9.4.3: Deep Wells and Well Hydraulics
- Page ID
- 44595
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)For deep wells, the casing and screen diameter can range from a few inches to a few feet and can range in depth from less than 50 feet to more than several thousand feet.A cross section of a well installed in homogeneous material overlying an impervious rock formation is shown in Figure 9.6. Under static conditions when the well is not being pumped, the water level in the well will rise to the static water table position (Figure 9.7). When pumping begins, the water level in the well is lowered and water from the surrounding material flows into the well. The water table around the well is lowered to the general form of an inverted cone. The vertical distance from the static water table to the water level at the well is known as the drawdown. If pumping continues at a constant rate, the shape of the water table surrounding a well will become nearly stable. The horizontal distance from the well to where the water table is not noticeably lowered by drawdown is known as the radius of influence.
There is a definite relationship between drawdown and discharge from a well. Typical relationships are shown in Figure 9.8. For thick aquifers or artesian formations, the relationship is nearly a straight line. As the aquifer becomes thinner, less discharge occurs for the same drawdown as in a thick aquifer.
Figure 9.6. Well constructed in a sand and gravel formation. A casing and screen are always used. A gravel pack is optional.
Figure 9.7. Well hydraulics including static water level and drawdown.
Figure 9.8. Typical relationships between drawdown and discharge of wells.
Drawdown (s) is the difference between static water level (SWL) and the pumping water level in the well (PWL) and is calculated as:
s = PWL – SWL (9.1)
When a well functions like the straight line in Figure 9.8, the specific capacity, SC, is constant and is calculated as:
SC = Q/s (9.2)
where Q is discharge in gallons per minute (gpm) and s is drawdown in feet. Specific capacity is a useful term when predicting drawdown in a well for a given discharge because:
s = Q/SC (9.3)
See Example 9.1 for application of Equations 9.1, 9.2, and 9.3.
Given: Well and water table illustrated in Figure 9.7
SWL = 100 ft
PWL = 120 ft
Q = 800 gpm
Find: At 600 and 900 gallons per minute:
s
SC
PWL
Solution
\(SC=\dfrac{Q}{s}=\dfrac{800\text{ gpm}}{20\text{ ft}}=40\text{ gpm/ft}\)
For 600 gpm:
\(s=\dfrac{Q}{SC}=\dfrac{600\text{ gpm}}{40\text{ gpm/ft}}=15\text{ ft}\)
\(PWL=100+15=115\text{ ft}\)
For 900 gpm:
\(s=\dfrac{Q}{SC}=\dfrac{900\text{ gpm}}{40\text{ gpm/ft}}=22.5\text{ ft}\)
\(PWL=100+22.5=122.5\text{ ft}\)