# Osmotic flow of water across membrane

**Classical Mechanics**Level 4

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