Fluid Mechanics Workshop

October 22nd, 2012

Worksheet #14: Shell Balance

1)  Given the flow shown below, answer the following questions.

vz=vzr, ∂P∂z+ρgsin α=-K

a.  List all assumptions required to solve for the pressure field, Stress field, and velocity field.

b.  Draw the shell balance. (Don’t forget to include shear stress effects)

c.  Derive the governing differential equation of motion from your shell balance in part (b).

d.  Solve for the pressure field given the following boundary conditions:

  1. X=0, P=P0 + ρgcos(α)
  2. X=L, P=PL+ ρgcos(α)

e.  Solve for the stress field. (come up with your own boundary conditions)

f.  Solve for the velocity field. (come up with your own boundary conditions)

g.  What is the maximum velocity, and where is its location?

h.  What is the drag force in the z-direction of the fluid on the tube?