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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
Transcribed Image Text:W
y
1
3
8(x – y)
6(у — 2)
9z
Figure 1 (not to scale)
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