List of practice Questions

An airplane (5500 kg) initiates a pull-up at 225 m/s with curvature radius 775 m. CG, CP, and tail point T are shown. Thrust and drag cancel. Tail force is vertical. Find the tail force (round to one decimal place). 

A 3 m × 1 m signboard is subjected to a wind pressure of 7.5 kPa. It is supported by a hollow square pole of outer dimension 250 mm and inner dimension $d$ (unknown). The yield strength is 240 MPa. Find $d$ (round off to nearest integer).

Two cantilever beams AB and DC touch at their free ends through a roller. Both beams have a 50 mm × 50 mm square cross section and modulus \(E = 70\ \text{GPa}\). Beam AB carries a UDL of 20 kN/m. Determine the compressive force at the roller (round off to one decimal place). 

A two-cell wing box has wall thickness 1.5 mm and shear modulus \(G = 27\ \text{GPa}\). A torque of 12 kNm is applied. Determine the shear stress in wall AD (round off to one decimal place). 

At the design conditions of a single-stage axial compressor, the blade angle at rotor exit is \(30^\circ\). The absolute velocities at rotor inlet and exit are 140 m/s and 240 m/s, respectively. The relative flow velocities at rotor inlet and exit are 240 m/s and 140 m/s, respectively. Find the blade speed \(U\) at the mean radius (round off to two decimal places). 

A rigid horizontal bar ABC is supported by two columns BD and CE. BD is fixed at D, CE is pinned at E. A load $P$ is applied at distance $a$ from $B$. The columns are steel with $E = 200$ GPa and cross-section $1.5 \text{ cm} \times 1.5 \text{ cm}$. The lengths are: BD = 75 cm, CE = 125 cm. The value of $a$ for which both columns buckle simultaneously is \(\underline{\hspace{2cm}}\) cm (round off to one decimal place). 

A large water tank is fixed on a cart with wheels and a vane. The cart is tied to a fixed support with a rope. Water exits through a 5 cm diameter hole as a 10 m/s jet which is deflected by the vane by \(60^\circ\). The velocity of the jet after deflection remains 10 m/s. Density of water is \(1000\ \text{kg/m}^3\). The tension in the rope is \(\underline{\hspace{1cm}}\) N (round off to one decimal place). 

Consider a boundary-layer velocity profile: 
\[ \frac{u}{U} = \begin{cases} \left( \frac{y}{\delta} \right)^2 & y \le \delta \\ 1 & y > \delta \end{cases} \] The shape factor (ratio of displacement thickness to momentum thickness) is \(\underline{\hspace{2cm}}\) (round off to 2 decimal places).

For the matrix \[ \begin{bmatrix} 3 & 1 & 2 \\ 2 & -3 & -1 \\ 1 & 2 & 1 \end{bmatrix} \] find the ratio of the product of eigenvalues to the sum of eigenvalues (round off to nearest integer).

A conventional fixed-wing aircraft, with a horizontal tail and vertical fin, in steady and level flight is subjected to small perturbations. Which of the following statement(s) is/are true?

A shock moving into a stationary gas can be transformed to a stationary shock by a change in reference frame, as shown in the figure. Which of the following is/are true relating the flow properties in the two reference frames? 

To estimate aerodynamic loads on an aircraft flying at 100 km/h at standard sea-level conditions, a one-fifth scale model is tested in a variable-density wind tunnel ensuring similarity of inertial and viscous forces. The pressure used in the wind tunnel is 10 times the atmospheric pressure.
Assuming ideal gas law to hold and the same temperature conditions in model and prototype, the velocity needed in the wind tunnel test-section is ______________. 
 

The figure shows schematic of a set-up for visualization of non-uniform density field in the test section of a supersonic wind tunnel. This technique of visualization of high speed flows is known as: 

Which of the following statement(s) is/are true about the function defined as \( f(x)= e^{-x} \lvert \cos x \rvert \) for \( x>0 \)?