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 8 are assumed to be well stirred. We wish to construct a mathematical model that describes the number of pounds x₂ (t) and x₂(t) of salt in tanks A and B, respectively, at time t. pure water 3 gal/min mixture 1 gal/min mixture 4 gal/min This system is described by the system of equations = mixture 3 gal/min dx₂ 2 251 +52 dt dx₂ 2 25x2 dt 25 35 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 5 pounds of salt per gallon is pumped into tank A?
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 8 are assumed to be well stirred. We wish to construct a mathematical model that describes the number of pounds x₂ (t) and x₂(t) of salt in tanks A and B, respectively, at time t. pure water 3 gal/min mixture 1 gal/min mixture 4 gal/min This system is described by the system of equations = mixture 3 gal/min dx₂ 2 251 +52 dt dx₂ 2 25x2 dt 25 35 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 5 pounds of salt per gallon is pumped into tank 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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3.3-2
Transcribed Image Text: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.
mixture
4 gal/min
This system is described by the system of equations
25x1 + 5-10x
dx
=
dt
pure water
3 gal/min
m
dt
mixture
1 gal/min
=
25*1-25×2
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 5 pounds of salt per gallon is pumped into tank A?
dx₁ =
dt
dx₂
mixture
3 gal/min
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