Concept explainers
Stirred tank reactions For each of the following stirred tank reactions, carry out the following analysis.
- a. Write an initial value problem for the mass of the substance.
- b. Solve the initial value problem.
23. A 500-L tank is initially filled with pure water. A copper sulfate solution with a concentration of 20 g/L flows into the tank at a rate of 4 L/min. The thoroughly mixed solution is drained from the tank at a rate of 4 L/min.
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- 2. 1500-gallon tank initially contains 2271.2472 L of water with 2.267962 kg of salt dissolved in it. Water enters the tank at a rate of 9 gal/hr. and the water entering the tank has a salt concentration of 0.5(1 + cost) lbs/gal. If a well mixed solution leaves the tank at a rate of 6 gal/hr., how much salt is in the tank when it overflows?arrow_forward. A dolphin tank at Sea World is being filled. The tank has a volume of 50,000 liters. In order not to keep the dolphins in their small holding pools too long, they are released into the large tank when it is half full. Pure water is being pumped into the tank at 100 L/min. The dolphins release waste into the tank at a rate of 200 mg/min. Even though the tank is being filled, the waste removal system is operating and pumps 2 L/min of fluid from the tank. A) Derive a differential equation for the amount of waste in the tank as time goes on. B) Solve the differential equation (as much as possible by hand). C) How much waste will be in the tank when it finally fills? D) Once the tank fills, only the waste removal system is operating, so 2 L/min of water is removed from the tank, cleaned, and then returned to the tank. Derive a differential equation for the amount of waste in the tank after it fills. E) Solve the new differential equation. F) What is the long term outlook for the amount of…arrow_forwardA large, perfect cube of ice sits in the merciless Australian sun. It is melting. Each of its edges shrinks at 2 mm/min. How quickly does the volume of the ice cube decrease when it weighs 8 kg? (Hint: Assume that the specific volume of ice is the same as that of liquid water, which in turn we assume to be 1 litre/kg = 1000 cm /kg.) O 0.24 kg / min 240 kg / min 2.4 kg / min 24.0 kg / min 1600.0 kg / min 80.0 kg / min O 1.6 kg / min O 16.0 kg / min O 0.08 kg / min O 0.8 kg / min None of the other options.arrow_forward
- 0.5 kg/L Pollutant Pure Water 15 L/min 5 L/min 1000 L 15 L/min 1000 L Pure Water with 5 kg pollutant Tank A Tank B 20 L/min For the figure shown, consider the following: • Two tanks are connected by a pipe with flow rate of 15L/min. • Tank A and Tank B each contains 1000L volume of liquid. • A pollutant with concentration of 0.5kg/L is discharged to Tank A at a rate of 15L/min, while pure water is discharged to Tank B at a rate of 5L/min. • There is an outflow of 20L/min from Tank B. • Initially, the amount of the pollutant in Tank A and in Tank B are zero and 5kg, respectively. • It is assumed that the pollutant is well mixed in each tank at any time t. Let yA(t) and yB(t) be the amount of the pollutant at any time t in Tank A and Tank B, respectively. Determine the particular solution of the corresponding system of ODES using Method of Undetermined Coefficients. What is the final equation of yA(t)? What is the final equation of yB(t)?arrow_forward(b) In an oil refinery, a storage tank as shown in Figure 1 contains 2000 gal of gasoline that initially has 100 lb of an additive dissolved in it. Gasoline containing 2 lb of additive per gallon is pumped into the tank at a rate of 40 gal/min. The well-mixed solution is pumped out at the same rate. Determine the amount of the additive in the tank 20 min after the pumping process begins. 40 gal/min containing 2 lb/gal 40 gal/min containing lb/gal 2000 Figure 1 Hint: Let y be the amount (in pounds) of additive in the tank at time t. The differential equation modeling of the mixture process is given by dy dt = 80- y 50' y(0) = 100arrow_forward2. The sum of two numbers is 24 and their MW difference is 2. What are the numbers? +y=24 2nd 1st %3D24 - X =y=2 2x =26 2. Axty=24 13ty=24 ya (13arrow_forward
- 4. A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held 100 L of pure water. The solution inside the tank is kept well stirred and flows out of the tank at a rate of 3 L/min. If the concentration of salt in the brine entering the tank is 0.2 kg/L, deter- mine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.1 kg/L?arrow_forward2. A.tank initially contains 100 gal of a solution that holds 25 lb of a chemical. Water runs into the tank at the rate of 3 gal/min and the solution runs out at the same rate. How much of the chemical remains in the tank after of the chemical in to reduce the amount 15 min? How long does it take the tank to 1 lb?arrow_forwardsecond picture is what I got. Please answer the problem below 2. Now that you know m and b, calculate the volume of solution dispensedwhen the valve is open for 55.4 ms. Note you will need to look up thedensity of water!arrow_forward
- 1. A tank initially holds 100 gallons of brine solution containing 20 lbs. of salt. At t = 0, fresh water is poured into the tank at the rate of 5 gal/min., while the well- stirred mixture leaves the tank at the same rate. Find the amount of salt in the tank at any time t. 2. A tank 100 gallon capacity is initially full of water. Pure water is allowed to run into the tank at a rate of 1 gallon per minute, and at the same time containing one-fourth pound of salt per gallon flows into the tank also at a rate of 1 gallon per minute. The mixture flows out at a rate of 2 gallons per minute (it is assumed that there is perfect mixing). Find the amount of salt in the tank after t minutes. 3. The rate of growth of an investment is proportional to the amount of the investment at any time t. The initial investment is $1000 and after 10 years the balance is $3320.12. What is the particular solution? 4. The limiting capacity of the habitat of wildlife herd is 750. The growth rate dN/dt of the herd…arrow_forward9. The formula of a cone is given by the formula 1 v ==ar*h . (a) (i) Calculate the volume of the cone when TT= 3.142, r= 3cm and h 2.5cm. (ii) Calculate h when V= 183cm“, r= 5cm and n=3.142 (give your answer to the nearest whole number) (b) Rearrange the formula to make r the subject %3Darrow_forward5. How many 50 lb. bags of 'Applaud' perennial ryegrass are needed to overseed a soccer complex that has 2.5 acres of turf at a rate of 20 Ibs, of PLS / M? The 'Applaud' seed label indicates 95% germination and 92% purity. 6. If you had $3,000 in your budget for purchasing seed, what would the price per bag need to be for you to afford to seed 'Applaud' at the above rate?arrow_forward
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell