Navier-Stokes Solutions - Differential Analysis - Engineering Sciences Previous Year Questions

A two-dimensional laminar viscous liquid film of constant thickness (h) steadily flows down an incline as shown in figure. Acceleration due to gravity is g. If the velocity profile in the liquid film is given as, \(u = ky(2h - y); v = 0\), the value of constant k is

In a Cartesian coordinate system, a steady, incompressible velocity field of a Newtonian fluid is given by
\(V = u_0(1-ay^2)\mathbf{i}\)
Here, V is the velocity vector in m/s, i is the unit vector in the x-direction, \(u_0\) is a positive, real constant (in m/s), and a is a positive, real constant (in m-2). The viscosity of the fluid is μ (in Pa·s). The absolute value of the pressure gradient (in Pa/m) is

Consider steady fully-developed incompressible flow of a Newtonian fluid between two infinite parallel flat plates. The plates move in the opposite directions, as shown in the figure. In the absence of body force and pressure gradient, the ratio of shear stress at the top surface \(y = H\) to that at the bottom surface \(y = 0\) is

A two-dimensional incompressible flow field is defined as,
\(\vec{V}(x, y) = (Axy)\hat{i} + (By^2)\hat{j}\)
where, \(A\) and \(B\) are constants. The dynamic viscosity of the Newtonian fluid is \(\mu\). In the absence of body force, which among the following expressions represents the pressure gradient at the location (5, 0) in the concerned flow field?