derivative, we obtain a more general equation for the apparent velocity in the x-direction: where has units of velocity and is called the Darcy velocity (or the specific discharge, filtration velocity, or superficial velocity). The pore or interstitial velocity is the average velocity of fluid molecules in the pores; it is related to the Darcy velocity and the porosity through the Dupuit-Forchheimer relationship (Some authors use the term seepage velocity to mean the Darcy velocity, while others use it to mean the pore velocity.) Civil engineers predominantly work on problems that involve water and predominantly work on problems on earth (in earth's gravity). For this class of problems, civil engineers will often write Darcy's law in a much simpler form: where is the hydraulic conductivity, defined as , and is the hydraulic gradient. The hydraulic gradient is the rate of change of total head with distance. The total head, at a point is defined as the height (measured relative to the datum) to which water would rise in a piezometer at that point. The total head is related to the excess water pressure by: and the is zero if the datum for head measurement is chosen at the same elevation as the origin for the depth, z used to calculate . Typical values of hydraulic conductivity Values of hydraulic conductivity, , can vary by many orders of magnitude depending on the soil type. Clays may have hydraulic conductivity as small as about , gravels may have hydraulic conductivity up to about . Layering and heterogeneity and disturbance during the sampling and testing process make the accurate measurement of soil hydraulic conductivity a very difficult problem. Flownets Darcy's Law applies in one, two or three dimensions. In two or three dimensions, steady state seepage is described by Laplace's equation. Computer programs are available to solve this equation. But traditionally two-dimensional seepage problems were solved using a graphical procedure known as flownet. One set of lines in the flownet are in the direction of the water flow (flow lines), and the other set of lines are in the direction of constant total head (equipotential lines). Flownets may be used to estimate the quantity of seepage under dams and sheet piling. Seepage forces and erosion When the seepage velocity is great enough, erosion can occur because of the frictional drag exerted on the soil particles. Vertically upwards seepage is a source of danger