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Capillary action in trees can transport water from the roots to the tree's branches. The capillaries (Xyelem) in a certain tree have radii of approximately 6 micrometers (1 micrometer=1x10-6 m). How high (in meters) above the ground would water rise in this tree? Assume Xylem is perfectly hydrophilic, meaning the contact angle between water and the Xylem tubes is 0o, and the density of water is 1000 kg/m3. The surface tension of water at room temperature is about 0.070 N/m. (Hence, can capillary action be the only mechanism that transports water to the tops of trees?)

Respuesta :

Answer:

[tex]h=14.2857\,m[/tex]

Explanation:

Given:

radius of capillary, [tex]r=10^{-6}\,m[/tex]

angle of contact, [tex]\theta=0^{\circ}[/tex]

density of water, [tex]\rho=1000\,kg.m^{-3}[/tex]

surface tension of water, [tex]T=0.07 \,N.m^{-1}[/tex]

height, h = ?

We have the equation for the height of meniscus as:

[tex]h=\frac{2T.cos\, \theta}{\rho.g.r}[/tex]

[tex]h=\frac{2\times 0.07\times cos\,0^{\circ}}{1000\times 9.8\times 10^{-6}}[/tex]

[tex]h=14.2857\,m[/tex]

No, the capillary action alone cannot be the mechanism of water transportation to the top of the trees. Transpiration also creates a suction pressure in the xylem complementary to the ascent of sap and cohesion of water being the other causes of movement of water up in the plants.

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