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EPA On-line Tools for Site Assessment Calculation

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Vertical Gradient Calculator
Vertical Gradient

Water levels in nested well clusters (wells located closely together) indicate upward or downward flow in aquifers or flow between adjacent geologic units. Flow is governed by Darcy's Law:

Equation showing Darcy's Law

where q is the Darcy flux (volume of water per unit area per unit time) and K is the hydraulic conductivity. The change of head (roughly water level) divided by the distance determines the gradient and direction of flow.

Different assumptions about the distances are used in the calculator and are illustrated below.

The vertical gradient calculator determines vertical gradients between adjacent wells. (They are assumed to be located very close together; for wells far apart use one of the horizontal gradient calculators.) It illustrates the effects of screen length on gradient calculations. These differences come about because the gradients are theoretically determined from piezometers that are only open at the bottom and thus have an effective screen length of zero. In practice, wells with screens of various lengths are used to calculate the gradients and the screen lengths may have an influence on the calculated gradients. For reference, the gradients are also calculated assuming that the screen lengths are zero, as if the wells were true piezometers. More information ...

Definition of input parameters for vertical gradient calculation

Definition of inputs for each well (piezometer):

  • dw = depth to water
  • d = depth to top of screen
  • s = screen length

Assumptions concerning screen lengths:

  • Distance is from top of screen to top of screen (H:H)
  • Distance is from mid-point of screen to mid-point of screen (M:M)
  • Distance is from bottom of screen to bottom of screen (L:L)
  • Distance is from top of screen to bottom of screen (H:L)
  • Distance is from bottom of screen to top of screen (L:H)

Input Parameters
Surface Elevation Depth to Well Screen Screen Length Depth to Water
Shallow Well
Deep Well

Magnitude Flow Direction
Low to high value (L:H)
High to high value (H:H)
Mid-point value (M:M) Concise version
Low to low value (L:L)
Low to high value (H:L)
Gradient Estimate Between Piezometers (screen lengths equal to zero)

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