# Summary

### Author

Brendan Choat

### Summary

The following summary concerns hydraulic conductance and conductivity of *stems and roots* but will be expanded to include measurements on leaves, flowers and fruit.

### Definition

*Hydraulic conductance is a measure of the efficiency of bulk flow through a material, and defined as the flow rate per unit pressure driving force.*

### Stems and roots

**Terminology and equations**

Hydraulic conductance (k_{h}) describes the relationship between flow rate (F, kg s^{-1}) and driving force ( P, MPa) for a plant organ (stem or root), ie. what mass flow of water can be achieved for a given pressure drop across the segment (k_{h}= F/ P, kg s^{-1}MPa^{-1}). This measurement can be undertaken from the whole shoot or root system down to a single unbranched twig or fine root. The hydraulic conductance of a segment can be normalized to either the cross sectional sapwood (xylem) area (A_{sw}, m^{2}) or the total leaf area supplied by the measured segment (A_{L}, m^{2}) giving sapwood specific conductance (k_{s}= k_{h}/A_{sw}, kg s^{-1}m^{-2}MPa^{-1}) and leaf specific conductance (k_{L}= k_{h}/A_{L}, kg s^{-1}m^{-2}MPa^{-1}). If there is a single linear flow path then the hydraulic conductance can be normalized to the length (L, m) of the segment giving hydraulic conductivity (K_{h}= F L / ( P), kg s^{-1}m MPa^{-1}). Just as with conductance, hydraulic conductivity can be normalized to A_{sw}or A_{L}: (K_{s}: sapwood-specific conductivity) or to the leaf area supported by the xylem (K_{L}: leaf-specific conductivity): K_{s}= F L / ( P A_{sw}), kg s^{-1}m^{-1}MPa^{-1}; K_{L}= F L/( P A_{L}) kg s^{-1}m^{-1}MPa^{-1}. These two conductivities are inter-related by the ratio of sapwood cross-sectional area to supplied leaf area, a parameter known as the -Huber value’, HV: K_{L}= HV K_{s}. Therefore, HV is a dimensionless variable describing the ratio of sapwood area to leaf area for a given stem. These variable are useful in describing the capacity of stems or roots to supply water to the leaves for a given pressure gradient and the capacity to supply water relative to the investment in sapwood area. **Note on terminology: Conductance and resistance, conductivity and resistivity** Hydraulic resistance (R_{h}) is the reciprocal of k_{h}and has units of MPa s kg^{-1}. Hydraulic resistivity (r_{h}) is the reciprocal of K_{h}with units of MPa s m^{-1} kg^{-1}. Resistances are additive in series while conductances are additive in parallel and expression as either R_{h}or k_{h}will have advantages depending on the questions being studied, eg. R_{h}is useful for understanding how much a series of components contribute to the overall resistance of a system.

### Measurement approaches

For stems and roots, conductance and conductivity can be measured by multiple methods, in the field or lab, for stem segments in vivo, or for excised segments. The choice of method will depend upon the target segment (whole plant, shoot or root system, branched segment, single unbranched stem or root segment) and on the specific questions being asked in the study.

**In vivo methods**

- Sapflow to derive a flow rate using the water potential gradient as the driving force. When using the sapflow method for hydraulic conductance the k
_{s}can be determined as one of several other water use and water relations traits (e.g., whole plant hydraulic conductance, whole plant water use, etc). - Weigh loss off balance (lysimiter) to measure flow rate and water potential gradient as the driving force. This method is often used to measure whole plant transpiration and conductance of potted plants.
- Transpiration to derive flow rate and water potential gradient as the driving force. The transpiration method is relatively simpler, as it depends on leaf-level gas exchange measurements rather than more logistically intense sapflow work.

**Excised segment methods**

**Balance**: This method allows for continuous logging of flow rate and is best suited for a controlled laboratory environment. The driving force for flow is typically provided by a reservoir raised by some height (0.1-1.0 m) above the balance but a pressurized water source (tank) or vacuum pump can also be used. When water is drawn off the balance, this method can be used to measure the conductance of branched root of shoot systems.**Pipette method**: More portable and suitable for field based measurements but does not allow for continuous monitoring of flow rate. Flow rates are measured by tracking the movement of a meniscus through a calibrated pipette.**Flow meter**: Also more portable and suitable for field based measurements and may allow for continuous monitoring of flow rate depending on flow meter and software used. Flow rates are using a commercial flow meter or by measuring the pressure drop across calibrated HPLC tubing.

### Ranges of values

K_{s}: kg s^{-1}m^{-1}MPa^{-1}

Angiosperm root: 0.25 – 49.0

Angiosperm stem: 0.1 – 210.0

Gymnosperm root: 0.22 – 14.7

Gymnosperm stem: 0.02 – 7.8 K_{L}: kg s^{-1}m^{-1}MPa^{-1}

Angiosperm stem: 1.4 x 10^{-5}– 3.9 x 10^{-3}

Gymnosperm stem: 1.2 x 10^{-5}– 1.1 x 10^{-3}

### Health, safety and hazardous waste disposal considerations

Care in handling pressurized gas and acidic flow solutions.

### Related techniques

### Literature references

Kolb KJ, Sperry JS, Lamont BB (1996) A method for measuring xylem hydraulic conductance and embolism in entire root and shoot systems. *Journal of Experimental Botany*, 47, 1805-1810.

Sperry JS, Donnelly JR, Tyree MT (1988) A Method for Measuring Hydraulic Conductivity and Embolism in Xylem. *Plant Cell and Environment*, 11, 35-40.

Tyree MT, Patino S, Bennink J, Alexander J (1995) Dynamic Measurements of Root Hydraulic Conductance Using a High-Pressure Flowmeter in the Laboratory and Field. *Journal of Experimental Botany*, 46, 83-94.