The brine solution is recycled using a series of mixing tanks before being released outside of the tanks.Tank A receives pure water at a rate of 4 L/min. The solution is pumped to Tanks B and C at rates of 2L/min and x L/min, respectively, from Tank A, which originally contains 500 L of brine solution in which200 g of salt is first dissolved. At a rate of 4 L/min, Tank B from its original 400 L of brine solution inwhich 1000 g of salt has been dissolved pumps the solution to Tank C. At a rate of y L/min, Tank C, whichoriginally holds 400 L of pure water, pumps the solution back to Tank B. Meanwhile, Tank C releases zL/min of solution out of the system.a. Determine the values of x, y, and z if the volume of the solution within each tank stays constantthroughout time.b.Find out the brine solution's concentration coming out of each tank at time t-8 minutes.2 L/minTANK BTANKA4 L/miny L/minPure water@4 L/minx L/minTANK Cz L/min

The brine solution is recycled using a series of mixing tanks, with the solution being pumped…

Answered: The brine solution is recycled using a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A 100-gal tank initially contains 25 gal of 50% salt solution. Fresh water is then poured into the tank at the rate of 4 gal/min, while the well-stirred mixture leaves the tank at the rate of 2 gal/min. Find (a) the amount of time required for overflow to occur and (b) the percentage of salt in the tank at the moment of overflow.
A tank contains 175 liters of fluid in which 20 grams of salt is dissolved. Brine containing 0.75 gram of salt per liter is then pumped into the tank at a rate of 3 L/min; the well-mixed solution is pumped out at the same rate. What is the exponent of e in the integrating factor if qin is the inflow rate? Select one: a. (Inflow rate divided by tank volume) b. (Inflow rate divided by outflow rate) c. (Inflow rate divided by outflow concentration) d. (Outflow rate divided by tank volume) Which of the following statements is TRUE about the mixture model? Select one: a. The solution to the mixture model is obtained using the separation of variables. b. In a steady state system, the inflow is equal to the outflow. c. The value of k is positive. d. In an unsteady state system, the inflow is equal to the outflow. How much salt in grams is in the tank in 30 minutes? Select one: a. 106.70 b. 13.888 c. 165.69 d. 34.781 e. 235.96 f. 64.731 At what time in minutes will the concentration of…
Two tanks are interconnected. Tank A contains 70 grams of salt in 50 liters of water, and Tank B contains 80 grams of salt in 20 liters of water. A solution of 4 gram/L flows into Tank A at a rate of 5 L/min, while a solution of 1 grams/L flows into Tank B at a rate of 10 L/min. The tanks are well mixed. The tanks are connected, so 6 L/min flows from Tank A to Tank B, while 1 L/min flows from Tank B to Tank A. An additional 15 L/min drains from Tank B. Letting a represent the grams of salt in Tank A, and y represent the grams of salt in Tank B, set up the system of differential equations for these two tanks. dx dt dy dt x (0) = 11 2 y(0) =
A cylindrical container, 80 cm in diameter is initially filled with water to a depth of 119.367 cm. Then 0.05 kilograms of salt are dissolved in the tank. Brine containing 2 grams of salt per liter is then pumped into the tank at the rate of 0.006 m3 per minute and the solution mixed well is pumped out of the same rate. Find:a. The number of grams of salt in the tank at any time (in minutes)b. The amount of salt(grams) in the tank after 8 minutes. c. The time when the amount of salt in the tank is 200 grams.
Suppose there are two tanks, each containing 20 L of fluid. Tank 1 initially contains water with 4kg of salt dissolved and Tank 2 initially contains pure water. The tanks are stirred constantly so their solutions have uniform concentration. There is a pipe which takes 15 L/min from tank 1 to tank 2, and another pipe which takes 15 L/min from tank 2 to tank 1. Also, pure water is being pumped into each of tank 1 and tank 2 at a rate of 5 L/min, and solution is being removed at a rate of 5 L/min from each of tank 1 and tank 2. Model the initial value problem as a system of two first order differential equations, solve the initial value problem, and find the amount of salt in tank 1 after one minute.
A device used for treating of agri-effluents has an inflow of 8 cubic feet per second and the amount of phosphorous in it is 20 milligrams per liter. The device media consists of wood and charcoal. This device eliminates 0.8 milligrams per liter of phosphorous for every 1 cubic feet of media. If the device is required to have an outflow phosphorous concentration of 0.9 milligrams per liter then find the volume of the filter media required for the device.
For an auditorium: Room condition: 26oC DPT, 19 oC WPT; Outside conditions: 35 oC DPT 27 oC WPT; Room heat gains: Sensible heat= 11.1 kW Latent Heat= 3.9 kW The conditioned air supplied to the room is 50 cm/min and contains 25 percent fresh air and 75 percent re-circulated room air. Determine; a) The DBT and WBT of supply air. b) The DBT and WBT of mixed fresh and re-circulated air before the cooling coil. c) The apparatus due point in bypass factor of the coil d) The refrigeration load on the cooling coil and the moisture removed by the coil.
A sewage disposal plant has a big concrete holding tank of 800 m³ capacity. It is half full of liquid to start with and contains 25,000 kg of organic material suspended in water. Water runs into the holding tank at the rate of 125 m³/hr and the solution leaves at the rate of 100 m³/hr. How much organic material is in the tank at the end of 5 hr?
Consider two interconnected tanks as shown in the figure above. Tank 1 initial contains 100L (liters) of water and 310 g of salt, while tank 2 initially contains 100 L of water and 480 g of salt. Water containing 15 g/L of salt is poured into tank1 at a rate of 1.5 L/min while the mixture flowing into tank 2 contains a salt concentration of 30 g/L of salt and is flowing at the rate of 3.5 L/min. The two connecting tubes have a flow rate of 4 L/min from tank 1 to tank 2; and of 2.5 L/min from tank 2 back to tank 1. Tank 2 is drained at the rate of 5 L/min. You may assume that the solutions in each tank are thoroughly mixed so that the concentration of the mixture leaving any tank along any of the tubes has the same concentration of salt as the tank as a whole. (This is not completely realistic, but as in real physics, we are going to work with the approximate, rather than exact description. The 'real equations of physics are often too complicated to even write down precisely, much less…
A cylindrical container, 80 cm in diameter is initially filled with water to a depth of 119.367 cm. Then 0.05 kilograms of salt are dissolved in the tank. Brine containing 2 grams of salt per liter is then pumped into the tank at the rate of 0.006 m³ per minute and the solution mixed well is pumped out of the same rate. Find: a. The number of grams of salt in the tank at any time (in minutes) b. The amount of salt(grams) in the tank after 8 minutes. c. The time when the amount of salt in the tank is 200 grams.
A 500 gal capacity tank initially contains 200 gal of water and 5 Ibs of salt per gallon. To reduce the concentration, water at the rate of 3 gal/min enters the tank and the thoroughly mixed solution flows out at the same rate. After 20 min. the process is stopped and brine solution flows into the tank at the same rate of 3 gal/min and at a concentration of 2 Ibs/gal. The mixed solution flows out at the rate of 2 gal/min. Find the amount of salt in the tank 30 min. after resumption of the process. O 699.79 Ib O 717.71 lb O 560.17 Ib O 913.68 Ib
Write down the 4 by 4 matrix S that scales by a constant c. Multiply ST and also TS, where T is translation by (1, 4, 3). To blow up the picture around the center point (1, 4, 3), would you use vST or vT S?

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