Question

2. Consider the two interconnected tanks shown in the figure below. Tank 1 initially contains 30 gal of water and 25 oz of salt, and Tank 2 initially contains 20 gal of water and 15 oz of salt. Water containing 1 oz/gal of salt flows into Tank 1 at a rate of 1.5 gal/min. The mixture flows from Tank 1 to Tank 2 at a rate of 3 gal/min. Water containing 3 oz/gal of salt also flows into Tank 2 at a rate of 1 gal/min (from the outside). The mixture drains from Tank 2 at a rate of 4 gal/min, of which some flows back into Tank 1 at a rate of 1.5 gal/min, while the remainder leaves the system. 1.5 gal/min 1 ga/min oz/gal 3 oziga 3 galimin 30 gal water 20 gal water 1.5 gal/min Tank 1 Tank 2 2.5 gaVmin

(10p) (b) Use the Laplace transform method to find Q1 (t); Q2 (t) in terms of convolution products

Answer 1

ve that to tanks are Interconnectac Corrtatns 3o o wa and02 Salt Tank 2 Contains 2o of oct and 15 02 tank at vtaof 5 min dt 2ひ imtlar 30 20 d L ①ard (2) are the differ entied-Grat

The inttial Conalttions ave b) dtdt 1.5- 00 0 o and uue can get32 and of = 4202 be exponential unchions are dt 5( C2) dt do dt Usna the tilrdl -Pa Constants , ard it