 Theis Equation Example | Texas Water Development Board

# Drawdown vs Time | Drawdown vs Distance

## Drawdown vs Time

Distance from pumping well: (feet)

Drawdown after 24 hours is feet

## Drawdown vs Distance

Elapsed time since pumping started: (hours)

Radius of influence is * feet

Pumping rate: (gpm)

Storativity: (dimensionless)

Transmissivity: (feet 2/day)

*Radius of influence assumes the farthest distance from the pumping well where drawdown is 0.1 feet. The maximum distance is one mile (5280 feet).

## Hydraulics of Groundwater

The Texas Water Development Board developed the following interactive tools to assist interested parties in understanding the effects of pumping at select locations where aquifer properties are either known or can be estimated with a certain degree of certainty. This implementation is based on the text "Hydraulics of Groundwater" by Jacob Bear (2007) and makes the following assumptions:

• the aquifer is infinite, confined, homogeneous, and isotropic;
• the aquifer is horizontal and groundwater flow is horizontal; and
• the well diameter is negligible.

The following formulae are used:

$u = r 2 S 4Tt$

$W(u) = − 0.5772 − In(u) + u − u 2 2 * 2! + u 3 3 * 3! - u 4 4 * 4! + ...$

$s = Q 4πT W (u)$

Where:

$s:\text{drawdown}$
$u:\text{well function argument}$
$W\left(u\right):\text{well function}$
$r:\text{distance from the pumping well (feet)}$
$S:\text{storativity (dimensionless)}$
$T:\text{transmissivity}\left({\text{feet}}^{2}/\text{day}\right)$
$t:\text{elapsed time since pumping started (hours)}$
$Q:\text{pumping rate (gallons per minute)}$
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