In an industrial process, water flows through three tanks in succession, as illustrated in Figure 5.6. The

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In an industrial process, water flows through three tanks in succession, as illustrated in Figure 5.6. The tanks have unit cross-section and have heads of water x, y and z respectively. The rate of inflow into the first tank is u, the flowrate in the tube connecting tanks 1 and 2 is 6(x – y), the flowrate in the tube connecting tanks 2 and 3 is 5(y – z) and the rate of outflow from tank 3 is 4.5z.

Figure 5.6

1 u 6(x - y) 2 5(y-z) 3 Z 4.5z

Show that the equations of the system in the steady flow situation are

u = 6x - 6y  0 = 6x - 11y + 5z 0 = 5y-9.5z

and hence find x, y and z.

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