# 3.1.5 - What drives water flow?

Water flows throughout the plant in three different ways: (a) in bulk, (b) by diffusion in a liquid, and (c) by diffusion as a vapour. Different mechanisms are involved in these three types of flow.

Bulk flow is driven by gradients in hydrostatic pressure. It is much faster than diffusive flow because the molecules are all travelling in the same direction and hence their movement is cooperative. This is the flow that occurs in xylem vessels, in the interstices of cell walls, and in water-filled pores in soil. The resistance to such flow depends very strongly on the size of the flow channels.

Tall trees and fast-growing cereal crops like maize have large xylem vessels, of 100 µm in diameter or more. Flow rates are fast because the rate of volume flow increases in proportion to the fourth power of the radius for a given pressure gradient. Volume flow rate (m3s-1) in a cylindrical tube of radius $r$ is proportional to $r^4$ and to the gradient in pressure along the tube, and inversely proportional to the viscosity $η$ (Pa s) (Poiseuille’s Law)

$\text{Volume flow rate} = \left(\frac{\pi r^4}{8\eta}\right) * \left(\frac{\Delta P}{\Delta x}\right) \tag{6}$

Where $η$ is the solution viscosity and $ΔP/Δx$ (Pa m-1)is the gradient in hydrostatic pressure. From equation (5) we understand that wide tubes are enormously more effective than narrow tubes. The importance of the relationship between tube radius and conductive efficiency becomes apparent when we examine long distance transport of water through the xylem (Section 3.2).

Diffusive flow in the liquid phase is driven by gradients in osmotic pressure. It is much slower than bulk flow because the net flows of solute and water molecules are in opposite directions and therefore impede each other. Where two liquid phases are separated by a semi-permeable membrane the flow of water across the membrane to the phase with the higher osmotic pressure is essentially diffusive, and the flow is driven by the difference in water potential across the membrane.

Vapour flow, for example through the stomata, is driven by gradients in vapour concentration, which are usually expressed in terms of partial pressure, but are nevertheless mechanistically concentrations.

As water in the transpiration stream moves from the soil to the roots, through the plant, and out through the stomata, all three types of flow are involved at various stages.