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FLUID MECHANICS - CASE STUDY SOLUTION


Capillary Action



 

The height of the water column is given as a function of the contact angle (θ), radius of the tube (R), density (ρ) and surface tension (σ) of the liquid as follows:

     h = 2σcosθ / ρgR

For water in contact with a clean glass, the contact angle is zero, hence the equation reduces to

     h = 2σ / ρgR

For water at 30oC, the surface tension and density are 0.0712 N/m and 995.7 kg/m3 respectively, as noted in the theory page.

For a tube with a radius of 1 mm:

     h = 2(0.0712)(106)/(995.7)(9.8)(1)
       = 14.6 mm

For a tube with a radius of 10 mm:

     h = 2(0.0712)(106)/(995.7)(9.8)(10)
       = 1.46 mm

Note that the water rise in the capillary tube decreases with an increase of the radius of the tube.

   
 
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