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What is capillary action ? Derive the formula for rise of liquid in a capillary tube immersed vertically in liquid. |
Answer» Solution :The phenomenon, the surface tension of liquid plays an important role. Capillary rise , (a) SCHEMATIC picture of a narrow tube immersed water .(b) Enlarged picture near interface. The word Capilla means hair in Latin . If the tube were hair thin the rise WOULD be very lrge for liquid of angle of contact is acute (This type tubeis known as capillary tube) In figure , consider a vertical capillary tube of circular cross action (radius a) inserted into an open vessel of water . The contact angle between water and glass is acute .`(thetalt(90^(@))`. Thus the surface of water in the capillary is concave .This means that there is a pressure difference between in two SIDES of the TOP surface. `P_(i)-P_(0)=(2S)/(r)` where r is radius of meaniscus ..(1) From figure `costheta=(a)/(r)` `thereforer=(a)/(costheta)` ....(2) Putting value of equation(2) in (1), `P_(i)-P_(0)=(2s)/(a)costheta`....(3) Hence , the pressure `P_(i)` of the water inside the tube , justat the meniscus (air -water interface) is less thenthe atmospheric pressure `P_(0)`. According to figure (a) , consider two points A and and B . they must be at the same pressure, Hence , here `P_(B)=P_(A)` ....(4) but `P_(B)=` pressure on convex surface of meniscus + pressure of liquid column of height h. `thereforeP_(B)=P_(0)+hrhog` and `P_(A)=P_(i)"" (because` From equ .(4) and (5))Where `rho` is the density of liquid and h is the height of liquid column in capillary. `thereforeP_(i) -P_(0)=hrhog` From equation (3),(4), `hrhog=(2Scostheta)/(a)` `h=(2Scostheta)/(arhog)` As theradius a is small , the height of column is more . If meniscus is convex (for example mercury), means `costheta` is negative , liquid depressed in capillary. |
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