Consider a cell with an initial water potential of –0.2 MPa, submerged in pure water. From this information we know that water will flow into the cell and that the driving force is ΔΨ = 0.2 MPa, but what is the initial rate of movement? The rate depends on permeability of the membrane to water, a property usually called the hydraulic conductivity (Lp) of the membrane (see textbook Figure 3.13).

Driving force, membrane permeability, and flow rate are related by the following equation:

Hydraulic conductivity expresses how readily water can move across a membrane and has units of volume of water per unit area of membrane per unit time per unit driving force (for instance, m³ m^–2 s^–1 MPa^–1 or m s^–1 MPa^–1). The larger the hydraulic conductivity, the larger the flow rate. In textbook Figure 3.13, the hydraulic conductivity of the membrane is 10^–6 m s^–1 MPa^–1. The transport (flow) rate (J_v) can then be calculated from the following equation:

where J_v is the volume of water crossing the membrane per unit area of membrane and per unit time (m³ m^–2 s^–1 or, equivalently, m s^–1). Please note that this equation assumes that the membrane is ideal—that is, that solute transport is negligible and water transport is equally sensitive to ΔΨ_s and ΔΨ_p across the membrane. Nonideal membranes require a more complicated equation that separately accounts for water flow induced by ΔΨ_s and by ΔΨ_p (Nobel 1999).

In our example, J_v has a value of 0.2 × 10^–6 m s^–1. Note that J_v has the physical meaning of a velocity. We can calculate the flow rate in volumetric terms (m³ s^–1) by multiplying J_v by the surface area of the cell.

The resulting value is the initial rate of water transport. As water is taken up, cell Ψ increases and the driving force (ΔΨ) decreases. As a result, water transport slows with time. As elaborated on pp. 94–95 of the textbook, the rate approaches zero in an exponential manner (see Dainty 1976).