Viscous liquid, at volume flow rate Q. is pumped through the central opening into the narrow gap between the parallel disks shown. The flow rate is low, so the flow is laminar, and the pressure gradient due to convective acceleration in the gap is negligible compared with the gradient caused by viscous forces (this is termed creeping flow). Obtain a general expression for the variation of average velocity in the gap between the disks. For creeping flow, the velocity profile at any cross section in the gap is the same as for fully developed flow between stationary parallel plates. Evaluate the pressure gradient, dp/dr, as a function of radius. Obtain an expression for p(r). Show that the net force required to hold the upper plate in the position shown is

The laminar flow takes place between closely spaced parallel plates as shown in figure below. u > V y Ľ The velocity profile is given by u = v. The gap height h is 5 mm and the space is filled with oil (specific gravity = 0.86, viscosity μ = 2 x 10-4 N-s/m²). The bottom plate is stationary and the top plate moves with a steady velocity of v= 5cm/s. The area of the plate is 0.25 m². The rate of rotation of a fluid particles is given by

Consider a system where a horizontal, laminar, separated flow of air and water at 100 kPa pressure and 20 C temperature are moving between two infinitely-sized parallel plates. The water flow is not forced, but is carried along by the air flow. The 'superficial velocity' of the air is 0.1 m/s (superficial velocity is volume flow rate / flow area, representing the average velocity of the flow). The depth of the water film is 2 mm and the thickness of the air layer is 5 mm. Use the multiphase balance equations and interfacial boundary conditions to derive the velocity profile in the air and water, with y=D0 being the interface between the two.