Use a control volume analysis to verify that the flow over a sphere defined in Problem 6.13 conserves mass. How could you use the vector concept of a gradient to simplify this problem? Problem 6.13...

Use a control volume analysis to verify that the flow over a sphere defined in Problem 6.13 conserves mass. How could you use the vector concept of a gradient to simplify this problem?

Problem 6.13

Creeping (very low Re) flow around a sphere is illustrated in Figure P6.9. In spherical coordinates the Eulerian velocity field is given by

(a) Determine the location of the maximum fluid velocity in this flow field.

(b) Determine the position of the minimum fluid velocity in this flow field.

(c) Sketch (by hand or with a computer) the velocity profile as a function of the coordinate r (at θ = φ = 0) for this flow field.