Question

A tank contains 100 gallons of pure water. A salt solution with concentration 2.5 lb/gal enters the tank at a rate of 4 gal/min. Solution drains from the tank at a rate of 4 gal/min. Find the eventual concentration of the salt solution using a qualitative analysis rather than by actually solving the DE.

Answer #1

A tank contains 40 lb of salt dissolved in 400 gallons of water.
A brine solution is pumped into the tank at a rate of 4 gal/min; it
mixes with the solution there, and then the mixture is pumped out
at a rate of 4 gal/min. Determine A(t), the amount of salt in the
tank at time t, if the concentration of salt in the inflow is
variable and given by cin(t) = 2 + sin(t/4) lb/gal.

A tank contains 70 lb of salt dissolved in 200 gallons of water.
A brine solution is pumped into the tank at a rate of 2 gal/min; it
mixes with the solution there, and then the mixture is pumped out
at a rate of 2 gal/min. Determine A(t), the amount of salt in the
tank at time t, if the concentration of salt in the inflow is
variable and given by cin(t) = 2 + sin(t/4) lb/gal.

A tank initially contains 100 gal of a salt-water solution
containing 0.05 lb of salt for each gallon of water. At time zero,
pure water is poured into the tank at a rate of 2 gal per minute.
Simultaneously, a drain is opened at the bottom of the tank that
allows the salt-water solution to leave the tank at a rate of 3 gal
per minute. What will be the salt content in the tank when
precisely 50 gal of...

A tank contains 100 gal of brine made by dissolving 80 lb of
salt in water. Pure water
runs into the tank at the rate of 4 gal/min, and the mixture,
kept uniform by stirring runs
out at the same rate. Find the amount of salt in the tank at
t=8 min.

A tank contains 100 kg of salt and 1000 L of water. Pure water
enters a tank at the rate 12 L/min. The solution is mixed and
drains from the tank at the rate 6 L/min.
(a) What is the amount of salt in the tank initially?
(b) Find the amount of salt in the tank after 4.5 hours.

A 100-gallon tank initially contains pure water. A solution of
dye containing 0.3 lb/gal flows into the tank at the rate of 5
gal/min and the resulting mixture flows out at the same rate. After
15 min, the process is stopped and fresh water flows into the tank
at the same rate. Find the concentration of dye in the tank at the
end of 30 min. Ans.: 0.075 lb/gal

A tank contains 80 kg of salt and 1000 L of water. Pure water
enters a tank at the rate 6 L/min. The solution is mixed and drains
from the tank at the rate 3 L/min. Find the amount of salt in the
tank after 2 hours. What is the concentration of salt in the
solution in the tank as time approaches infinity?

A tank contains 90 kg of salt and 2000 L of water: Pure water
enters a tank at the rate 8 L/min. The solution is mixed and drains
from the tank at the rate 8 L/min. What is the amount of salt in
the tank initially? Find the amount f salt in the tank after 4.5
hours. Find the concentration of salt in the solution in the tank
as the time approaches infinity. (Assume your tank is large enough
to...

A 300-gal capacity tank contains a solution of 200 gal of water
and 50 lb of salt. A solution containing 3 lb of salt per gal is
allowed to flow into the tank at the rate of 4 gal/min. The mixture
flows from the tank at the rate of 2 gal/min. How many pounds of
salt are in the tank at the end of 30 min? When does the tank start
to overflow? How much salt is in the tank...

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 5 gal/min, with the mixture again
leaving at the same rate. Find the amount of salt in the tank at
the...

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