osmotic pressure , we found a relationship between the pressure across a membrane and the flux of liquid across it, .
In calculating theWe can flip this relation around and expose a powerful perspective:
Does this look familiar?
In fact, this has the same form as Ohm's circuit law, .
Here, our rate of volume flow is akin to current, the osmotic pressure takes the place of voltage, and the resistance is given by the inverse of hydraulic conductivity times surface area of the membrane. I.e.
In any situation where we have a flow resulting from a pressure, we can characterize the circuit element (membrane, pipe, etc.) according to this ratio ( ), which we call the hydraulic resistance .
Calculate the hydraulic resistance (in Pascal seconds per meter ) of the semipermeable membrane connecting xylem and phloem,
Assumptions
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If one models the membrane as a cylinder, then all we have is simple algebra:
R = 2 π r h L p 1 = 2 π × 2 0 × 1 0 − 6 0 . 1 × 5 × 1 0 − 1 4 1 = 1 . 5 9 × 1 0 1 8 Pa s/m 3 .