Basic fluid mechanics - Aerodynamics - Aerospace Engineering Previous Year Questions

In a low-speed airplane, a venturimeter with 1.3:1 area ratio is used for airspeed measurement. The airplane’s maximum speed at sea level is 90 m/s. If the density of air at sea level is 1.225 kg/m³, the maximum pressure difference between the inlet and the throat of the venturimeter is ____ kPa (rounded off to two decimal places).

The following equation with respect to \(\varphi(x, t)\), where \(a\) is a non-zero constant, represents ______.
\[\frac{\partial \varphi}{\partial t} + a \frac{\partial \varphi}{\partial x} = 0\]

The state of stress at a point in a 2-D body, in the \(x-y\) Cartesian coordinate system, is represented in matrix form as \([\sigma]\). The transformation matrix \([Q]\) rotates the coordinate system to a new \(x'-y'\) Cartesian coordinate system. Select the CORRECT option(s) that represent(s) the state of stress in the new coordinate system.

The vortex shedding frequency behind a landing gear model is found to be 50 Hz when tested in a wind tunnel operating at 5 m/s. If the actual landing gear size is 10 times that of the model, and it is designed to operate at 50 m/s, then the expected vortex shedding frequency behind it is _______ Hz (rounded off to the nearest integer).

Consider a unit square body as shown in the figure below. The body is subjected to the deformation field \(u = -ay\) and \(v = ax\), where 'a' is a constant. Due to the application of this deformation field, the body undergoes ______ in the \(x-y\) plane.

An experimental study is planned to map out the low-Reynolds number incompressible steady two-dimensional aerodynamic characteristics of a promising novel airfoil. The operational parameters of the problem are the speed, density and viscosity of the freestream, the chord of the airfoil and its angle of attack. If the objective is to achieve this with the minimum number of test runs \( N_{min} \) while taking 10 equally-spaced test values of each independent parameter of the problem in a suitable range, then \( N_{min} \) is ________.

An object of mass 1 kg is launched with an initial speed of \( v_o \) into a large tank filled with a viscous liquid. The liquid exerts a resistive force (drag) of the form \( D = \alpha v \) on any object that is moving inside it, where \( v \) is the instantaneous speed of the object and \( \alpha = 1 \) kg/s. If the effect of gravity is ignored, the time taken by the object to slow down to the speed \( v_o / 2 \) is __________ s (rounded off to 2 decimal places).
Assume that the tank is sufficiently large for the above deceleration to happen inside the tank.

A centrifugal compressor has a constant-width radial diffuser. The diameters at the diffuser inlet and outlet are 0.2 m and 0.3 m, respectively. The flow at the diffuser inlet and outlet is assumed to be steady and uniform. The average velocity at the diffuser inlet and outlet are \((60 \hat{e}_r + 75 \hat{e}_\theta) \text{ m/s}\) and \((u \hat{e}_r + 50 \hat{e}_\theta) \text{ m/s}\), respectively. If the flow through the diffuser is treated as steady and incompressible, the value of \(u\) is __________ (rounded off to the nearest integer).