4 5 6 Time t in Days

FIG. 9.7.2 Drawdown versus time due to pumping from a well.

4 5 6 Time t in Days

FIG. 9.7.2 Drawdown versus time due to pumping from a well.

Note that Equation 9.7(24) is similar in expression to the steady-state flow. Equation 9.7(22) allows direct calculation of drawdown in terms of distance r and time t for given aquifer characteristics T and S at a known pumping rate Q.

The exact solution of Equation 9.7(13) is difficult for unconfined aquifers because T = K$ is not constant but varies with distance r and time t. The average head $ can be estimated and used in the Theis solution for small drawdowns. For large drawdowns, however, the use of $ for the Theis solution is not valid.

For large drawdowns, Boulton (1954) presents a solution which is valid if the water depth in the well exceeds 0.5 $o. Boulton's equation is:

where V is Boulton's well function, and Ck is a correction factor. The t' and r' are defined as

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