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Unformatted text preview: CE 3101 Fall 2011 Some Thoughts on Homework 04 Objective Your objective in this assignment is to determine four well locations, { ( x 1 , y 1 ) , ( x 2 , y 2 ) , ( x 3 , y 3 ) , ( x 4 , y 4 ) } , and the four associated pumping rates, { Q 1 , Q 2 , Q 3 , Q 4 } , so that the total pumping rate, Q T = Q 1 + Q 2 + Q 3 + Q 4 (1) is as small as possible and the excavation remains dry. This dewatering constraint can be written as h ( x , y ) 6 h e for all ( x , y )  p ( x x e ) 2 + ( y y e ) 2 6 R e (2) where ( x e , y e ) are the coordinates of the center point of the excavation, R e is the radius of the excavation, and h e is the maximum water table elevation in the excavation. Applying our Engineering Reasoning From this problem statement it appears that we have 12 degrees of freedom – that is, 12 decision variables. However, as we reasoned last class, there is a series of simplifying conclusions that we can draw from our knowledge of science, engineering, and mathematics. • The influence (drawdown) of a well diminishes as the distance from the well increases; see Figure 1. X [m] Y [m] 100 200 300 40020015010050 50 100 150 200 28.4 28.6 28.8 29 29.2 29.4 29.6 29.8 Figure 1: Drawdown (head) due to a well next to a long straight river. The surface is a plot of the component of the discharge potential due to a single well: Φ j ( x , y ) = Q j 2 π log r j s j . The closer the wells are to the excavation, the greater dewatering influence. Thus, we want to place the wells as close to the excavation as possible. However, the wells are not allowed to be placed in the excavation....
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 Spring '11
 Barnes
 outer edge

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