Thermodynamics Review Problems for Mechanical Engineering Students | Series 28
This is the 28th series of my "Thermodynamics Review Problems for Mechanical Engineering Students". If you've missed the previous series you may try scrolling this blog and head over to the "Curriculum". For this series, I randomly selected a review problem from the Thermodynamics textbook that I’ve been using for years and that review problem is about Brayton cycle.
Review Problem
The turbine section of a Brayton cycle gas turbine receives the hot compressed air at
150 psia
and 2100°R
and expands it to 15 psia
and develops a gross output of 15000 hp
. Air enters the compressor section at 15 psia
and 500°R
. Determine the net power output, WNET
in horsepower, hp
; and cycle efficiency, e
.Solution
This review problem is a continuation of the 27th series and the data obtain in that series are used in solving this review problem. So for this review problem, the net power output of the Brayton cycle is easily obtained by simply subtracting the compressor power,
WC
from the turbine output, WT
. And by doing so, we’ve found out that WNET
is equal to 8104 hp
. The last parameter that would check the performance of the Brayton cycle is its efficiency and before we can obtain it, let’s define the efficiency of the Brayton cycle for which it is expressed as a ratio of the net power output WNET
to the QA
of the cycle; wherein QA
is the power being generated during combustion in the combustor. As for the heat that is being added to the cycle, the formula for it is expressed in the following equation, QA
= mcp(T3 - T2), since process 2 -> 3 is an isobaric heat addition process, that’s why we are using specific heat capacity at constant pressure, cp
. And by using the mentioned formula, we’ve found out that the heat that is being added to the cycle is equal to 16814 hp
. Finally, we can now compute for the efficiency of the Brayton cycle and by using the formula for efficiency that is expressed as a ratio of WNET
and QA
; we’ve found out that the Brayton cycle is 0.4820 = 48.20 %
efficient.Net power output, WNET |
|
Heat added, QA |
|
Cycle efficiency, e |
Curriculum
Reference
- Sta. Maria, H. [1990] 2012. Thermodynamics 1. Mandaluyong City: National Bookstore Inc..
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