(10.83) |

According to Equations (A.175) and (A.176), we can automatically satisfy the incompressibility constraint (10.79) by writing (see Section 7.4)

where is the Stokes stream function (i.e., ). It follows that

(10.85) | ||

(10.86) |

Moreover, according to Section C.4, , and

where (see Section 7.4)

Hence, given that , we can write

It follows from Equations (A.176) and (A.178) that

Thus, by analogy with Equations (10.84) and (10.89), and making use of Equations (A.173) and (A.177), we obtain

(10.91) |

Equation (10.82) implies that

(10.92) |

which is the governing equation for axisymmetric Stokes flow. In addition, Equations (10.81) and (10.90) yield

(10.93) |