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Working To Restore Nature <br /> These two components can be characterized by the following equation <br /> s = AQ + BQP (Equation 1) ' <br /> where AQ -- linear head loss <br /> BQ = non-linear head loss <br /> s — drawdown at a given time <br /> Q — discharge rate <br /> P — a discharge rate dependent value <br /> between 15 and 3 5 <br /> A and B are constants <br /> A value of 2 for P is commonly accepted in this equation (Ramey, 1982), which yields the <br /> equation <br /> S = AQ + BQ2 (Equation 2) <br /> or dividing by Q <br /> s/Q = A + BQ <br /> . The latter equation represents a straight line on an s/Q versus Q plot (Plate 2-PT) Using <br /> the approach of Jacob as outlined in Todd (1980), the data indicate a significant non-darcy <br /> (non-linear) component of the drawdown This non-linear component of the head loss <br /> includes some effects related to well slots (Krusemann and de Ridder, 1989) A further <br /> indication of the well losses is revealed on the plot of the recovery in well PTW-1 after <br /> pumping was halted (Plate 6-PT) This plate shows extremely rapid recovery (over 90 <br /> percent of total drawdown in the first 4 minutes) which is characteristic of wells with <br /> wellbore and near-wellbore head losses due to turbulent flow <br /> The least squares best fit line shown in Plate 2-PT yields the following relationship between <br /> drawdown and pumping rate <br /> s = 0 33Q + 0 23Q2 <br /> Using the coefficients (A and B) calculated from the best fit line shown on Plate 2-PT, the <br /> well efficiency can be calculated for various times and pumping rates Using the 20-minute <br /> drawdown data shown, the well efficiency at 3 55 gpm is approximately 30 percent This <br /> efficiency is similarly indicated on the drawdown versus distance from the pumping well plot <br /> (Plate 8-PT) When the trend line of this plot is extrapolated to a distance of approximately <br /> 0 25 feet (outer edge of casing), the expected drawdown (formation loss only) is <br /> approximately 18 feet This indicates a well efficiency of 20 percent Low well efficiencies <br /> are common in unconfined aquifers when drawdown encompasses a significant portion of <br /> . the saturated screen thickness This is due to the partial penetration effect which induces <br /> steep vertical flow gradients in the vicinity of the well screen Some modification of well <br /> 38032-10 <br />