Consider a steady, isentropic, supersonic flow (\(M > 1\)) entering a convergent-divergent (CD) duct as shown. Which option correctly describes the flow at the throat?
Steady, incompressible, inviscid flow past two airfoils is shown. The pressure coefficient at the trailing edge of (I) with a finite included angle is \(C_{pI}\); for (II) with a cusp (zero included angle) it is \(C_{pII}\). Which statement is TRUE?
Which of the following statements about a general aviation aircraft, while operating at point $Q$ in the $V$-$n$ diagram, is/are true?
Two fair dice with faces numbered 1 to 6 are rolled together. Find the probability that both dice show odd numbers. (Give your answer rounded off to 2 decimal places.)
A constant force \(\vec{F} = (4\hat{i} + \hat{j} - 3\hat{k}) \, \text{N} \) moves a particle from \( A: (1, 2, 3) \, \text{m} \text{to} B: (5, 4, 1) \, \text{m}. \)Find the work done by the force (in joules). Answer as an integer.
A material has Poisson's ratio \(\nu=0.5\) and Young's modulus \(E=2500\ \text{MPa}\). Under a hydrostatic stress of magnitude \(10\ \text{MPa}\), the percentage change in its volume is _________,(answer in integer).
During landing, an airplane experiences a net vertical ground reaction of \(15{,}000\ \text{N}\). The weight of the airplane is \(10{,}000\ \text{N}\). The landing vertical load factor, defined as the ratio of inertial load to the weight of the aircraft, is __________ (rounded off to 1 decimal place).
An aircraft with a turbojet engine is flying with \(V_0=250\ \text{m s}^{-1}\) at an altitude where \(\rho=1\ \text{kg m}^{-3}\). The inlet area is \(A_0=1\ \text{m}^2\). The average exhaust-gas speed at the nozzle exit, with respect to the aircraft, is \(V_{e,\text{rel}}=550\ \text{m s}^{-1}\). The exit pressure equals ambient and fuel–air ratio is negligible. Find the uninstalled thrust (rounded to the nearest integer).
A circle of radius \(R\) is centered at the origin. The shaded top portion is bounded above by the circle and below by the horizontal chord through the point where the radius makes \(60^\circ\) with the \(\boldsymbol{y}\)-axis (see figure). The solid formed by a complete rotation of this shaded part about the \(y\)-axis has volume \(k\pi R^{3}\). Find \(k\).
As per the International Standard Atmosphere (ISA), which statement about density variation with altitude in an isothermal layer is correct?
A multistage axial compressor, with overall isentropic efficiency of \(0.83\), compresses air at a stagnation temperature \(T_{01}=300\ \text{K}\) through a pressure ratio of \(10{:}1\). Each compressor stage is similar, and the stagnation temperature rise across each stage is \(20\ \text{K}\). Assume \(C_p=1005\ \text{J\,kg}^{-1}\text{K}^{-1}\) and \(\gamma=1.4\). How many stages are there in the compressor?
A turbojet–powered aircraft flies at \(V_0=250\ \text{m s}^{-1}\). The (uninstalled) thrust is \(T=60{,}000\ \text{N}\). Fuel heating value is \(44\times 10^{6}\ \text{J kg}^{-1}\); fuel flow is \(\dot m_f=3\ \text{kg s}^{-1}\). The engine thermal efficiency is \(35\%\). Exit pressure equals ambient. What is the propulsion efficiency (in %)?
Consider a flat plate with a sharp leading edge in a uniform flow of speed \(U\). The free stream is steady, incompressible and laminar. At a fixed streamwise station \(L\) from the leading edge, the boundary–layer thickness is \(\delta\). How does \(\delta\) vary with \(U\)?
Attached weak oblique shocks over the same wedge are sketched for three different upstream Mach numbers \(M_1, M_2, M_3 > 1\). Which ordering is TRUE?
Air at Mach number \(M=2\) expands around a convex corner to \(M=3\). What is the angle \(\delta\) between the forward and rearward Mach lines of the Prandtl–Meyer expansion fan (in degrees)? Given \(\nu(3)=49.76^\circ\) and \(\nu(2)=26.38^\circ\).
The figure shows two yield loci for an isotropic material in the \((\sigma_I,\sigma_{II})\) plane. Here \(\sigma_I,\sigma_{II}\) are principal stresses and \(\sigma_Y\) is the uniaxial tensile yield stress. Which statements are correct?
Which of the following statements about absolute ceiling and service ceiling for a piston–propeller aircraft is/are correct?
