Fluid Mechanic Integration

  • Thread starter chronicals
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  • #1
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Homework Statement


For turbulent flow in a smooth, circular tube with a radius R, the velocity profile varies according to the following expression at a Reynolds number of about 10^5.

Vx= Vxmax * [(R-r)/R)]^(1/7)

where r is the radial distance from the center and Vmax the maximum velocity at the center. Derive equation relating the average velocity ( bulk velocity ) Vav to Vmax for an incompressible fluid.
( Hint: The integration can be simplified by substitution z for R-r )


Homework Equations





The Attempt at a Solution


i don't know which equation i should integrate and how?
 

Answers and Replies

  • #2
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I guess the average speed is defined as [tex]<v>=\frac{Q}{A}[/tex] where Q is the volume of fluid passing through the cross section of area A in 1 second. How do you find Q? :wink:
 
  • #3
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I guess the average speed is defined as [tex]<v>=\frac{Q}{A}[/tex] where Q is the volume of fluid passing through the cross section of area A in 1 second. How do you find Q? :wink:
i think working with volume rate is useless
 
  • #4
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Okay, why and what do you think of the solution?
 

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