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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.

  width= 

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

  width= 

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)

 width=

Eqs. (9.1-84)

 

 width=

 width= 

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

  width= 

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

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