Step 1: The Thiem equation for steady-state discharge \(Q\) from a well in an unconfined aquifer is \( Q = \frac{\pi k (H^2 - h^2)}{\ln(R/r)} \), where \(k\) is permeability, \(H\) is initial saturated thickness, \(h\) is head in the well, \(R\) is radius of influence, and \(r\) is well radius.
Step 2: To analyze the effect of doubling the well radius, let initial yield be \(Q_1\) with radius \(r_1\) and new yield be \(Q_2\) with radius \(r_2 = 2r_1\). The ratio of yields is:
\[ \frac{Q_2}{Q_1} = \frac{\ln(R/r_1)}{\ln(R/r_2)} = \frac{\ln(R/r_1)}{\ln(R/(2r_1))} = \frac{\ln(R) - \ln(r_1)}{\ln(R) - \ln(2r_1)} = \frac{\ln(R) - \ln(r_1)}{\ln(R) - \ln(2) - \ln(r_1)} \]
Step 3: Evaluate the increase with typical values, assuming \(R = 200\) m and \(r_1 = 0.2\) m, where \(R\) is significantly larger than \(r\).
\[ \frac{Q_2}{Q_1} = \frac{\ln(200/0.2)}{\ln(200/0.4)} = \frac{\ln(1000)}{\ln(500)} = \frac{6.907}{6.214} \approx 1.11 \]
This indicates an approximate 11% increase in yield. Doubling the well diameter results in a modest yield increase, not a doubling, with 10% being a common approximate value.