The topic is about Applications of First Order Differential Equations. The problem given is about Mixture and flow. The first image attached is how I want to answer the given problem which can be seen on the second image attached. Please provide a complete solution. (of how I want to answer it) Thanks! Will give you a thumbs up A tank contains 400 liters of brine made by dissolving 30 kg of salt in water. Saltwater containing 0.1 kg of salt per liter runs intothe tank at the rate of 8 liters per minute. A well – stirred mixture runs out of the tank at the rate of 12 liters per minute.Determine the percentage of the salt in the mixture at the end of an hour. Cout3QOUT =100-t100-tdądą30= 2.100-t= 2A tank contains 100 gallons of brine made by dissolving 60 lbsof salt in water. Salt water containing 1 lb of salt per gallonruns in at the rate of 2 gal/min., and the mixture kept uniform P(t) :by stirring, runs out at the rate of 3 gal/min. Find the amountof salt in the tank at the end of 1 hour.dtdt100-t3W (t) = 2;%3D%3D100-tØ = (100 – t)-3%3DGiven:Solution:Q(100 – t)-3 = 2 | (100 – t)-3dtV(0) = 100 galQ(0) = 60 lbslb= 1galgaldQ= IN – OUTdtQ(100 – t)-3 = (100 – t)-2 + KCinlbQ = 100 – t + K(100 – t)³galIN = RinCin = 2;(1gal%3DminRin= 2minQ(0) = 60:= -4.000x10-5%3DK =lb: IN = 2тinRoutgal= 3minQ(t) = 100 – t – 4x10-5(100 – t)3OUT = RoutCout; CoutRequired:Q(60)v(t)Q(60)= 100 – 60 – 4x10-5(100 – 60)3V(t) = 100 gal + 2t – 3t = 100 – t%3D:: 0(60) = 37.44 lbs|

Answered: Image /qna-images/answer/00569a1b-07f5-48f4-b0f8-09bfae73ff2d.jpg

Answered: A tank contains 400 liters of brine…

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

Concept explainers

Question

The topic is about Applications of First Order Differential Equations. The problem given is about Mixture and flow. The first image attached is how I want to answer the given problem which can be seen on the second image attached. Please provide a complete solution. (of how I want to answer it) Thanks! Will give you a thumbs up

A tank contains 400 liters of brine made by dissolving 30 kg of salt in water. Saltwater containing 0.1 kg of salt per liter runs into
the tank at the rate of 8 liters per minute. A well – stirred mixture runs out of the tank at the rate of 12 liters per minute.
Determine the percentage of the salt in the mixture at the end of an hour.

Cout
3Q
OUT =
100-t
100-t
dą
dą
30
= 2.
100-t
= 2
A tank contains 100 gallons of brine made by dissolving 60 lbs
of salt in water. Salt water containing 1 lb of salt per gallon
runs in at the rate of 2 gal/min., and the mixture kept uniform P(t) :
by stirring, runs out at the rate of 3 gal/min. Find the amount
of salt in the tank at the end of 1 hour.
dt
dt
100-t
3
W (t) = 2;
%3D
%3D
100-t
Ø = (100 – t)-3
%3D
Given:
Solution:
Q(100 – t)-3 = 2 | (100 – t)-3dt
V(0) = 100 gal
Q(0) = 60 lbs
lb
= 1
gal
gal
dQ
= IN – OUT
dt
Q(100 – t)-3 = (100 – t)-2 + K
Cin
lb
Q = 100 – t + K(100 – t)³
gal
IN = RinCin = 2;
(1
gal
%3D
min
Rin
= 2
min
Q(0) = 60:
= -4.000x10-5
%3D
K =
lb
: IN = 2
тin
Rout
gal
= 3
min
Q(t) = 100 – t – 4x10-5(100 – t)3
OUT = RoutCout; Cout
Required:
Q(60)
v(t)
Q(60)
= 100 – 60 – 4x10-5(100 – 60)3
V(t) = 100 gal + 2t – 3t = 100 – t
%3D
:: 0(60) = 37.44 lbs|

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 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