6. Tanks A, B, and C (of volumes VA, VB, and Ve, respectively) containing a salt solution (initialmass concentrations CA.0, CB.0, and cc.o) are connected by pipes in that order. Pure waterflows into tank A at a volumetric rate r; liquid flows from A to B, from B to C, and from Cto waste at rate r.(a) Using a mass balance for salt on each tank, set up a system of differential cquations todescribe the salt concentration in cach tank (CA(t), CB(t), cc(t)) as a function of time.Also state the initial conditions needed to find a unique solution.(b) Without solving, predict limiting values of ca(t), CB(t), and cc(t) as t → o.

(a) The volumes in tanks A, B, and C are VA, VB, VC respectively. The initial concentration of salt…

Answered: Tanks A, B, and C (of volumes VA, VgB,…

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

Please answer a. c. & g. Thanks
NEED FULLY CORRECT HANDWRITTEN SOLUTION FOR THIS... ASAP!!!!
Consider the two tanks shown in the figure below. Assume that tank A contains 50 gallons of water in which 25 pounds of salt is dissolved. Suppose tank B contains 50 gallons of pure water. Liquid is pumped into and out of the tanks as indicated in the figure; the mixture exchanged between the two tanks and the liquid pumped out of tank B are assumed to be well stirred. We wish to construct a mathematical model that describes the number of pounds x₁(t) and x₂(t) of salt in tanks A and B, respectively, at time t. dx₁1 dt dx1 dt pure water 3 gal/min mixture 4 gal/min This system is described by the system of equations 1 50 2 25 dx2 dt 2 25 2 25*1 1 + -X2 mixture 1 gal/min -X2 B with initial conditions x₁(0) = 25, x₂(0) = 0 (see (3) and the surrounding discussion on mixtures on page 107). What is the system of differential equations if, instead of pure water, a brine solution containing 3 pounds of salt per gallon is pumped into tank A? -2 25*1 + 50x2+6× dx2 2 - (25)*₁- (25)×₂2 - = x2 dt…
1. A machine produces metal pieces that are cylindrical in shape. A sample of these pieces is taken and the diameters are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, and 1.03 centimeters. Use these data to calculate three interval types and draw interpretations that illustrate the distinction between them in the context of the system. For all computations, assume an approximately normal distribution. The sample mean and standard deviation for the given data are ¯x = 1.0056 and s = 0.0246. (a) Find a 99% confidence interval on the mean diameter. (b) Compute a 99% prediction interval on ameasured diameter of a single metal piece taken from the machine. (c) Find the 99% tolerance limits that will contain 95% of the metal pieces produced by this machine.
114 Exercise 12. 2 Flow Diagrams: 1. Use the rule to find out the following and show all your calculations: n = m+5 2-n = m+5 15 2: Use the rule to find out the following and show all your calculations: y =÷r %3D 2y = Grade 7 Worksheet (Activities)
Let V1, Vk be the points in R³ and suppose that for j = 1, ..., k an object with mass m; is located at point vj. Physicists call such objects point masses. The total mass of the system of point masses is m = m₁ + ... + mk. The center of gravity (or center of mass) of the system is 1 Point V₁ = (3,-5,3) V₂ = (6,3,-3) Mass 69 15g V3 ( 4, 3, 2) 6 g V4 = (-6,9,7) 3 g v = +... Compute the center of gravity of the system consisting of the point masses above.
What value of μ makes the above system inconsistent?
An Automotive Association (AA) analysed the relationship between engine volume and mileage, given the same volume of petrol. Table 6 is tabulated for nine standard-transmission, four cylinders, petrol-fuelled cars from different car manufacturer. The engine volume is in total cubic kilometre (km). Table 6: Engine volume and mileage of different car manufacturer Engine volume, x (cubic km) Mileage, y (km) Car manufacturer Honda 97 24 Datsun 85 29 Chevrolet 98 26 Mazda 105 24 Proton 120 24 Perodua 151 22 Toyota Nissan 140 23 134 23 Kia 146 21 Based on the given data, i) Find the least squares equation (i.e., linear regression) for the data. ii) Use the least-square equation to estimate the mileage for a car which has 125 cubic km engine volume.
Consider a system of three tanks connected to one another with rates of flow r12 = 4, r21 = 3, r13 = 2, r31 = 3, r23 = 6, and r32 = 5 (rij denotes the rate of flow from tank i into tank j), all in liters/sec, and volumes V1 = 5, V2 = 10, V3 = 15, all in liters. Initially x1(0)=0, x2(0)=20, x3(0)=40, all in grams (of salt). Find the amounts of salt x1(t), x2(t), x3(t) in the three tanks as t goes to infinity.
In order to ensure the stability of the crane, you decide to analyze the vibrations the crane would undergo in a windy environment. For a preliminary analysis, the crane is modelled as a mass-spring system comprising three springs. The following equations are derived in the first test condition:
. .... 2. Let V₁, Vk be points in R³ and suppose that for j = 1,..., k an object with mass m is located at point vj. Physicists call such objects point masses. The total mass of the system of point masses is m = = m₁ + The center of mass of the system is 1 (m₁v₁ + +mkok). m ·+mk. Compute the center of mass of the system consisting of the following point masses. Point (5,-4,3) (4,3,-2) (-4,-3,-1) (-9, 8, 6) Mass 2 g. 5 g. 2 g. 1 g.
1. Consider two interconnected tanks as shown below. Tank 1 initially contains 600 gal of water with 3 lb of salt, and Tank 2 initially contains 400 gal of water with 1 lb of salt. Water containing 0.4 lb/gal of salt flows into Tank 1 at a rate of 3 gal/min. The well stirred mixture in Tank 1 flows into Tank 2 at a rate of 4 gal/min. The well stirred mixture in Tank 2 leaves the tank at a rate of 6 gal/min and additionally, flows back into Tank 1 at a rate of 2 gal/min. Let Q₁(t) and Q₂(t) denote the amounts of salt (in lb) in Tank 1 and Tank 2 at time t in minutes. Let V₁ (t) and V₂(t) denote the volumes of solutions (in gal) in Tank 1 and Tank 2 at time t in minutes. Set up the initial value problem satisfied by Q₁(t) and Q₂(t) describing the mixing process. (Show your work to get a full credit) Tank 1 72 Tank 2 T4

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