Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

DIAGRAM 5
For the most interesting case where 0 < C w < et , Diagram 5 shows that these
two curves cross. 'this must be so because, given a particular ratio of rates
C w /C t , the position and the shape of the hyperbola change with the distance
Z ab.
• the larger will be Z the more open will be the hyperbola. In this case
ab
Z is smaller than Z
ab1
ab °
2
It is easily seen that the producers located in the area completely
enclosed by b 1 and b 2 prefer to use the waterway via B 1 . Also, the producers
located above b 1 but below b 2 in the top part of the diagram, and those located
below b 1 but above b 2 in the lower part of the diagram, prefer to use the
waterway via B 2 . However, it is not yet clear what will be the choice of the
farmers to the right' of b 2 and inside b l ; some of them could very well prefer
to ship via B 1 , if there was such a possibility. The solution consists in
drawing a new boundary, the locus of the points where the producers would be
indifferent to shipping via Bl or via B 2 where the possibility of direct
shipment to A is excluded. The equation of this third boundary is:
••■•■■•
(18) CtZb + CwZab = Ct Zb + CwZab
1 1 2 2
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