The problem data are the nominal hamiltonian matrix h

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: er supply network connects water supplies (such as reservoirs) to consumers via a network of pipes. Water flow in the network is due to gravity (as opposed to pumps, which could also be added to the formulation). The network is composed of a set of n nodes and m directed edges between pairs of nodes. The first k nodes are supply or reservoir nodes, and the remaining n − k are consumer nodes. The edges correspond to the pipes in the water supply network. We let fj ≥ 0 denote the water flow in pipe (edge) j , and hi denote the (known) altitude or height of node i (say, above sea level). At nodes i = 1, . . . , k , we let si ≥ 0 denote the flow into the network from the supply. For i = 1, . . . , n − k , we let ci ≥ 0 denote the water flow taken out of the network (by consumers) at node k + i. Conservation of flow can be expressed as Af = −s c , where A ∈ Rn×m is the incidence matrix for the supply network, given by −1 if edge j leaves node i +1 if edge j enters node i Aij = 0 otherwise. We assume that each edge is oriented from a node of higher altitude to a node of lower altitude; if edge j goes from node i to node l, we have hi > hl . The pipe flows are determined by fj = 2 αθj Rj (hi − hl ) , Lj where edge j goes from node i to node l, α > 0 is a known constant, Lj > 0 is the (known) length of pipe j , Rj > 0 is the...
View Full Document

This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

Ask a homework question - tutors are online