Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev

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Computer Science Engineering (CSE) : Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev

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Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev
Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev
Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev
Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev

 

Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev   (3.7.5) 


Variation of CD (Drag-coefficient) 

In laminar zone, Stoke’s law is applicable  

Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev  (3.7.6) 

Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev   (3.7.7) 

For transition zone, Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev

Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev (3.7.8) 

 

For turbulent zone, CD is independent of Re and CD=0.4 

For non-spherical particles, formula for Reynold number and settling velocity calculation are modified using the shape factor ( φ ) [1]: 

Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev  (3.7.9) 

Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev   (3.7.10) 

Problem 3.7.1: A sand particle has an average diameter of 1 mm and a shape factor of 0.90 and a specific gravity of 2.1, determine the terminal velocity of the particle settling in water at 20 oC (kinematic viscosity of water=1.003×10-6 m2/s and specific gravity=1). Drag coefficient can be computed using the following equation:   

Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev

Solution: kinematic viscosity(V) = Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev

Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev

Settling velocity using stokes law is: 

Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev

Since Re>1, therefore, Newton’s law should be used for finding terminal velocity in transition zone. For initial assumption of settling velocity, stoke’s law is used. This initially assumed velocity is used to determine the Reynold number which is further used to find settling velocity. This iterative procedure is repeated till initial assumed velocity is approximately equal to settling velocity calculated from Newton’s equation.

Initial drag coefficient is calculated as: 

Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev

Now, iterative procedure is continued:  

Setting and Sedimentation (Part - 1) Computer Science Engineering (CSE) Notes | EduRev     

Final settling velocity=0.1419 m/s. 

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