Question

A tank is initially filled with 1000 litres of a salt solution containing 1000 grams of salt. A solution containing 10 g/l runs into the tank at the rate of 5 l/min and the well stirred mixture runs out of the tank at the same rate.

(i) Determine the differential equation with initial condition that models this situation.

(ii) Determine how long it will take for the salt in the tank reaching 2500g.

Answer #1

A tank initially contains 120 L of pure water. A mixture
containing a concentration of 9 g/L of salt
enters the tank at a rate of 3 L/min, and the well-stirred
mixture leaves the tank at the same rate.
Determine the differential equation for the rate of change of
the amount of salt in the tank at any time t
and solve it (using the fact that the initial amount of salt
in the tank is 0g).

A 500-gallon tank initially contains 100gal of brine containing
50lb of salt. Brine containing 2lb of salt per gallon enters the
tank at the rate of 4gal per minute and the well stirred solution
leaves the tank at a rate of 8gal per minute.
(a) How long will it be before the tank is empty
(b) Determine the differential equation that gives the amount
A(t) of salt (in pounds) in the tank at any time t before it is
emptied....

A tank contains 30 gallons of brine solution containing 10 lb of
salt. Another brine solution of concentration of 3 lb/gallon is
poured into the tank at the rate of 2 gallons/min. The well stirred
solution in the tank is drained out at the rate of 2 gallons/min.
Let the amount of salt in the tank at time ? be ?(?).
Write the differential equation for A(t) and solve it.

A salt solution containing 2 grams of salt per liter of water
is poured into the tank at a rate 3 liter/min where initially
contains 30 liters of pure water. The mixture then was drained at
the same rate as its poured into the tank. Solve,
Hint:
(??(?) = ???????? ????????????? (??) × ???? ???? (??)? −
????(???? ????????????? (???) ×
i. the initial-value problem that describes the amount of salt
in the tank for t > 0
??
????...

A tank initially contains 100 liters of water in which 50 grams
of salt are dissolved. A salt solution containing 10 grams of salt
per liter is pumped into the tank at the rate of 4 liters per
minute, and the well-mixed solution is pumped out of the tank at
the rate of 6 liters per minute. Let t denote time (in minutes),
and let Q denote the amount of salt in the tank at time t (in
grams). Write...

A 100 gallon tank is filled with brine solution containing 50
pounds of salt. Pure water enters the tank a rate of 10 gal per
hour. Well mixed solution leaves the first tank at the same rate
(10 gal/hr) and enters a second 100 gallon tank initially
containing 10 pounds of salt. How much salt is in tank 2 at any
time?

a tank is filled half-full of a mixture 100 liters of water and
50kg of salt. water runs in to the tank at a rate of 10 liters per
second. the mixture is kept uniform by stirring, runs out at the
same rate. what is the amount of salt inside the tank after 10
seconds? from the solution of the formulated differential equation,
sketch the amount of salt as time approaches infinity.

A tank initially holds 100 gal of brine solution. At t = 0,
fresh water is poured into the tank at the rate of 5 gal/min, while
the well-stirred mixture leaves the tank at the same rate. After 20
min, the tank contains 20/e lb of salt. Find the initial
concentration of the brine solution inside the tank. Ans.: 0.20
lb/gal

A brine solution of salt flows at a rate of 3 L/min into a large
tank that initially held
200 L of pure water. The solution flowing into the tank has a
concentration that is given
by c(t) = 5. The solution inside the tank is kept super stirred. It
flows out
of the tank at a rate of r(t) = 5 in L/min. Set up a DE that
governs this situation in
terms of the mass of salt in...

A brine solution of salt flows at a constant rate of 10 L/min
into a large tank that initially held 100 L of pure water. The
solution inside the tank is kept well stirred and flows out of the
tank at a rate of 6 L/min. If the concentration of salt in the
brine entering the tank is 4 kg/L, determine the mass of salt in
the tank after t min.

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