# Gas turbine (mean line) analysis question

• Engineering
Homework Statement:
A single stage gas turbine for power generation is designed for the following overall duty:
- Power output is 4.2 MW, and mass flow rate is 70 kg/s
- Inlet stagnation pressure = 3 bar, inlet stagnation temperature = 1000 K
- Rotational speed = 3000 rpm
- No inlet swirl: ## \alpha_1 = 0 ##
- Operating fluid is air, ## \gamma ## = 1.4, ## c_p ## = 1004 J/kgK
- The total-to-total isentropic efficiency ## \eta_{TT} = 0.93 ##
Perform a mean line analysis and find the following:
(a) Total temperature and total pressure at the turbine outlet
Relevant Equations:
Euler work equation
Hi,

I was attempting another turbomachinery question and am struggling with a few concepts. The question is:
"A single stage gas turbine for power generation is designed for the following overall duty:
- Power output is 4.2 MW, and mass flow rate is 70 kg/s
- Inlet stagnation pressure = 3 bar, inlet stagnation temperature = 1000 K
- Rotational speed = 3000 rpm
- No inlet swirl: ## \alpha_1 = 0 ##
- Operating fluid is air, ## \gamma ## = 1.4, ## c_p ## = 1004 J/kgK
- The total-to-total isentropic efficiency ## \eta_{TT} = 0.93 ##
Perform a mean line analysis and find the following
(a) Total temperature and total pressure at the turbine outlet
"

Attempt:
From the power and mass flow, we can get the specific work done (per second):
$$\dot w_s = \frac{P}{\dot m} = \frac{4.2 \times 10^6}{70} = 6 \times 10^4$$
Then we can use the steady flow energy equation to write (## \dot q = 0 ##):
$$- \dot w_s = \Delta h_0 \rightarrow - \dot w_s = c_p \Delta T_0$$
I am confused of how to utilize the total-to-total isentropic efficiency. If we are told what the machine was designed for, has the efficiency already been accounted for in the power, or do we need to include it separately. I.e. is the 4.2 MW output after accounting for the 93% isentropic efficiency, or is that the 'ideal 100% efficient' condition?

Thank you for any help.