# Osmotic flow of water across membrane

Given an osmotic pressure across a semipermeable membrane, water will cross the membrane with a particular rate of volume transport (mL/s).

The flux per unit area, $$J_w$$, of water across a membrane is proportional to the difference in pressure between the two sides, $$\Delta p_{osm}$$. There is also an empirically determined parameter, $$L_p$$, called the hydraulic conductivity, a measure of how permeable a given membrane material is to flows.

$\displaystyle J_w=\Delta p_{osm}L_p$

Assuming that the pressure difference between the water-filled xylem and sap-filled phloem is dominated by the osmotic pressure, what will be the overall rate of water flow from xylem to phloem (in mL/s)?

Assumptions

• The xylem and phloem are packed such that the entire surface of the phloem is adjacent to neighboring phloem surface and vice versa.
• The osmotic pressure is $$\Delta p_{osm} =10^6$$ Pa.
• The length of the phloem is given by $$l_p$$ = 1 cm, and the radius of the phloem is $$r_p = 20 \mu$$m.
• The value of the hydraulic permeability is $$L_p=5 \times 10^{-14}$$ m/s/Pa

Illustration by Maxicat Rhododendron

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