Oklahoma State University

Driving Force

Driving Force: The driving force causing water to move between two points in the soil is the difference between the total potential at those points divided by the distance between the points. For the soil illustrated below, this becomes

where df is the driving force and LAB is the distance between points A and B in the soil column. Note that the driving force is dimensionless when the potential is taken on a unit weight basis or as hydraulic head. 


In the illustration above we calculated the driving force across nearly the entire soil system. However, we could calculate it between any two points within the soil. Moreover, in unsaturated soils (as in the illustration above) and in layered soils, the driving force usually changes with position. As points A and B become closer and closer together, the driving force becomes

where TH is the total head and x is the position coordinate. That is, the driving force is the negative derivative of the total head with respect to distance or the negative of the slope of the total head vs. distance graph. This is illustrated below for steady-state flow in a soil that is saturated at point A but unsaturated at point B. Note that the driving force is not uniform but increases rapidly for positions near point B.


The figure below shows the total head as a function of distance from point A for steady-state flow in a uniform soil that is saturated at both ends. Here the total head decreases linearly from point A to point B and the slope is a constant. In soils such as this, the driving force does not change with position in the soil.


For more insight into driving forces in soils under one-dimensional steady-state flow, utilize the Steady-state Water Movement software and associated exercises.

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