Page 83 - Water Engineering Hydraulics, Distribution and Treatment

This is independent of Q and depends only on the diffusivity of the aquifer. The change in drawdown per log cycle from Eq. (3.23) is
Δs = 528 Q∕T
For 150 gpm: Δs = 528 × 150∕1 × 10 = 7.9ft(2.4m)
1
For 200 gpm: Δs = 10.6ft(3.23 m)
2
For 250 gpm: Δs = 13.2ft(4.02 m).
3
Using the value of r = 30,000 ft (9,144 m) as the starting point, straight lines having slopes of 7.9, 10.6, and 13.2 ft (2.4 m,
3.2 m, and 4.0 m) are drawn in Fig. 3.8.
Distance (ft) 4 3.11 Prediction of Drawdown 61
1 10 100 1000 10,000
0
10
Q = 150 gpm
Q = 250 gpm
20 Q = 200 gpm
Drawdown (ft) 30
40
50
60
Figure 3.8 Distance–drawdown curves for various rates of pumping (Example 3.4). Conversion factors: 1 ft = 0.3048 m;
3
1 gpm = 5.45 m ∕d.

The contours of the piezometric surface can be drawn by subtracting the drawdowns at several points from the initial values.

3.11.2 Variable Discharge 3.11.3 Intermittent Discharge

The rate at which water is pumped from a well field in a water In a water supply system, a well (or a well field) may be
supply system will vary with time in response to changes operated on a regular daily cycle, pumping at a constant rate
in demand. The continuous rate of pumping curve can be for a given time interval and remaining idle for the rest of
approximated by a series of steps as shown in Fig. 3.9. Then the period. Brown (1963) gives the following expression for
each step can be analyzed, using one of the conventional computing the drawdown in the pumped well after n cycles
equations. From the principle of superposition, the drawdown of operation:
at any point at any specific time can be obtained as the sum
s = (264 Q∕T) log[(1 ⋅ 2 ⋅ 3 ⋯ n)∕(1 − p)(2 − p) ⋯ (n − p)]
of increments in drawdowns caused by the step increases up n
to that time: (US customary units) (3.35a)

s =Δs +Δs + ⋯ +Δs (3.33)
1 2 t where s is the drawdown in the pumped well after n cycles
n
in ft, p is the fractional part of the cycle during which the
Using a semilogarithmic approximation,
well is pumped, Q is the discharge in gpm, and T is the
2
s = (264ΔQ ∕T) log[(0.3 Tt )∕(r S)] (3.34) transmissivity in gpd/ft.
i
i
where s = (380, 160 Q∕T) log[(1 ⋅ 2 ⋅ 3 ⋯ n)∕(1 − p)(2 − p)
n
t = t − t i−1 ⋯ (n − p)] (SI units) (3.35b)
i
Increments of drawdown are determined with respect to where s is the drawdown in the pumped well after n cycles
n
the extension of the preceding water level curve. in m, p is the fractional part of the cycle during which the