Question

hydraulics Q3

Question3 a) Discuss the principle of Linear Superposition as applied to interacting ells in a multiple well field and show how this principle can be used to represent the effects of a stream. 5 marks b) i. Calculate the steady state drawdown at a 0.2m diameter pumping well fined aquifer if the pumping well is 50m which fully penetrates a con from a river which is in full hydraulic connection with the aquifer. The Transmissivity of the aquifer is 470m2/day and the pumping rate is 4000m3/day. Include a sketch showing the representation of the river using Image Well Theory. 15 marks drawdown be in a piezometer 100m from the well and 25m from the river 5 marks (Total marks available 25)

Answer 1

considered at a distance of x on the other side of the line of zero drawdown. The distance of the observation well from the pumping well is rand from the image well isr For the steady state condition of a confined aquifer, the drawdown at the observation well can be obtained as (21.2) s (a, b)-오 In (2) (21.3) (at)+ (21.4) For the unsteady condition, the drawdown at r at any time can be obtained as (21.5) 47 47: (21.6) 47t 4T:

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Multiple well systems In a well field, when cone of depression of one well overlaps with the cone of depression of other wells, then the actual drawdown will be more than the drawdown calculated for the individual well (Fig. 20.1). In this case, the actual drawdown can be calculated using the principle of superposition of linear system Q1 Q2 Q3 Initial potential line Drawdown Composit drawdow curve Drawdown Drawdown curve of Q2 curve of Q curve of Qs Fig. 21.1 Multiple well system For a well field of wells, the actual drawdown can be calculated as sa (r,t)s (r,t) s2 Cr,t) +sz (rt) +s4(r,t) s (r,t) +s(r,t) (21.1) or Where Sa is the actual drawdown at a distance r at time , S is the drawdown at that point caused by the discharge of the well i at time t, n is the number of wells in the well fields Fig. 21.2 explains the interference of cone of depression of two pumping wells. The coordinates of the two wells are (3,5) and (7,5). The individual cone of depression of the two wells are shown on Fig. 21.2 (a) and (b). The combine effect of the two wells can be obtained by adding the individual drawdown of the two wells, i.e. if drawdown of the first well is Si and the second well is S2, the combine drawdown will be S-SS2. The combine effect is shown in Fig. 21.2(c)

a) Drawdown of first well (b) Drawdown of second wel 35 小..小…} 10 (c) Combine drawdown Fig. 21.2 Cone of depression of multiple wells system Wells near aquifer boundaries The assumption of infinite horizontal extend is no longer valid when water is pumped from a well near the aquifer boundary. Method of superposition can be used to implement the effect of aquifer boundary by adding a wel at different location. The well that creates the same effect as boundary is called image well Well near a stream Fig. 21.3 shows a well near a stream. In this case, the actual drawdown at the stream boundary will be zero as stream is considered as an infinite source. In order to maintain zero drawdown, an imaginary recharge well is considered at a distance equal to the distance between the pumping well and the stream boundary 01 Initial potential line Cone of depression Fig. 21.3 Well near a stream

Fig. 20.4 shows an equivalent hydraulic system in an aquifer of infinite areal extend. For the equivalent hydraulic system, the time drawdown relationship for the pumping well and also for the imagery recharge well can be obtained separately. The actual drawdown can be obtained using the principle of superposition Zero drawdown line Pumpng well Recharge image well 0, Cone of 01 impression Buildingup omponent-; Initial potential line Sream Actual cone of depresson Cone of Aquifer Drawdown depression component Fig. 21.4 Equivalent hydraulic system in a aquifer of infinite areal extend Consider the Fig. 21.5 below. The pumping well is at a distance of x from the stream boundary. In order to calculate the actual drawdown at the observation location, an image well is Observation (a,b) well Line of zero drawdown Pumping well Image well (x,0) Fig. 21.5 Pumping well, Observation well and Image well