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Unformatted text preview: EAS 44600 Groundwater Hydrology Lecture 9: Flow Nets Dr. Pengfei Zhang Specific Discharge and Average Linear Velocity Recall Darcy’s law: − = − − = dl dh KA L h h KA Q b a (9-1) It states that the flow (discharge) will be proportional to the hydraulic gradient ( dh/dl ), the hydraulic conductivity ( K ), and the cross-sectional area of flow ( A ). The specific discharge ( Darcian velocity ), q , of groundwater is equal to Q/A : − = dl dh K q (9-2) The specific discharge is an apparent velocity only, since flow of water does not occur through the entire cross section (Figure 9-1A). Remember that flow occurs only in the void spaces between grains (Figure 9-1A). Hence, the specific discharge given above underestimates the actual velocity of water moving through the void spaces. B A Flow No flow Figure 9-1. Cross section of an R.E.V. (A) and average linear velocity (B). To find the actual average linear velocity , v , at which the water is moving, one divides the specific discharge by the porosity ( n ) to account for the actual open space available for flow: − = = dl dh n K n q v (9-3) in terms of units: 2 3 1 REV w L T L A Q q = = (9-4) 9-1 T L L L L T L n A Q v REV w REV REV w = = = 3 3 2 3 1 1 (9-5) Notice that in the above units for porosity it is assumed that all voids are filled with water ( versus ), in other words, we are talking about groundwater, not the unsaturated zone. 3 3 / REV w L L 3 3 / REV voids L L The units are useful because they help us to distinguish between specific discharge ( L 3 w /L 2 REV T ) and the average linear velocity ( L REV /T ). The specific discharge concerns the volume of water that passes by a particular cross section of the R.E.V. in a given amount of time, whereas the average linear velocity concerns the length of R.E.V. that the average molecule of water travels in a given amount of time. The specific discharge is less straightforward to understand physically, and the units show that....
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This note was uploaded on 12/29/2010 for the course EAS 44600 taught by Professor Pengfeizhang during the Spring '10 term at CUNY City.
- Spring '10