List of top Engineering Sciences Questions asked in GATE Engineering Sciences

For a steady and incompressible flow, the velocity field \( \vec{V} \) in Cartesian \( (x, y, z) \) coordinate system is given as:
\[ \vec{V} = 5x\hat{i} - Py\hat{j} + 3k\hat{k} \] Here, \( \hat{i}, \hat{j}, \hat{k} \) are unit vectors along \( x, y, z \) directions, respectively and \( P \) is a constant.
Which one of the following options is the correct value of \( P \) that satisfies the conservation of mass for the given velocity field?

Conservation of mass for a steady axisymmetric flow field in the cylindrical \( (r, z) \) coordinates is:
\[ \frac{1}{r} \frac{\partial}{\partial r} (r V_r) + \frac{\partial V_z}{\partial z} = 0 \] Here, \( V_r \) and \( V_z \) are radial and axial components of velocity, respectively.
Which one of the following options is correct if \( \psi \) is the stream function?

Consider the steady, incompressible, and fully developed laminar flow of a fluid through a circular pipe. Here, \( \Delta P \) is the pressure drop in the direction of the flow and \( V \) is the average axial velocity of the fluid at any cross-section. The relation between \( \Delta P \) and \( V \) is:
\[ \Delta P = K V^n \] Here, \( K \) and \( n \) are constants.
Which one of the following options is the correct value of \( n \)?

A doublet is the resulting flow pattern when a sink and a source of equal strength are brought together.
Which one of the following options correctly represents the nature of the product of the strength and the distance between them during approach?

Fluid at a constant flow rate passes through a long, straight, cylindrical pipe that has an axisymmetric convergent section at the end.
Which one of the following options correctly represents the velocity field in the converging section in cylindrical \( (r, \theta, z) \) coordinates?

A sharp flat plate of length \( L \) and infinite width is immersed parallel to a fluid stream having velocity \( u_\infty \).
At a point on the plate, far away from the leading edge and not near the trailing edge, the boundary layer thickness, the displacement thickness, and the momentum thickness are denoted as \( \delta \), \( \delta^* \), and \( \theta \), respectively.
Which one of the following options correctly represents the relation between these thicknesses?