A tank initially contains 50 gal of pure water. A salt solution containing 2 pounds of salt per gallon of water is poured into the tank at a rate of 3 gal/min. The mixture is stirred and is drained out of the tank at a rate of 3 gal/min. The mixture is stirred and is drained out of the tank at the same rate. (a) Find the initial-value problem that describes the amount Q of salt in the tank at any time. (b) Find the amount of salt in the tank at any time. (c) Find the amount of salt in the tank after 20 minutes. (d) Find the amount of salt in the tank after a long time. [3.1]

A tank initially contains 50 gal of pure water. A salt solution containing 2 pounds of salt per gallon of water is poured into the tank at a rate of 3 gal/min. The mixture is stirred and is drained out of the tank at a rate of 3 gal/min. The mixture is stirred and is drained out of the tank at the same rate. (a) Find the initial-value problem that describes the amount Q of salt in the tank at any time. (b) Find the amount of salt in the tank at any time. (c) Find the amount of salt in the tank after 20 minutes. (d) Find the amount of salt in the tank after a long time. [3.1]

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

Related questions

Q: When a vertical beam of light passes through a transparent medium, the reason that its intensity I…

A: We have to find What is the beam intensity at 15 feet below the surface.

Q: A tank contains 150 liters of fluid in which 40 grams of salt is dissolved. Brine containing 1 gram…

A: We have to find the solution for given problem.

Q: In the absence of predators the population of mosquitoes in a certain area would increase at a rate…

A: Given initial population of mosquitos is 200000 and the get triple every week, Flock birds eats…

Q: Radium decomposes at a rate proportional to the amount at any instant. In 100 years, 100 mg of…

A: Radium decomposed proportional to amount dy/dt ∞ y dy/dt =ky dy/y = kdt Integrate on both sides ∫…

Q: vimming pool whose volume is 10,000 gal contains water that is 0.01% chlorine. Starting at t=0, city…

A: The solution is given by

Q: A tank has initially 10 lb of salt dissolved in 100 gal of water. A solution containing a variable…

Q: A tank initially contains 50 gal of pure water. Brine containing 3 lb of salt per gallon enters the…

A: According to the given information, let x(t) denote the amount of salt in the tank at time t, t in…

Q: A tank originally contains 500 gallons of pure water. Brine containing 2 lb of salt per gallon is…

Q: ine solution of salt flows at a constant rate of 7 L/min into a large tank that initially held 100 L…

Q: A tank contains 200 liters of fluid in which 30 grams ofsalt is dissolved. Brine containing 1 gram…

A: See solution in image Explanation:The rate of salt means the rate at which the amount of salt is…

Q: A tank contains 14,000 L of brine with 21 kg of dissolved salt. Pure water enters the tank at a rate…

Q: A large tank is filled to capacity with 300 gallons of pure water. Brine containing 4 pounds of salt…

A: Tank has been filled to capacity with 300 gallons of pure water. Incoming rate of brine solution is…

Q: A tank initially contains 80 gal of pure water. Brine containing 3 lb of salt per gallon enters the…

A: Given a condition wherein, " A tank initially contains 80 gal of pure water. Brine containing 3lbof…

Q: Q2: In the two-tank mixing process shown in Fig.(2), x varies from 0 lb salt/ft³ to 1 lb salt/ft²…

Q: A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram…

Q: Two tanks are connected in tandem as shown in the following figure. Each tank contains 60 gal of…

A: (a) What is the initial amount of salt (in lb) in tank 2? At t = 0 A(0) = 180(1 − e−0/30) −…

Q: In a natural habitat, the population of a certain species of snails is given by P= 0.8(Ae* +500),…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

A tank initially contains 50 gal of pure water. A salt solution
containing 2 pounds of salt per gallon of water is poured into the
tank at a rate of 3 gal/min. The mixture is stirred and is drained out
of the tank at a rate of 3 gal/min. The mixture is stirred and is
drained out of the tank at the same rate.
(a) Find the initial-value problem that describes the amount Q of
salt in the tank at any time.
(b) Find the amount of salt in the tank at any time.
(c) Find the amount of salt in the tank after 20 minutes.
(d) Find the amount of salt in the tank after a long time.
[3.1]

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

P(A)= 0.33, P(B)= 0.44, P(A and B)= 0.16 Calculate P(A and B')?
A tank contains 210 liters of fluid in which 50 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 3 L/min; the well-mixed solution is pumped out at the same rate. Let the A(t) be the number of grams of salt in the tank at time t. Find the rate at which the number of grams of salt in the tank is changing at time t. Find the number A(t) of grams of salt in the tank at time t.
Consider the cascade of two tanks of brine shown in the figure below, with V1=99 gallons and V2=204 gallons being the volumes of brine in the two tanks. Each tank also initially contains 51 lb of dissolved salt. The three flow rates indicated in the figure are each 4.6 gal/min, with pure water flowing into tank 1. (a) Find the amount x(t) of salt in tank 1 at time t. x(t)=? (b) Suppose that y(t), the amount of salt in tank 2 at time t, is given by the differential equation dy/dt=(4.6x/99)−(4.6y/204). Solve for y(t) using the function x(t) found in part (a) y(t)=?
Set up an I.V.P. and solve using the following: Suppose a large mixing tank initially holds 500 liters of pure water. A brine solution is pumped into the tank at a rate of 3 L/min with a concentration of 0.2 kilograms of salt per liter. If the well-stirred solution is pumped out at the same rate, find the number of kilograms of salt in the tank at time t, A(t).
A tank contains 120 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 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. Find the number A(t) of grams of salt in the tank at time t. A(t) = 9
A large tank is filled to capacity with 600 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is pumped out at the same rate. Find the number A(t) of pounds salt in the tank at time t.
A tank initially contains 60 gallons of pure water. Brine containing 1 lb of salt per gallon enters the tank at 2 gal/min, and the perfectly mixed solution leaves the tank at 3 gal/min; thus the tank is empty after exactly 1 h. (a) Find the amount of salt in the tank after 20 minutes. (b) What is the maximum amount of salt ever in the tank?
Example: A tank initially contains 800 gallons of fresh water. Water containing 1/2 lb/gal of salt flows into the tank with the rate 6 gal/min and the well stirred mixture flows out at the rate of 2 gal/min. Write the initial value problem for Q(t), the amount of salt in pounds in the tank.
A tank contains 7070 kg of salt and 10001000 L of water. A solution of a concentration 0.035 kg of salt per liter enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the same rate.(a) What is the concentration of our solution in the tank initially?(b) Find the amount of salt in the tank after 2.5 hours.(c) Find the concentration of salt in the solution in the tank as time approaches infinity.