1. **Problem Statement:** Determine if the given turbojet cycle is ideal or real based on the provided data and solve for the ideal cycle if applicable. 2. **Given Data:** - Ambient temperature $T_a = 233$ K - Ambient pressure $P_a = 26.4$ kPa - Inlet velocity $u_1 = 0.85$ Mach - Combustion chamber temperature $T_3 = 1200$ K - Nozzle exit velocity $u_4 = 600$ m/s - Nozzle exit area $A_4 = 0.2$ m$^2$ - Fuel heating value $HV = 43000$ kJ/kg 3. **Assumptions for Ideal Turbojet Cycle:** - Isentropic compression and expansion (no losses) - Perfect gas behavior with constant specific heats - No pressure losses in combustion chamber - Complete combustion 4. **Step 1: Check if cycle is ideal or real** - The problem does not provide efficiency or loss data. - Since velocities and temperatures are given without losses, assume ideal cycle. 5. **Step 2: Calculate inlet velocity $u_1$ in m/s** - Speed of sound $a = \sqrt{\gamma R T}$, for air $\gamma=1.4$, $R=287$ J/kg.K - Calculate $a_1 = \sqrt{1.4 \times 287 \times 233} = \sqrt{93386.6} \approx 305.6$ m/s - Then $u_1 = 0.85 \times 305.6 = 259.8$ m/s 6. **Step 3: Calculate mass flow rate $\dot{m}$ at nozzle exit** - Use continuity: $\dot{m} = \rho_4 A_4 u_4$ - Need $\rho_4$ (density at nozzle exit). Assume ideal gas and find $P_4$ and $T_4$. 7. **Step 4: Estimate $T_4$ using energy balance** - For ideal cycle, kinetic energy at inlet and outlet relate to enthalpy changes. - Use $h_3 - h_4 = \frac{u_4^2 - u_1^2}{2}$ - Specific heat at constant pressure $c_p \approx 1005$ J/kg.K - Calculate $h_3 = c_p T_3 = 1005 \times 1200 = 1,206,000$ J/kg - Calculate kinetic energy difference: $\frac{600^2 - 259.8^2}{2} = \frac{360000 - 67588}{2} = 146206$ J/kg - Then $h_4 = h_3 - 146206 = 1,059,794$ J/kg - Calculate $T_4 = \frac{h_4}{c_p} = \frac{1,059,794}{1005} \approx 1054$ K 8. **Step 5: Calculate pressure at nozzle exit $P_4$ assuming isentropic expansion** - Use $\frac{T_4}{T_3} = \left(\frac{P_4}{P_3}\right)^{\frac{\gamma-1}{\gamma}}$ - Need $P_3$, assume compressor pressure ratio $r_c$ (not given), so cannot calculate $P_4$ exactly. - Without $P_3$, cannot proceed further. 9. **Conclusion:** - Insufficient data to fully solve the ideal cycle. - Since no losses or efficiencies are given, and problem asks to ignore if real cycle, we treat this as ideal. - Partial calculations show inlet velocity, outlet temperature, and kinetic energy relations. **Final answer:** - The cycle is assumed ideal based on data. - Inlet velocity $u_1 \approx 259.8$ m/s. - Nozzle exit temperature $T_4 \approx 1054$ K. - Further calculations require compressor pressure ratio or pressures.