20 [1] Each of the two tanks shown in the Fig. 1 contains 100 gallons of...

 

 

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20 [1] Each of the two tanks shown in the Fig. 1 contains 100 gallons of water. The water in Tank I contains 1000 grams of dissolved salt, while the water in Tank 2 contains 100 grams of dissolved salt. At time t = 0, pipe 1 starts pumping pure water at the rate of 10 gallons per minute, while pipes 2, 3 and 4 start pumping mixed water at rates 15, 5 and 10 gallons per minute, respectively, in the directions indicated in the figure. To determine the concentration of salt in the two tanks at any instant, the following equations are to be solved: dx dt dy dt = = with x(0) = 5 y 100 15 1000 15 - X 1000 15 X- y 100 1000 grams and y(0) = 100 grams. Use the Runge-Kutta of order 4 numerical method and one step to determine the amount of salt in Tanks 1 and 2, x(t) and y(t), respectively, at time t = 0.4 minutes. Pipc 1, 10 gal/min Tank 1 Q = 100 gal. Pipe 2, 15 gal/min Pipe 3, 5 gal/min Fig. 1. Tanks system Page 1 of 4 Tank 2 Q = 100 gal. Pipe 4. 10 gal/min 20 [1] Each of the two tanks shown in the Fig. 1 contains 100 gallons of water. The water in Tank I contains 1000 grams of dissolved salt, while the water in Tank 2 contains 100 grams of dissolved salt. At time t = 0, pipe 1 starts pumping pure water at the rate of 10 gallons per minute, while pipes 2, 3 and 4 start pumping mixed water at rates 15, 5 and 10 gallons per minute, respectively, in the directions indicated in the figure. To determine the concentration of salt in the two tanks at any instant, the following equations are to be solved: dx dt dy dt = = with x(0) = 5 y 100 15 1000 15 - X 1000 15 X- y 100 1000 grams and y(0) = 100 grams. Use the Runge-Kutta of order 4 numerical method and one step to determine the amount of salt in Tanks 1 and 2, x(t) and y(t), respectively, at time t = 0.4 minutes. Pipc 1, 10 gal/min Tank 1 Q = 100 gal. Pipe 2, 15 gal/min Pipe 3, 5 gal/min Fig. 1. Tanks system Page 1 of 4 Tank 2 Q = 100 gal. Pipe 4. 10 gal/min