(7.29) |

where is a spherical coordinate. Consider a spherical surface of radius whose center coincides with the source. In a steady state, the rate at which fluid crosses this surface must be equal to the rate at which the source emits fluid. Hence,

(7.30) |

which implies that

(7.31) |

Of course, .

According to Equations (7.4), the Stokes stream function associated with a point source at the origin is such that , and is obtained by integrating

(7.32) |

It follows that

It is clear, from a comparison of Equations (7.10) and (7.33), that the previously specified flow pattern is irrotational. Hence, this pattern can also be derived from a velocity potential. In fact, by symmetry, we expect that . The potential itself is obtained by integrating

(7.34) |

It follows that