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The example provided outlines an afterburning turbojet engine and provides key parameters for various engine properties. Here's a breakdown of how to approach the calculations requested:

**Given Parameters:**
- \( M_0 = 2.0 \) (Mach number)
- \( p_0 = 10 \, \text{kPa} \) (ambient pressure)
- \( T_0 = -45^\circ C \) or \( T_0 = 228.15 \, \text{K} \) (ambient temperature)
- \( \gamma_c = 1.4 \) (specific heat ratio in the compressor)
- \( c_p_c = 1004 \, \text{J/kgK} \) (specific heat capacity of air through the compressor)
- \( \pi_d = 0.88 \) (diffuser efficiency)
- \( \pi_c = 12 \) (compressor pressure ratio)
- \( \eta_c = 0.90 \) (compressor efficiency)
- \( \tau_t = 8.0 \) (turbine pressure ratio)
- \( Q_R = 42,000 \, \text{kJ/kg} \) (fuel heating value)
- \( \eta_b = 0.98 \) (combustion efficiency)
- \( \pi_b = 0.95 \) (burner pressure ratio)
- \( \gamma_t = 1.33 \) (specific heat ratio in the turbine)
- \( c_p_t = 1156 \, \text{J/kgK} \) (specific heat capacity of air in the turbine)
- \( \eta_m = 0.995 \) (mechanical efficiency)
- \( \eta_AB = 0.98 \) (afterburner efficiency)
- \( \pi_AB = 0.93 \) (afterburner pressure ratio)
- \( \gamma_AB = 1.30 \) (specific heat ratio in the afterburner)
- \( c_p_AB = 1243 \, \text{J/kgK} \)
- \( \tau_{AB} = 11 \)
- \( Q_{RAB} = 42,000 \, \text{kJ/kg} \)
- \( \pi_n = 0.93 \) (nozzle pressure ratio)
- \( p_9 = p_0 \) (exit pressure equal to ambient pressure)

**Tasks:**
1. **Calculate total pressure and temperature throughout the engine, fuel-to-air ratios \( f \) and \( f_{AB} \)**:
   - You need to compute the pressure and temperature at each stage of the engine. This involves the isentropic relationships and efficiencies across the compressor, combustor, turbine, and afterburner.
   
2. **Non-dimensional specific thrust \( F_n / \dot{m}_a \)**:
   - Specific thrust can be calculated using the momentum equation for jet engines.

3. **Thrust specific fuel consumption (TSFC)**:
   - TSFC is given by the ratio of fuel consumption rate to thrust. In SI units, it's often expressed in \( \text{mg/Ns} \).

4. **Thermal and propulsive efficiencies \( \eta_t \) and \( \eta_p \)**:
   - Thermal efficiency relates to how efficiently the energy from fuel is converted into useful work.
   - Propulsive efficiency relates to how effectively the jet converts this work into thrust.

### Would you like me to begin with a step-by-step calculation for one of these parts or all together?

Here are some follow-up questions:
1. Would you like to see the detailed equations for calculating pressures and temperatures across the engine?
2. Should I go into more detail about how to compute fuel-to-air ratios \( f \) and \( f_{AB} \)?
3. Do you want to understand how specific thrust is derived from jet engine principles?
4. Should I explain the process to calculate TSFC for this specific afterburning turbojet?
5. Would you like to focus on either the thermal or propulsive efficiency in more detail?

**Tip:** When solving these problems, always remember the role of isentropic relationships and efficiencies when moving through different engine components!

An afterburning turbojet engine operates at given parameters. Calculate the total pressure and temperature throughout the engine, fuel-to-air ratios, non-dimensional specific thrust, thrust specific fuel consumption (TSFC), and thermal and propulsive efficiencies.

This example details the performance analysis of an afterburning turbojet engine, covering calculations for total pressure and temperature, fuel-to-air ratio, non-dimensional specific thrust, TSFC, and thermal and propulsive efficiencies. Learn how to apply key thermodynamics and fluid dynamics principles in aerospace engineering.

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