hydraulic conductivity

In Question 5 of the problem set, I am having a hard time understanding if hydraulic conductivity flows quicker (and is thus higher) when matric potential is lower (-0.5) versus higher (-0.01). The definition of Darcy's law says that the rate at which water flows is directly proportional to the water potential gradient, but this would make me think that, the lower the matric potential (more negative), the faster the water will flow. This doesn't make sense when I think about it, though, because, the lower the matric potential, the more it is directly countering the gravitational potential. Could you clarify this for me?

Sara, 1st consider Darcy's Law q = -K (dΨ/dx) q (the flux density) is proportional to the water potential gradient BUT it also depends on K (the hydraulic conductivity, which varies with soil water content)

Have a look at the graph of hydraulic conductivity versus soil matric potential in the class notes (slide 19 in lecture #11). Your thinking is correct, that K is maximum when the soil is saturated, i.e. all pores are filled with water; but consider how K changes as the soil matric potential (and consequently the soil water content) change. Note to be careful to distinguish between K and dΨ/dx