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Ascent Formula

When one end of capillary tube of radius r is immersed into a liquid of density d which wets the sides of the capillary tube (water and capillary tube of glass), the shape of the liquid meniscus in the tube becomes concave upwards.
 
50760.png
Fig. 19
 
In Fig. 19,
 
R = radius of curvature of liquid meniscus
T = surface tension of liquid
P = atmospheric pressure
50754.png50748.png
   
Important Points
  • The capillary rise depends on the nature of liquid and solid both, i.e., on Tdθ, and R.
  • The capillary action for various liquid–solid pairs has been shown in Table 5.
    1. 53393.png
       
      Meniscus Angle of contact Level
      Concave θ < 90° Rises
    2. 53387.png
       
      Meniscus Angle of contact Level
      Plane θ = 90° No rise no fall
    3. 53440.png
       
      Meniscus Angle of contact Level
      Convex θ > 90° Fall
  • For a given liquid and solid at a given place, 53477.png[as Tθd, and g are constant]
     
    i.e., lesser the radius of capillary, greater will be the rise and vice versa. This is called Jurin’s law.
  • If the weight of the liquid contained in the meniscus is taken into consideration, then more accurate ascent formula is given by
     
    53471.png
  • In case of capillary of insufficient length, i.e., L < h, the liquid will neither overflow from the upper end like a fountain nor will it tickle along the vertical sides of the tube (Fig. 21). The liquid after reaching the upper end will increase the radius of its meniscus without changing nature such that
     
    hr = Lr  L < h  r > r
53465.png
Fig. 21
  • If a capillary tube is dipped into a liquid and tilted at an angle α from vertical, then the vertical height of liquid column remains same whereas the length of liquid column (l) in the capillary tube increases (Fig. 22).
53626.png
Fig. 22
 
h = l cos α or 53620.png
  • It is important to note that in equilibrium the height h is independent of the shape of capillary if the radius of meniscus remains the same (Fig. 23). That is why the vertical height h of a liquid column in capillaries of different shapes and sizes will be same if the radius ofmeniscus remains the same.
53613.png
Fig. 23

 




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