Three monitoring wells exist in an aquifer as shown below. North is upward (toward the top of thepage). The land surface elevations and depths to water are shown below. Find the magnitudeand direction of the head gradient.Well Land Surface Elevation (ft) | Depth to Water (ft)A3208.546.1В3209.243.33210.045.0300 ftABY200 ft120 ft

Answered: Three monitoring wells exist in an…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Three monitoring wells exist in an aquifer as shown below. North is upward (toward the top of the
page). The land surface elevations and depths to water are shown below. Find the magnitude
and direction of the head gradient.
Well Land Surface Elevation (ft) | Depth to Water (ft)
A
3208.5
46.1
В
3209.2
43.3
3210.0
45.0
300 ft
A
BY
200 ft
120 ft

Expert Solution

Step 1-Calculation of the magnitude and direction of head gradient

Determine the length between wells:

$A B = 300 f t A p p l y i n g p y t h a g o r o u s t h e o r e m : A C = \sqrt{150^{2} + 200^{2}} A C = 269.072 f t B C = \sqrt{120^{2} + 200^{2}} B C = 233.238 f t$

Calculate the head gradient:

$h e a d g r a d i e n t = \frac{∆ h}{L} ∆ h = h_{A} - h_{C} (H e a d d i f f e r e n c e) L = L e n g t h b e t w e e n t h e w e l l s (A C) ∆ h = h_{A} - h_{C} ∆ h = 46.1 - 45 ∆ h = 1.1 f t L = d i s \tan c e b e t w e e n A C = 269.072 f t h e a d g r a d i e n t = \frac{∆ h}{L} h e a d g r a d i e n t = \frac{1.1}{269.072} h e a d g r a d i e n t = 0.00408 f t / f t$

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