For the liquid in the interspace between α and η,
| φ | = | m ch 2 (η − α) sin 2ξ |
| φ1 | ¼ Rc2 sh 2η sin 2ξ (a2 − b2) / (a2 + b2) |
= 1/th 2 (η − α) th 2η;
(8)
and the effective k2 of the liquid is reduced to
¼ c2/th 2 (η − α) sh 2η,
(9)
which becomes ¼ c2/sh 2η = 1⁄8 (a2 − b2)/ab, when α = ∞, and the liquid surrounds the ellipse η to infinity.
An angular velocity R, which gives components −Ry, Rx of velocity to a body, can be resolved into two shearing velocities, −R parallel to Ox, and R parallel to Oy; and then ψ is resolved into ψ1 + ψ2, such that ψ1 + ½Rx2 and ψ2 + ½Ry2 is constant over the boundary.
Inside a cylinder