List of top Aerodynamics Questions on Fluid Mechanics asked in GATE AE

A rotational velocity field in an air flow is given as $ \vec{V} = a y \hat{i} + b x \hat{j} $, with $ a = 10 \, \text{s}^{-1} $, $ b = 20 \, \text{s}^{-1} $. The air density is 1.0 kg/m$^3$ and the pressure at $ (x, y) = (0, 0) $ is 100 kPa. Neglecting gravity, the pressure at $ (x, y) = (6 \, \text{m}, 8 \, \text{m}) $ is _________ kPa (rounded off to the nearest integer).

Consider a solid cylinder housed inside another cylinder as shown in the figure. Radius of the inner cylinder is 1 m and its height is 2 m. The gap between the cylinders is 5 mm and is filled with a fluid of viscosity $ 10^{-4} $ Pa-s.
The inner cylinder is rotating at a constant angular speed of 5 rad/s while the outer cylinder is stationary. Friction at the bottom surfaces can be ignored. Velocity profile in the vertical gap between the cylinders can be assumed to be linear.
The driving moment required for the rotating motion of the inner cylinder is _________ Nm (rounded off to two decimal places).

In a converging duct, area and velocity at section P are 1 m$^2$ and 15 m/s, respectively. The temperature of the fluid is 300 K.
Air flow through the nozzle can be assumed to be inviscid and isothermal. Characteristic gas constant is 287 J/(kg-K) and the ratio of specific heats is 1.4 for air.
To ensure that the air flow remains incompressible (Mach number, $ M \leq 0.3 $) in the duct, the minimum area required at section Q is _________ m$^2$ (rounded off to two decimal places).

Across an oblique shock wave in a calorifically perfect gas,

Consider steady, two-dimensional, incompressible flow over a non-porous flat plate as shown in the figure. For the control volume PQRS, the speed $u_{\infty}$ at section PQ is uniform and the speed at section RS is given by $u(y)=A_0\left(\frac{y}{h}\right)^n$, where $n$ is a positive integer. The value of $A_0$ for which the flow through section PS will vanish is:

Consider the velocity distribution $u(y)$ shown in the figure. For two adjacent fluid layers L1 and L2, the viscous force exerted by L1 on L2 is _________.

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).

The figure shows three glasses P, Q and R with water and floating ice cube. Glass P has a solid ice cube, glass Q has an ice cube with a small solid steel ball embedded in it and glass R has an ice cube with an air bubble. After the ice cube melts, the level of water in glasses P, Q and R, respectively: