The two-tank liquid-level system shown in Fig. 1 P7−3 is operating at a steady state when a step change is made in the flow rate to tank 1. The transient response is critically damped, and it takes 1.0 min for the change in the level of the second tank to reach 50 percent of the total change.

If the ratio of the cross-sectional areas of the tanks is A1/A2 = 2, calculate the ratio R1/R2. Calculate the time constant for each tank. How long does it take for the change in the level of the first tank to reach 90 percent of the total change?

 

R R2 FIGURE P7-3