External Flows - Engineering Sciences Previous Year Questions

The dimensionless velocity profile is

Let \( \delta \), \( \delta_1 \) and \( \delta_2 \) denote respectively the boundary-layer thickness, displacement thickness and the momentum thickness for laminar boundary layer flow of an incompressible fluid over a flat plate. The correct relation among these quantities is

Consider an incompressible, laminar flow past a circular cylinder of diameter \( d \). The flow is uniform at the far upstream. Which one of the following figures typically represents the wake velocity profile just downstream of the cylinder?

Which one of the following is true at the point of separation of a boundary layer:

Consider the following figures shown below. The objects are marked as A1, A2, B1, B2 and C1, C2 and the flow directions over these objects are shown by the respective arrow placed to the left of the object. Freestream velocities are same for all the cases. Amongst these objects, A1, A2, B1 and C1 are having smooth surfaces while B2 and C2 are having rough surfaces. Reynolds number is such that flow over rough surfaces become turbulent and flow over smooth surfaces can be considered laminar. All the airfoils can be considered as thin slender airfoil. Among the statements (i) to (vi) made about the drag of these objects which is/are correct?
(i) Drag of object A1 is less than drag of object A2.
(ii) Drag of Object A1 and A2 are same.
(iii) Drag of Object B1 is more than drag of object B2.
(iv) Drag of object B2 is more than drag of object B1.
(v) Drag of Object C1 is more than drag of object C2.
(vi) Drag of object C2 is more than drag of object C1.

A spherical bubble of radius \( r \) is rising upward with a constant velocity \( U \), in quiescent water of dynamic viscosity \( \mu \). The density of air and water are denoted by \( \rho_a \) and \( \rho_w \), respectively, and \( g \) is acceleration due to gravity. The bubble motion is such that, the Reynolds number, \( Re << 1 \). The density of air can be neglected in comparison to the water density (\( \rho_a << \rho_w \)). Which one of the following expressions is TRUE for the density of water?