GATE Mechanical Engineering (ME) 2019 Shift 1 Solved Paper

Question : 56 of 65

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A gas turbine with air as the working fluid has an isentropic efficiency of 0.70 when operating at a pressure ratio of 3. Now, the pressure ratio of the turbine is increased to 5, while maintaining the same inlet conditions. Assume air as a perfect gas with specific heat ratio γ = 1.4. If the specific work output remains the same for both the cases, the isentropic efficiency of the turbine at the pressure ratio of 5 is ___________ (round off to two decimal places)

Your Answer:

Validate

Solution:

Given:

(r_{p})_{1}=3,(r_{p})_{2}=5

(η_{\;\text "isen "\;})_{1}=0.70

γ=1.4

T_{1}=

turbine inlet temperature is same for both the cases
Actual work done in case

1=(h_{1}-h_{2})_{1}=m c_{p} η_{1}(T_{1}-T_{2})

W_{1}=m c_{p} T_{1} η_{1}(1-\;{1}/{(r_{p})_{1}^{\;{γ-1}/{Y}}})

Actual work done in case

2=(h_{1}-h_{2})_{2}=m C_{p} η_{2}(T_{1}-T_{2})

W_{2}=C_{p} T_{1} η_{2}(1-\;{1}/{(r_{p})_{2}^{\;{γ-1}/{γ}}})

Now,

W_{1}=W_{2}

m C_{p} T_{1} η_{1}(1-\;{1}/{(r_{p})_{1}^{\;{γ-1}/{γ}}})=m C_{p} T_{1} η_{2}(1-\;{1}/{(r_{p})_{2}^{\;{γ-1}/{γ}}})

η_{1}(1-\;{1}/{(r_{p})_{1}^{\;{γ-1}/{γ}}})=η_{2}(1-\;{1}/{(r_{p})_{2}^{\;{γ-1}/{γ}}})

Substituting the values of

(r_{p})_{1}=3,(r_{p})_{2}=5

(η_{\;\text "isen "\;})_{1}=0.70

in the above equation, we get

η_{2}=0.51

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