The liquid storage tank shown in Figure 4 has two inlet streams with mass flow rates F1 and F2 and an exit stream with flow rate F3. The cylindrical tank is 2.5 m tall and 2 m in diameter. The liquid has a density of 800 kg/m?. Normal operating procedure is to fill the tank until the liquid level reaches a nominal value of 1.75 m using constant flow rates: F1=120 kg/min, F2 =100 kg/min, and F3 =200 kg/min. At that point, inlet flow rate F1 is adjusted so that the level remains constant. However, on this particular day, corrosion of the tank has opened up a hole in the wall at a height of 1 m, producing a leak whose volumetric flow rate q4 (m/min) is 4 = 0.025 yh – 1 where h is height in meters. Explain in detail the full procedure and include the right parameter's values and units. a) Obtain a model of the tank system's dynamics. b) If the tank was initially empty, how long did it take for the liquid to reach the corrosion point? c) If mass flow rates F1, F2, and F3 are kept constant indefinitely, will the tank eventually overflow? Justify your answer.

The liquid storage tank shown in Figure 4 has two inlet streams with mass flow rates F1 and F2 and an exit stream with flow rate F3. The cylindrical tank is 2.5 m tall and 2 m in diameter. The liquid has a density of 800 kg/m?. Normal operating procedure is to fill the tank until the liquid level reaches a nominal value of 1.75 m using constant flow rates: F1=120 kg/min, F2 =100 kg/min, and F3 =200 kg/min. At that point, inlet flow rate F1 is adjusted so that the level remains constant. However, on this particular day, corrosion of the tank has opened up a hole in the wall at a height of 1 m, producing a leak whose volumetric flow rate q4 (m/min) is 4 = 0.025 yh – 1 where h is height in meters. Explain in detail the full procedure and include the right parameter's values and units. a) Obtain a model of the tank system's dynamics. b) If the tank was initially empty, how long did it take for the liquid to reach the corrosion point? c) If mass flow rates F1, F2, and F3 are kept constant indefinitely, will the tank eventually overflow? Justify your answer.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

The liquid storage tank shown in Figure 4 has two inlet streams with mass flow rates F1
and F2 and an exit stream with flow rate F3. The cylindrical tank is 2.5 m tall and 2 m in diameter. The
liquid has a density of 800 kg/m?.
Normal operating procedure is to fill the tank until the liquid level reaches a nominal value of 1.75 m using
constant flow rates: F1 =120 kg/min, F2 =100 kg/min, and F3 =200 kg/min. At that point, inlet flow rate
F1 is adjusted so that the level remains constant. However, on this particular day, corrosion of the tank
has opened up a hole in the wall at a height of 1 m, producing a leak whose volumetric flow rate q4
(m/min) is 4 = 0.025 Vh – 1 where h is height in meters.
Explain in detail the full procedure and include the right parameter's values and units.
a) Obtain a model of the tank system's dynamics.
b) If the tank was initially empty, how long did it take for the liquid to reach the corrosion point?
c) If mass flow rates F1, F2, and F3 are kept constant indefinitely, will the tank eventually overflow?
Justify your answer.
F3
Figure 4

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