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Question
Sat February 09, 2013 By: Arathi M

# Derive Ascent formula.

Sat February 09, 2013

As the liquid rises, its weight increases and at a particular height say ' , the force due to surface tension in the upward direction becomes equal to the weight of the liquid in the downward direction. The liquid then ceases to rise.
The weight of the liquid in the capillary, W = (Volume of cylindrical liquid column of height + Volume of the liquid in meniscus) ? r ? ,
where is the acceleration due to gravity.
Now, volume of cylindrical liquid column = p
For convenience, we consider the meniscus as to be hemispherical in shape.
Volume of the liquid in the meniscus = Volume of cylinder of height and radius - Volume of hemisphere

 = p r 2 ? r - 1 4 p r 3 = p r 3 - 2 p r 3 2 3 3

 = 1 p r 3 3

 Weight of the liquid in the capillary W = p r 2 h + 1 p r 3 ? r ? g 3
 Liquid Meniscus
 W = p r 2 h + r ? r ? g ?(2) 3

In the equilibrium position, F = W
Equating equations (1) and (2), we get

 2 p r ? T cos q = p r 2 h + r ? r ? g 3

T =

 r h + r ? r ? g 3

?(3)

2cos q

 When the tube is of very fine bore, r << h . 3
 Capillary rise

 Neglecting r as compared to h in equation (3), we get, 3

 T = h r gr 2cos q

 h = 2Tcos q r r g

This expression is called the ascent formula.

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