Find specific thrust and SFC of a simple turbojet engine, having the following component performance at which the cruise speed and altitude are M 0.8 and 10000m. Select ambient condition from the gas table. Compressor pressure ratio 8.0 Turbine inlet temperature 1200K Isentropic efficiency: Of compressor ηc 0.87 Of turbine ηt 0.90 Of intake ηi 0.93 Of propelling nozzle ηj 0.95 Mechanical transmission efficiency ηm 0.99 Combustion efficiency ηb 0.98 Combustion chamber pressure loss ∆Pb 4% of compressor outlet pressure. C.V of fuel is 43,000 KJ/Kg, assume data if necessary, Cpa ≠ Cpg

 To calculate the specific thrust and specific fuel consumption (SFC) of a turbojet engine, we'll use the given component performance data and apply the relevant formulas. 

Given:

Cruise speed (Mach number) = 0.8

Altitude = 10000 m

Compressor pressure ratio (rp) = 8.0

Turbine inlet temperature (Tt4) = 1200 K

Compressor isentropic efficiency (ηc) = 0.87

Turbine isentropic efficiency (ηt) = 0.90

Intake efficiency (ηi) = 0.93

Propelling nozzle efficiency (ηj) = 0.95

Mechanical transmission efficiency (ηm) = 0.99

Combustion efficiency (ηb) = 0.98

Combustion chamber pressure loss (∆Pb) = 4% of compressor outlet pressure

Fuel Calorific Value = 43,000 KJ/kg

1. Calculate the ambient conditions:

Using the given altitude (10000 m), we can refer to the gas table to obtain the ambient conditions:

At 10000 m altitude, assume:

Ambient temperature (Ta) = 223.297 K

Ambient pressure (Pa) = 0.2649 bar

2. Calculate the compressor outlet pressure (P2):

P2 = rp * Pa

P2 = 8.0 * 0.2649 bar

P2 = 2.1192 bar

3. Calculate the combustion chamber pressure (Pb):

Pb = P2 - (∆Pb * P2)

Given: ∆Pb = 4% of P2

Pb = 2.1192 bar - (0.04 * 2.1192 bar)

Pb = 2.0365 bar

4. Calculate the turbine inlet pressure (P4):

P4 = Pb

P4 = 2.0365 bar

5. Calculate the compressor outlet temperature (T2):

T2 = Ta * (1 + ((rp)^((γ-1)/γ) - 1) / ηc)

Given: γ = specific heat ratio (assumed value of 1.4 for air)

T2 = 223.297 K * (1 + ((8.0)^((1.4-1)/1.4) - 1) / 0.87)

T2 ≈ 579.42 K

6. Calculate the turbine inlet temperature (Tt4_actual):

Tt4_actual = Tt4 / ηt

Given: Tt4 = 1200 K

Tt4_actual = 1200 K / 0.90

Tt4_actual ≈ 1333.33 K

7. Calculate the turbine inlet temperature (T4):

T4 = Tt4_actual - (Tt4_actual - T2) / ηm

T4 = 1333.33 K - (1333.33 K - 579.42 K) / 0.99

T4 ≈ 580.52 K

8. Calculate the exit velocity (Ve):

Ve = √(2 * γ * R * T4 * (1 - (Pb / Pa)^((γ-1)/γ)))

Given: R = specific gas constant for air (assumed value of 287 J/kg·K)

Ve = √(2 * 1.4 * 287 J/kg·K * 580.52 K * (1 - (2.0365 bar / 0.2649 bar)^((1.4-1)/1.