)} \frac{T_3 - T_1 \left( \frac{p_2}{p_1} \right)^{\left(1 - \frac{1}{k} \right)}}{T_3 - T_1 \left( \frac{p_2}{p_1} \right)^{\left(1 - \frac{1}{k} \right)}} \end{align*}

Hoophy and Maximilian Popelier
Ty man

Oh but you made a mistake i guess
Im not 100% sure

Maximilian Popelier said:
Oh but you made a mistake i guess
Why? I get the same equation as in the book.

Got it ty

Hi it isn't very clear for me sorry you hen you replace t4 u use a extra "-" before (1-1/k)
Sorry that i don't get it

Equation 5.4 is
$$T_4 = T_3 / (p_2/p_1)^{(k-1)/k}$$
so
$$T_4 = T_3 \left( \frac{p_2}{p_1} \right)^{-(k-1)/k} = T_3 \left( \frac{p_2}{p_1} \right)^{-(1-\frac{1}{k})}$$

Maximilian Popelier
Ty dude

## 1. How do jet engines work?

Jet engines work by sucking in air at the front of the engine, compressing it, mixing it with fuel, and igniting it in the combustion chamber. The hot gases produced by the combustion then expand and are forced out of the back of the engine, creating thrust that propels the aircraft forward.

## 2. What is the role of thermodynamics in jet engines?

Thermodynamics is crucial in jet engines as it helps to understand and optimize the processes involved in generating thrust. It involves the study of energy transfer and conversion, which is essential in the combustion process and the conversion of heat energy into mechanical energy to power the engine.

## 3. How does the second law of thermodynamics apply to jet engines?

The second law of thermodynamics states that in any energy conversion process, some energy will be lost as heat. In jet engines, this law applies to the conversion of heat energy from the combustion process into mechanical energy to power the engine. Some of this energy is lost to the surroundings, resulting in reduced efficiency.

## 4. What are the main components of a jet engine?

The main components of a jet engine include the compressor, combustion chamber, turbine, and nozzle. The compressor compresses the incoming air, the combustion chamber ignites the fuel-air mixture, the turbine extracts energy from the hot gases, and the nozzle accelerates the exhaust gases to create thrust.

## 5. How do engineers improve the efficiency of jet engines?

Engineers continuously work to improve the efficiency of jet engines by optimizing the design of the components, such as the compressor and turbine blades, to reduce energy losses. They also use advanced materials to withstand higher temperatures and develop more efficient combustion processes to increase the amount of thrust produced per unit of fuel consumed.

Replies
3
Views
2K
Replies
4
Views
1K
Replies
9
Views
4K
Replies
12
Views
2K
Replies
2
Views
1K
Replies
4
Views
2K
Replies
10
Views
2K
Replies
6
Views
1K
Replies
4
Views
2K
Replies
3
Views
2K