[futur123 (OP)]

Hi everyone,
I am working on calculating the actual efficiency of a gas turbine (real simple brayton cycle).The issue is that I found a formula of the efficiency on the internet (for this cycle) but I didn't find the same results using the formula that i already know "Efficiency = 1- (T4-T1)/(T3-T2)".The formula that i found is in the attached file.
Thanks in advance.

[paul cotter]

Nobody seems to be rushing to help. It's 50 years since I studied this stuff but there is a problem with your efficiency expression: the efficiency will be the net shaft work after the compressor work is subtracted from the turbine work all divided by the heat supplied. Your expression only has temperatures. Now if net shaft work is zero and you are employing a propulsion nozzle after the turbine then it's more complicated. I am in error, of course the net work can be expressed in terms of temperature values; on looking it up in my small tech library I find efficiency= T1-T2+T3-T4/T3-T2.

[Eternal Student]

Hi.

Nobody seems to be rushing to help.

   I don't know enough about turbines.   This website looks authoritative  (It's got an mit.edu domain name) and supports the formula  you ( @futur123 ) and also you ( @paul cotter  ) have suggested,   given some re-shuffle or proper presentation so that you can see what divides what.



with the points  a,b,c,d  as identified on this   P-V  diagram:


Best Wishes.


    Reference:  equation  (3.8 )   on  this  website:    https://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node27.html

[futur123 (OP)]

Nobody seems to be rushing to help. It's 50 years since I studied this stuff but there is a problem with your efficiency expression: the efficiency will be the net shaft work after the compressor work is subtracted from the turbine work all divided by the heat supplied. Your expression only has temperatures. Now if net shaft work is zero and you are employing a propulsion nozzle after the turbine then it's more complicated. I am in error, of course the net work can be expressed in terms of temperature values; on looking it up in my small tech library I find efficiency= T1-T2+T3-T4/T3-T2.

Thank you for your answer.I already used the equation that you've mentioned, and it's equal to the one in the third picture.But using excel didn't find the same results because i was using the temperatures in °C not Kelvin. So the problem is solved after using temperatures in kelvin.
Thank you again, and have a great day.