## N R

Note that the expression for the head 4 for radial uncon-fined flow is different from that for radial confined flow even though the discharge potential for both types of flow is the same. Also, the principle of superposition applies to $ but not to 4. Superposition of two solutions in Equation 9.4(15), therefore, is allowed, but not in Equation 9.4(17).

The introduction of the drawdown s as s = 4o — 4 means 42 = 4 — s)2 = 4o — 2$0s + s2 = 4 — 2$0s (1 — s/24o). Hence, Equation 9.4(16) can be written as s 1 —

If drawdown s is small compared to 4o, then s/24 and Equation 9.4(18) can be written as

2^K4o

This equation is identical to the drawdown equation for confined flow, Equation 9.3(15). This fact is true only if the drawdown is small compared to the head 4o. However, Equation 9.4(19) can be accurate enough as a first approximation.

### Unconfined Flow with Infiltration

Water can infiltrate into an unconfined aquifer through the soil above the phreatic surface as the result of rainfall or artificial infiltration. As shown in Figure 9.4.4, water percolates downward into the acquifer at a constant infiltration rate of N per unit area and per unit time.

The continuity equation for unconfined flow, Equation 9.4(5), can be modified to read x or o

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