In the previous sections, the drawdown in a pumping well was assumed to be due only to head losses in the aquifer. In reality, however, additional drawdown is caused by head losses in the well system itself (screen or perforated casing) as water flows through it. The former is known as the drawdown due to the formation loss (sw) and the latter as the drawdown due to the well loss (sf) as shown in Figure 9.9.1. The total drawdown st is then st = sw + sf.
Since the flow in the aquifer is laminar, sw varies linearly with Q(sw = CwQ). However, the flow through the well system (screen and perforated casing) is turbulent, and thus sf can vary with some power of Q(sf = CfQn). The total drawdown can be expressed as st = sw + sf = CwQ + CfQn 9.9(1)
4Tt for steady-state 9.9(2)
for unsteady-state 9.9(3)
The best way to determine the values of Cw, Cf, and n is by experiment utilizing a step-drawdown test (Bear 1979;
Bouwer 1978). Well efficiency is related to the well loss and is defined as
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