Consider steady, incompressible, parallel, laminar flow of a film of oil falling slowly down an infinite vertical wall. The oil film thickness is h, and gravity acts in the negative z-direction. There is no applied (forced) pressure driving the flow. The oil falls by gravity alone. a) Simplify the continuity equation to show that w = w(x). b) Simplify the Navier-Stokes equations to model this flow field. c) Obtain expression for the liquid velocity profile d) Find the volume flow rate per unit width e) What is the pressure in the oil film ?

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Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.