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Hydraulic Gradient

Gradient Calculation from fitting a plane to as many as fifteen points

a x₁ + b y₁ + c = h₁
a x₂ + b y₂ + c = h₂
a x₃ + b y₃ + c = h₃
. . .
a x₁₅ + b y₁₅ + c = h₁₅

where (x_i,y_i) are the coordinates of the well and
h_i is the head

i = 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
The coefficients a, b, and c are calculated by a least-squares fitting of the the data to a plane

The gradient is calculated from the square root of (a² + b²) and the angle from the arctangent of a/b or b/a depending on the quadrant

Site Name

Date

Calculation basis

Coordinates
I.D.	x-coordinate	y-coordinate	head

Number of Points Used in Calculation
Max. Difference Between Head Values
Gradient Magnitude (i)
Flow direction as degrees from North (positive y axis)
Coefficient of Determination (R²)

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Page author: Jim Weaver, of U.S. EPA, Office of Research and Development, Athens Georgia who last modified this content on: July 27, 2005

EPA On-line Tools for Site Assessment Calculation

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