Determine expressions for the mass, volume, and momentum convective flux vectors for the flow described in Problem 6.4. Also calculate the total volume flux through a cross section of the pipe....

Determine expressions for the mass, volume, and momentum convective flux vectors for the flow described in Problem 6.4. Also calculate the total volume flux through a cross section of the pipe.

Problems 6.4

The Eulerian velocity field for upward flow through a simple cylindrical pipe of radius R_P
is given by

where W₀
is a constant.

(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 radial coordinate r (at constant z) for this flow field.