In the absence of solutes, ψ_m can be expressed as follows (Scott 2000):

2.29

Where R is the universal gas constant (8.314 J/K.mol), T is the temperature in Kelvin, M is the mass of a mole of water in kg (0.018015), ψ_m is in J/kg, e is the vapour pressure of soil pore water, e₀ is the vapour pressure of pure water at the same temperature. e is less than e₀ due to the attraction of pore water on soil solids. The term e/ e₀ is relative vapour pressure.

Problem: Relative vapour pressure at 20 °C is 0.85. Calculate ψ_m. If relative vapour pressure becomes 0.989 then what happens to ψ_m.

           When relative vapour pressure is 0.989, then ψ_m = -1496 J/kg.
A higher relative vapour pressure is associated with high water content of the soil sample.  From this example, it can be noted that as water content increases, matric suction reduces.
           Solutes present in soil-water results in ψ_o due to the semi-permeable membrane effect produced by plant roots, air-water inter phase and clays. As concentration of solute increases, ψ_o also increases.
According to Vant-Hoff’s equation, ψ_o = RTC_s                                                                       2.30
Where ψ_o is in J/kg, C_s is the concentration in mol/m³, R and T as defined earlier.
According to US Salinity laboratory, ψ_o = -0.056 TDS                                                           2.31
Where TDS is the total dissolved solids of soil pore water in mg/L and ψ_o is in kPa.
Also, ψ_o = -36 EC                                                                                                                 2.32
Where EC is the electrical conductivity of soil pore water in dS/m and ψ_o is in kPa.

sed as .

2.33

where ρw is the density of water in kg/m³, M is the mass of one mole of water (kg/mol), R and T as defined earlier, e is the equilibrium vapour pressure of soil pore water containing solutes, e₀ is the vapour pressure of pure water in the absence of solute, and ψ_o is in kPa.

Problem: Calculate total potential of a saturated soil at 200C at a point through which reference datum passes. Saturated volumetric water content is 0.5. 1cm³ of soil at reference datum has 3x10^-4 moles of solute. Water table is 1.2 m above reference datum.

Note: It is important to put the sign for each of the potential.

Movement of water: Soil water moves from higher ψ_t to lower ψ_t. If we are concerned only about liquid flow, then the contribution of ψ₀ is considered negligible because the solutes also move along with the flowing water. While considering flow of water, ψ_t can be rewritten as ψ_g + ψ_p + ψ_m. This total potential is termed as hydraulic potential causing flow. Under hydraulic equilibrium, ψ_t is same everywhere, spatially.