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What is capillarity? Derive an expression for the ascent of liquid in a capillary. |
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Answer» Solution :The RISE or fall of a liquid in a narrow tube is called capillarity. Let us consider a capillary tube which is held vertically in a beaker containing water, the water rises in the capillary tube to a height h due to surface tension.  The surface tension force `F_(T)` acts along the tangent at the point of contact downwards and its reaction force upwards. Surface tension T, is resolved into two components. (i) Horizontal component T `sintheta` and (ii) Vertical component T `costheta` acting upwards, all along the whole circumference of the meniscus. Tota upward force `=(Tcostheta)(2pir)=2pirTcostheta` Where `THETA` is the angle of contact, R is the RADIUS of the tube. Let `rho` be the density of water and h be the height to which the liquid rises inside the tube. Then, `{:(("the volume of"),("liquid column"),("in the tube,V")):}={:(("volume of the"),("liquid column of"),("radius r height h")):}+{:(("volume of the liquid of radius"),("r and height h-volume of"),("the hemisphere of radius of r")):}` `V=pir^(2)h+(pir^(2)xxr-(2)/(3)pir^(3))` `rArrV=pir^(2)h+(1)/(3)pir^(3)` The upward force supports the weight of the liquid column above the free surface, therefore, `2pirTcostheta=pir^(2)(h+(1)/(3)r)rhog` `rArr""T=((h+(1)/(3)r)rhog)/(2costheta)` If the capillary is a very FINE tube ofradius (i.e., radius is very small) then `(r)/(3)` can be neglected when it is compared to the height h. Therefore, `T=(rrhogh)/(2costheta)` |
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