Step 1: Afterburner principle.
An afterburner injects fuel downstream of the turbine, using oxygen in the core stream to produce extra thrust by reheating. It is inefficient (high SFC), but gives large thrust augmentation for short duration (military).
Step 2: Evaluate each statement.
(A) True: Afterburner ON dramatically increases fuel consumption per thrust produced, so SFC rises.
(B) True: Variable area nozzle is essential. Afterburning raises jet temperature and volume flow; nozzle throat must enlarge to prevent choking and excessive back–pressure on turbine.
(C) False: Afterburning never reduces SFC; it always increases it.
(D) False: Afterburner increases stagnation temperature, not stagnation pressure. In fact, pressure drops across the burner due to frictional losses.
Final Answer:
\[
\boxed{(A),\ (B)}
\]
An ideal turbofan with a bypass ratio of 5 has core mass flow rate, \( \dot{m}_a,c = 100 \, {kg/s} \). The core and the fan exhausts are separate and optimally expanded. The core exhaust speed is 600 m/s and the fan exhaust speed is 120 m/s. If the fuel mass flow rate is negligible in comparison to \( \dot{m}_a,c \), the static specific thrust (\( \frac{T}{\dot{m}_a,c} \)) developed by the engine is _________ Ns/kg (rounded off to the nearest integer).
Two designs A and B, shown in the figure, are proposed for a thin-walled closed section that is expected to carry only torque. Both A and B have a semi-circular nose, and are made of the same material with a wall thickness of 1 mm. With strength as the only criterion for failure, the ratio of maximum torque that B can support to the maximum torque that A can support is _________ (rounded off to two decimal places).
A thin flat plate is subjected to the following stresses: \[ \sigma_{xx} = 160 \, {MPa}; \, \sigma_{yy} = 40 \, {MPa}; \, \tau_{xy} = 80 \, {MPa}. \] Factor of safety is defined as the ratio of the yield stress to the applied stress. The yield stress of the material under uniaxial tensile load is 250 MPa. The factor of safety for the plate assuming that material failure is governed by the von Mises criterion is _________ (rounded off to two decimal places).
A prismatic vertical column of cross-section \( a \times 0.5a \) and length \( l \) is rigidly fixed at the bottom and free at the top. A compressive force \( P \) is applied along the centroidal axis at the top surface. The Young’s modulus of the material is 200 GPa and the uniaxial yield stress is 400 MPa. If the critical value of \( P \) for yielding and for buckling of the column are equal, the value of \( \frac{l}{a} \) is __________ (rounded off to one decimal place).
A uniform rigid bar of mass 3 kg is hinged at point F, and supported by a spring of stiffness \( k = 100 \, {N/m} \), as shown in the figure. The natural frequency of free vibration of the system is ___________ rad/s (answer in integer).
A jet-powered airplane is steadily climbing at a rate of 10 m/s. The air density is 0.8 kg/m³, and the thrust force is aligned with the flight path. Using the information provided in the table below, the airplane’s thrust to weight ratio is ___________ (rounded off to one decimal place). 