Three tanks connected by pipes are shown on a figure below. Originally they contain 10, 20, and40 gallons of pure water respectively. A brine with salt concentartion of 11b/gal flows into the firsttank with the rate 5 gal/min and a well-mixed solution flows from the first to the second tank withthe rate 8 gal/min. From the second tank the well-mixed solution flows into the third tank with therate 8 gal/min and part of a well-mixed solution flows from the third to the first tank with the rate3 gal/min while another part flows outside the system with the rate 5 gal/min. Write down the sys-tem of differential equations describing the amount of salt in each tank and put it into the matrix form.mixture 11b/galflow 5 gal/min10 gal8 gal/minJ20 gal3 gal/min8 gal/min40 gal5 gal/min

Water tank with the flow of water is marked. To write: Set up the system of differential equation.…

Answered: Three tanks connected by pipes are…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

A container made of steel, which has a coefficient of linear expansion 11 ✕ 10−6 (°C)−1, has a volume of 46.0 gallons. The container is filled to the top with gasoline, which has a coefficient of volume expansion of 9.6 ✕ 10−4 (°C)−1, when the temperature is 10.0°C. If the temperature rises to 25.0°C, how much gasoline (in gal) will spill over the edge of the container? gal
1. At 12:00 p.m. a tank contains 150 g of salt dissolved in 8 L of water. Pure water begins flowing into the tank at a rate of 2 L per hour and the well-mixed solution flows out of the tank at a rate of 3 L per hour. At What time will the tank contain 100 g of salt (or will the tank empty before this happens)? 2. At 12:00 p.m. the next day, another tank contains 150 g of salt dissolved in 8 L of water. Water containing 10 g of salt per L begins flowing into the tank at a rate of 2 L per hour and the well-mixed solution flows out of the tank at the same rate. At What time will the tank contain 100 g of salt (or will this never happen)?
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 tank contains 2000 liters (L) of a solution consisting of 120 kg of salt dissolved in water. Pure water is pumped into the tank at the rate of 4 L/s, and the mixture-kept uniform by stirring-is pumped out at the same rate. How long will it be until only 12 kg of salt remains in the tank? It will take about seconds. (Round to the nearest second as needed.)
The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when the side is 4 m. O 336 m³ / sec 224 m3 / sec - 336 m³ / sec - O -112 m³ / sec 448 m³ / sec
the nurse is caring for a client who is 39 weeks gestation and has a prescription for an intravenous infusion of oxytocin 1mu/min for induction of labor. The nurse has 10 units of oxytocin in 1000mL of lactated ringers solution available. How many mL/hr should the nurse set the infusion pump to administer
3) Problem: A large tank holds 300 gallons of brine solution with 40 pounds (Ib) of salt. A concentration of 2 lb/gallon is pumped in a rate of 4 gal/min. The concentration leaving the tank is pumped out at a rate of 3 gal/min. How much salt is in the tank after 12 minutes?
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.
The rectangular tank shown here, with its top at ground level, is used to catch runoff water. Assume that the water weighs 62.3 lb/ft³. a. How much work does it take to empty the tank by pumping the water back to ground level once the tank is full? b. If the water is pumped to ground level with an (8/11)-horsepower (hp) motor (work output 400 ft-lb/sec), how long will it take to empty the tank (to the nearest minute)? c. Show that the pump in part (b) will lower the water level 15 ft (halfway) during the first 20 minutes of pumping. d. What are the answers to parts (a) and (b) in a location where water weighs 62.16 lb/ft³? 62.42 lb/ft³? a. Set up an integral to find the work done. W = Ground 5 ft level 0 30 14 ft
The density of pure iron is 7.874 g/cm.Apiece of steel made of pure iron and other types of iron is in the shape of a rectangular pyramid. The rectangular pyramid has a base edge length of 4 cm, a base edge width of 9 cm, a height of 5 cm, and a mass of 425 g. What is the difference between the density of pure iron and the density of the steel rectangular pyramid? Round your answer to the nearest thousandth. Type your answer.
an ice cube is shrinking uniformly at a rate of 8 cubic inches per hour. when the cube has a volume of 27 cubic inches, at what rate is each side shrinking?
A.5,000,094kg B.12,600kg C.7.99kg D.317.46kg

SEE MORE QUESTIONS

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS