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The sap in trees, which consists mainly ...

The sap in trees, which consists mainly of water in summer, rises in a system of capillaries of radius `r = 2.5 xx 10^(-5) m.` The surface tension of sap is `T =7.28 xx 10^(-2) Nm^(-1)` and the angle of contact is `0^@.` Does surface tension alone ac count for the supply of water to the top of all trees ?

Text Solution

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Given, radius (r) `=2.5 xx 10^(-5) m`
Surface tension (S) `=7.28xx 10^(-2)` N/m
Angle of contact `(theta)=0^(@)`
The maximum height to which sap can rise in tress through capillarity action is given by
`h=(2S cos theta)/(r rho g)` where S=surface tension , `rho`=Density , r=Radius
`=(2xx7.28xx10^(-2)xx"cos" 0^(@))/(2.5xx10^(-5)xx1xx9.8)=0.6` m
This is the maximum height to which the sap can rise due to surface tension. Since, many trees have heights much more than this, capillary action alone cannot account for the rise of water in all trees.
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Knowledge Check

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