OCR Text |
Show The flow Fb crossing the boundary segment is then given as F. « Fsin( 18( T- e) + Fcos( 180*- e) if 9 > 90° j « F sin 6 + Fv cos 6 if 6 < 90° ( 3.5) y where 8 is the angle between the boundary and x- axis. The heads Hjj, Hj+ j j and Hn+ i can be estimated as a function of the pumping rates at candidate well sites at any time t, using equation 3.2, since the flow FD is a linear function of these heads, and the heads are a linear function of the pumping rates. The boundary flows may thus be described in terms of a response matrix to pumping. The response matrix coefficients fDWt are defined as the incremental flow across the boundary segment b, in the time period t- 1 to t, as a response to unit pumping at the well site w. These response matrix coefficients can be evaluated directly using equation 3.2, once the response matrices for drawdown have been computed, by computing the associated heads at the nodes of interest. The flow F^ across the boundary segment b, at any time t may then be written in terms of the flow response matrix coefficients, and the pumping rates as t w Fb, - Fbo - « b. - X X W Q « < 3- 6) t' « l w « l where Fy) is the flow across the boundary segment b at time t= 0 ffto is the total flow across the boundary segment b due to all background pumping/ natural recharge up to time t fbwt- is the incremental flow across the boundary segment b in time period t\ due to unit pumping at well w 46 |