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# Oil spills on water can be removed by lowering a moving belt of width W into the water The belt moves upward and skims the oil into a reservoir aboard the ship as shown in the figure below width

Oil spills on water can be removed by lowering a moving belt of width into the water. The belt moves upward and skims the oil into a reservoir aboard the ship as shown in the figure below.

a) Show that the velocity profile and the volumetric flow rate are given by

b) Determine the belt speed that will give a zero volumetric flow rate and specify the design criteria for positive and negative flow rates.

9.4 For laminar flow of a Newtonian fluid in a circular pipe, the velocity profile is parabolic and Eqs. (9.1-80) and (9.1-84) indicate that

Eqs. (9.1-80)

Eqs. (9.1-84)

In the case of a turbulent flow, experimentally determined velocity profiles can be represented in the form

where depends on the value of the Reynolds number. Show that the ratio <vz>/vmax is given as (Whitaker, 1968)

 Re n vz/vmax 4×103 6 0.79 1×105 7 0.82 3×106 10 0.87

This is the reason why the velocity profile for a turbulent flow is generally considered “flat” in engineering analysis.

Jul 25 2020 View more View Less