Two-Dimensional Uniform Flow

(5.27) |

which corresponds to flow at the uniform speed in a fixed direction that subtends a (counter-clockwise) angle with the -axis. It follows, from Equations (5.5) and (5.6), that the stream function for steady uniform flow takes the form

When written in terms of cylindrical coordinates, this becomes

(5.29) |

Note, from Equation (5.28), that . Thus, it follows from Equation (5.10) that uniform flow is irrotational. Hence, according to Section 4.15, such flow can also be derived from a velocity potential. In fact, it is easily demonstrated that

(5.30) |