In an industrial process, water flows through three tanks in succession, as illustrated in Figure 1. 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, in the second v and in the third w. The flow rate in the tube connecting tanks 1 and 2 is 8(x − y), the flow rate in the tube connecting tanks 2 and 3 is 6(y − z) and the rate of outflow from tank 3 is 9z. Figure 1 (not to scale) Show that the equations of the system in the steady flow situation are 8x - 8y + u 8x - 14y + 6z + v = 0 6y - 15z + w = 0 Take u = 100, v = 30, w = 20 and find the values of x, y and z using Cramer’s rule.

In an industrial process, water flows through three tanks in succession, as illustrated in Figure 1. 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, in the second v and in the third w. The flow rate in the tube connecting tanks 1 and 2 is 8(x − y), the flow rate in the tube connecting tanks 2 and 3 is 6(y − z) and the rate of outflow from tank 3 is 9z. Figure 1 (not to scale) Show that the equations of the system in the steady flow situation are

8x - 8y + u

8x - 14y + 6z + v = 0

6y - 15z + w = 0

Take u = 100, v = 30, w = 20 and find the values of x, y and z using Cramer’s rule.