List of top Fluid Mechanics and Mechanical Operations Questions asked in GATE CH

A three-dimensional velocity field is given by $V = 5x^2y\,\mathbf{i} + Cy\,\mathbf{j} - 10xyz\,\mathbf{k}$, where $\mathbf{i},\mathbf{j},\mathbf{k}$ are unit vectors in $x,y,z$ directions. If $V$ describes an incompressible fluid flow, the value of $C$ is
 

A batch settling experiment is performed in a long column using a dilute dispersion containing equal number of particles of type A and type B in water (density 1000 kg m–3) at room temperature.

Type A are spherical particles of diameter 30 μm and density 1100 kg m–3.
Type B are spherical particles of diameter 10 μm and density 1900 kg m–3.
Assuming that Stokes’ law is valid throughout the duration of the experiment, the settled bed would

Seawater is passed through a column containing a bed of resin beads. Density of seawater = 1025 kg m\(^{-3}\)
Density of resin beads = 1330 kg m\(^{-3}\)
Diameter of resin beads = 50 \(\mu\)m
Void fraction of the bed at the onset of fluidization = 0.4
Acceleration due to gravity = 9.81 m s\(^{-2}\)
The pressure drop per unit length of the bed at the onset of fluidization is \(\underline{\hspace{1cm}}\) Pa m\(^{-1}\) (round off to nearest integer).
A fluid is sheared between parallel plates in two experiments, and the required shear stresses are given. Determine the rheological behavior of the fluid.
Consider a steady flow of an incompressible Newtonian fluid through a smooth circular pipe. For turbulent flow, the kinetic energy correction factor is \[ \alpha_{turbulent} = \left(\frac{V_0}{\overline{V}}\right)^3 \frac{2n^2}{(3+n)(3+2n)} \] and the ratio of average velocity to centerline velocity is \[ \frac{\overline{V}}{V_0} = \frac{2n^2}{(n+1)(2n+1)}. \] For n = 7, the value of \(\frac{\alpha_{turbulent}}{\alpha_{laminar}}\) is \(\underline{\hspace{1cm}}\) (round to 2 decimals).
A soil sample was consolidated at a cell pressure of 10 K Pa for 24 hours during a cu test. The cell pressure increases to 30. Now it results in a core water pressure increment of 1 K Pa. Soil failed when the agsist test gradually increased to 50 K Pa. Core water pressure at failure was recorded as 21 K Pa. What is the scamton core water pressure B?