title: Mathematics for Water & Wastewater Treatment Plant Operators, Volume I (Bk. 1)
author: Joanne K. Price
description: Mathematics for Water & Wastewater Treatment Plant Operators.
zlib_text: Unit 5
  Linear algebra
  
  Introduction
  Introduction
  Figure 1 shows the network of water pipes connecting the pump and ﬁve
  Pump
  T1
  T2
  T3
  T4
  T5
  f1
  f2
  f3
  f1
  f2
  f3
  f3
  f1 − f2
  f2 − f3
  Figure 1
  The pump and
  network of taps that control a
  hot water heating system
  taps that control the heating system in a (ﬁctional) greenhouse. The
  engineer who maintains the pump can determine the pressure P at which
  hot water is supplied to the system, and the tightness Ti (i = 1, . . . , 5) of
  each tap. He knows from experience that making the system perform as
  required throughout the day is no easy matter. The eﬀect of each part of
  the system depends on the rate at which hot water ﬂows through it.
  Because the system is closed, all the water that ﬂows into any junction
  must ﬂow out again. As a result, there are only three key rates of ﬂow,
  namely f1, f2 and f3, that together determine the rate of ﬂow in every
  part of the system (see Figure 1). However, the equations that relate these
  ﬂow rates to the supply pre