Question

Capillarity helps carry water and dissolved nutrients to upper parts of plants through tiny tubules called xylem. Assuming ONLY capillarity is driving fluid flow, (a.) estimate the height water could rise in a tree thru xylem of radius 0.0026 mm; for water, take 𝜎 = 0.07 𝑁 𝑚⁄ and a contact angle 𝜃 = 15º. Obviously, this can’t be the only force involved for water to reach the leaves in large Redwood trees. In reality, two other effects become relevant: (i.) water intake at the roots by diffusion and osmosis creating a “root pressure” as high as 0.6 MPa that pushes water upward and (ii.) evaporation in the leaves creating a negative pressure as low as -2 MPa known as “transpirational pull”. (b.) Using a force balance, re-derive the capillary height equation to account for pressure and estimate the new height water could rise to

          Capillarity helps carry water and dissolved nutrients to upper parts of plants through
tiny tubules called xylem. Assuming ONLY capillarity is driving fluid flow, (a.) estimate
the height water could rise in a tree thru xylem of radius 0.0026 mm; for water, take 𝜎 =
0.07 𝑁 𝑚⁄ and a contact angle 𝜃 = 15º.
Obviously, this can’t be the only force involved for water to reach the leaves in large
Redwood trees. In reality, two other effects become relevant: (i.) water intake at the roots
by diffusion and osmosis creating a “root pressure” as high as 0.6 MPa that pushes water
upward and (ii.) evaporation in the leaves creating a negative pressure as low as -2 MPa
known as “transpirational pull”. (b.) Using a force balance, re-derive the capillary height
equation to account for pressure and estimate the new height water could rise to

Added by Jamie T.

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