Question
In: Mechanical Engineering
Two tanks each contain 100 gal of water and tank 2 initially has 50 lbs of...
Two tanks each contain 100 gal of water and tank 2 initially has 50 lbs of salt uniformly dissolved in it. An external flow brings adds 5 gal/min to tank 1 with 5 lbs of salt in it. Tank 1 feeds tank 2 at 10 gal/min, and tank 2 feeds back to tank 1 at 5 gal/min. Finally, an exit stream leaves tank 2 at 5 gal/min.
1) Use Laplace transforms to solve the system of ODEs modeling this system and report the amount of salt in tank 2 as a function of time.
2)find the Homogeneous solution for the system of ODEs above without Laplace transforms; instead, using eigenvalues/eigenvectors.
3)Solve the Particular solution for the system of ODEs above using Undetermined Coefficients.
Solutions
samet mamat answered 10 months agoRelated Solutions
Two tanks contain a mixture of water and alcohol with tank A contain- ing 500 L...
Two tanks contain a mixture of water and alcohol with tank A
contain- ing 500 L and tank B 1000L. Initially, the concentration
of alcohol in Tank A is 0% and that of tank B is 80%. Solution
leaves tank A into B at a rate of 15 liter/min and the solution in
tank B returns to A at a rate of 5 L/min while well mixed solution
also leaves the system at 10 liter/min through an outlet. A mixture...
Two tanks contain a mixture of water and alcohol with tank A contain- ing 500 L...
Two tanks contain a mixture of water and alcohol with tank A
contain- ing 500 L and tank B 1000L. Initially, the concentration
of alcohol in Tank A is 0% and that of tank B is 80%. Solution
leaves tank A into B at a rate of 15 liter/min and the solution in
tank B returns to A at a rate of 5 L/min while well mixed solution
also leaves the system at 10 liter/min through an outlet. A mixture...
Tanks A and Bare filled with 100 gal and 200 gal of brine respectively. Initially, 40...
Tanks A and Bare filled with 100 gal and 200 gal of brine
respectively. Initially, 40 lb of salt dissolved in the solution in
tank A and 20 lb of salt dissolved in the solution in tankB. The
system is closed in that the well-mixed liquid pumped from A into B
and from B into A at a rate of 25gal/min each (so, the liquid
volumes do not change over the time in both tanks).
(a) Find the general equation...
A tank originally contains 100 gal of fresh water. Then water containing 1 2 lb of...
A tank originally contains 100 gal of fresh water. Then water
containing 1 2 lb of salt per gallon is poured into the tank at a
rate of 2 gal/min, and the mixture is allowed to leave at the same
rate. After 10 min the process is stopped, and fresh water is
poured into the tank at a rate of 4 gal/min, with the mixture again
leaving at the same rate. Find the amount of salt in the tank at...
A tank originally contains 100 gal of fresh water. Then water containing 1 2 lb of...
A tank originally contains 100 gal of fresh water. Then water
containing
1
2
lb of salt per gallon is poured into the tank at a rate of 2
gal/min, and the mixture is allowed to leave at the same rate.
After 10 min the process is stopped, and fresh water is poured into
the tank at a rate of
6 gal/min,
with the mixture again leaving at the same rate. Find the amount
of salt in the tank at...
A tank contains 100 gal of water. Brine enters the tank at the rate of 3...
A
tank contains 100 gal of water. Brine enters the tank at the rate
of 3 gal/min. The mixture, thoroughly stirred, leaves the tank at
the rate of 2 gal/min. If the salt concentration in the brine at
the end of 20 minutes is to be 2 lb/gal, what should be the salt
concentration in the brine entering the tank?
A tank contains 100 gal of water. Brine enters the tank at the rate of 3...
A
tank contains 100 gal of water. Brine enters the tank at the rate
of 3 gal/min. The mixture, thoroughly stirred, leaves the tank at
the rate of 2 gal/min. If the salt concentration in the brine at
the end of 20 minutes is to be 2 lb/gal, what should be the salt
concentration in the brine entering the tank?
1. A 100-gallon tank initially holds 50 gal of brine containing 5 pounds of salt. Brine...
1. A 100-gallon tank initially holds 50 gal of brine containing
5 pounds of salt. Brine
containing 1 pound of salt per gallon enters the tank at the rate
of 4 gal/s, and the
well-mixed brine in the tank flows out at the rate of 3
gal/s.
(a) How much salt will the tank contain at the time when the tank
is full of brine?
(b) If the tank had an infinite capacity, what is the maximum
amount of salt...
Five lbs of propane is contained in a closed, rigid tank initially at 80 lbf/in.2, 50°F....
Five lbs of propane is contained in a closed, rigid tank
initially at 80 lbf/in.2, 50°F. Heat transfer occurs
until the final temperature in the tank is 0°F. Kinetic and
potential energy effects are negligible.
Determine the amount of energy transfer by heat, in Btu.
Consider a large tank holding 50 gal of pure water into which a brine solution of...
Consider a large tank holding 50 gal of pure water
into which a brine solution of salt begins to flow at a constant
rate of 6 gal/min. the brine leaves the tank at a rate of 5
gal/min. If the concentration of salt in the brine entering the
tank is 0.1 lbs per gallon, determine the function X that will
determine the amount of brine in the tank at any time t.
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