.19 A liquid storage facility can be modeled by where y is the liquid level (m) and u is an inlet flow rate (m*/s) Both are defined as deviations from the nominal steady-state values. Thus, y-u0 at the nominal steady state. Also, the initial values of all the derivatives are zero. (a) If u(t) suddenly changes from 0 to 1 m/s at 0, deter- mine the liquid level response, y(). (b) If the tank height is 2.5 m, will the tank overflow? (c) Based on your results for (b), what is the maximum flow change, umax, that can occur without the tank overflowing? (Hint: Consider the Principle of Superposition.)

Question
.19 A liquid storage facility can be modeled by
where y is the liquid level (m) and u is an inlet flow rate (m*/s)
Both are defined as deviations from the nominal steady-state
values. Thus, y-u0 at the nominal steady state. Also, the
initial values of all the derivatives are zero.
(a) If u(t) suddenly changes from 0 to 1 m/s at 0, deter-
mine the liquid level response, y().
(b) If the tank height is 2.5 m, will the tank overflow?
(c) Based on your results for (b), what is the maximum flow
change, umax, that can occur without the tank overflowing?
(Hint: Consider the Principle of Superposition.)

Image Transcription

.19 A liquid storage facility can be modeled by where y is the liquid level (m) and u is an inlet flow rate (m*/s) Both are defined as deviations from the nominal steady-state values. Thus, y-u0 at the nominal steady state. Also, the initial values of all the derivatives are zero. (a) If u(t) suddenly changes from 0 to 1 m/s at 0, deter- mine the liquid level response, y(). (b) If the tank height is 2.5 m, will the tank overflow? (c) Based on your results for (b), what is the maximum flow change, umax, that can occur without the tank overflowing? (Hint: Consider the Principle of Superposition.)

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