Presentation on theme: "Navier-Stokes: We All Know What Happens When You Assume"— Presentation transcript:
1 Navier-Stokes: We All Know What Happens When You Assume Stephen McMullanBIEN 301
2 Problem 4.80Oil of density r and viscosity m, drains steadily down the side of a vertical plate.After a development region near the top of the plate, the oil film will become independent of z and of constant thickness d.
4 ProblemSolve the Navier-Stokes equation for w(x), and sketch its approximate shape.Suppose that film thickness d and the slope of the velocity profile at the wall are measured with a laser-Doppler anemometer (Chapter 6). Find an expression for oil viscosity m as a function of (r, d, g, [dw/dx]wall).
5 Assumptions Newtonian Viscous Incompressible Liquid Steady Fully developedNo slip condition at the plate surfacew = w(x)No shear due to pa