Ch 6. Modeling and Similitude     Multimedia Engineering Fluids
Dimensional
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Author(s):
Chean Chin Ngo
Kurt Gramoll
 
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FLUID MECHANICS - CASE STUDY
    Introduction


Deflection of a Cantilever Beam

   To illustrate that dimensional analysis introduced in fluid mechanics can also be used in other engineering problems (e.g., statics, dynamics and solid mechanics), students are challenged to find the important dimensionless parameters governing the deflection of a circular cantilever beam due to an applied force at its tip, as shown in the figure.
   
  Questions
   

Determine the dimensionless parameters involved using dimensional analysis.

     
    Approach

 
  • First, list all the parameters of the problem. Hint: One of the parameters is the modulus of elasticity (E) , which is a material property of the beam.
  • Determine the number of basic dimensions involved.
  • Find the number of pi terms using Buckingham Pi theorem.
  • Determine the pi terms.
     
   
 
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