Question
In: Advanced Math
(62). (Transient Behavior of a Mixing tank): A tank initially holds 80 gal of a brine...
(62). (Transient Behavior of a Mixing tank): A tank initially holds 80 gal of a brine solution containing 0.125 lb of salt per gallon. At t=0, another brine solution containing 1 lb of salt per gallon is poured into the tank at a rate of 4 gal/min, while the well-stirred mixture leaves the tank at a rate of 8 gal/min. (a) Formulate a model for describing the transient behavior of the tank (b) Find the amount of salt in the tank when the tank contains exactly 40 gal of the solution.
Solutions
Colby Messinger answered 2 years agoRelated Solutions
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...
A tank initially contains 150 gal of brine in which 20lb of salt are dissolved. A...
A tank initially contains 150 gal of brine in which 20lb of salt
are dissolved. A brine containing 3 lb/gal of salt runs into the
tank at the rate of 4 gal/min.The mixture is kept uniform by
stirring and flows out of the tank at the rate of 3 gal/min. Let y
represent the amount of salt at time t. Complete parts a through
e.
a. At what rate (pounds per minute) does salt enter the tank
at time t?...
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?
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...
Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds...
Suppose that a large mixing tank initially holds 500 gallons of
water in which 50 pounds of salt have been dissolved. Another brine
solution is pumped into the tank at a rate of 3 gal/min, and when
the solution is well stirred, it is then pumped out at a
slower rate of 2 gal/min. If the concentration of the
solution entering is 2 lb/gal, determine a differential equation
(in lb/min) for the amount of salt A(t) (in lb)
in the...
Suppose that a large mixing tank initially holds 400 gallons of water in which 65 pounds...
Suppose that a large mixing tank initially holds 400 gallons of
water in which 65 pounds of salt have been dissolved. Another brine
solution is pumped into the tank at a rate of 6 gal/min, and when
the solution is well stirred, it is pumped out at a slower rate of
5 gal/min. If the concentration of the solution entering is 3
lb/gal, find the amount of salt in the tank after 10 minutes.
PLEASE SHOW ALL WORK AND USE...
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.
A large tank holds 1000 L of water into which flows a brine solution with concentration...
A large tank holds 1000 L of water into which flows a brine
solution with concentration of 1 kg / L at a rate of 6 L / min. The
solution in the tank is kept well stirred and is flowing out of the
tank at a rate of 5 L / min. Determine when the concentration of
salt will reach 0.5 kg / L.
A closed, rigid tank is filled with water. Initially, the tank holds 0.6 lb of saturated...
A closed, rigid tank is filled with water. Initially, the tank
holds 0.6 lb of saturated vapor and 6.0 lb of saturated liquid,
each at 212°F. The water is heated until the tank contains only
saturated vapor. Kinetic and potential energy effects can be
ignored.
Determine the volume of the tank, in ft3, the temperature at
the final state, in °F, and the heat transfer, in Btu.
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