Electrorheological (ER) materials are suspensions of specialized, micr
on-sized particles in nonconducting oils. When electric fields are app
lied to ER materials, they exhibit dramatic changes (within milli-seco
nds) in material properties. Pre-yield, yielding, and post-yield mecha
nisms are all influenced by the electric field. Namely, an applied ele
ctric field dramatically increases the stiffness and energy dissipatio
n properties of these materials. A previously known cubic equation whi
ch describes the flow of fluids with a yield stress through a rectangu
lar duct can be applied to annular flow, provided that certain conditi
ons on the material properties are satisfied. An analytic solution and
a uniform approximation to the solution, for the rectangular duct Poi
seuille flow case is presented. A numerical method is required to solv
e the flow in annular geometries. The approximation for rectangular du
cts is extended to deal with the annular duct case.