Unformatted text preview: 1. A well-mixed tank contains 300 gal of water
with a salt concentration of 0.2 lb/gal. Water
water enters the tank at a rate of 6 gal/ min.
containing salt at a concentration of 0.4 lb/gal
An open valve allows water to leave at a rate
enters at a rate of 2 gal/min. An open valve
of 1 gal/ min. When full, the tank overflows.
allows water to leave the tank at the same rate.
a) Find the amount and concentration of io-
a) Determine the amount and the concentra-
dine in the tank for the first 100 min.
tion of salt in the tank as functions of time.
b) Find the amount and concentration of io-
b) How long will it take for the concentration
dine for the next 100 min,
to increase to 0.3 Ib/gal?
c) Graph both concentration and amount of
2. A room has a volume of 800 ft. The air in
the room contains chlorine at a concentration
6. A 100-gal tank is initially full of water contain-
of 0.1 g/ft . Fresh air enters at a rate of
ing 10 lb of salt in solution. The tank will
8 fta/ min. The air in the room is well mixed
overflow whenever additional water is added.
and flows out of a door at the same rate as
A pump is attached to a sensor. It pumps fresh
the fresh air comes in.
water into the tank at a rate proportional to
the concentration of salt in the tank. The
a) Find the chlorine concentration in the room
constant of proportionality is 10 (gal) /lb - min.
as a function of f.
Find the amount and concentration of salt in
b) Suppose that the flow rate of fresh air is
the tank as functions of t.
adjustable. Determine the flow rate re-
7. A well-circulated lake contains 1000 kL of
quired to reduce the chlorine concentration
water that is polluted at a concentration of 2
to 0.001 g/ft within 20 min.
kg/kL. Water from the effluent of a factory
3. A well-mixed tank contains 100 L of water with
enters the lake at the rate of 5 kL/h with a
a salt concentration of 0.1 kg/L. Water con-
concentration of 7 kg/kL of the pollutant.
taining salt at a concentration of 0.2 kg/L
Water flows out of the lake through an outlet
enters at a rate of 5 L/h. An open valve allows
at the rate of 2 kL/h. Determine the amount
water to leave at 4 L/h. Water evaporates
and concentration of the pollutant as a func-
from the tank at 1 L/h.
tion of time.
a) Determine the amount and concentration
In Exercises 8 through 14, formulate the differen
of salt as a function of time.
tial equations (before any tanks empty or overflow)
that would be used to solve the problems, but do
b) Is the limiting concentration the same as
nor solve the differential equations. Since Exer-
that of the inflow?
cises 9-13 involve more than one tank, they re-
4. A well-circulated pond contains 1 million L of
quire one equation for each tank.
water that contains a pollutant at a concentra-
8. A 600-gal tank initially contains 200 gal of
tion of 0.01 kg/L. Pure water enters from a
brine (salt water) with 25 lb of salt. Brine
stream at 100 L/h. Water evaporates from the
containing 2 lb of salt per gallon enters the
pond (leaving the pollutant behind) at 50 L/h
tank at the rate of 13 gal/s. The mixed brine
and flows out an outlet pipe at 50 L/h. How
in the tank flows out at the rate of 8 gal/s.
many days will it take for the concentration of
How much salt is there in each tank as a
pollutant to drop to 0.001 kg/L?
function of time?
5. A 1000-gal tank is initially half full of water
9. Consider two tanks. Initially, tank 1 contains
and contains 10 lb of iodine in solution. Pure
150 gal of brine (salt water) with 8 lb of salt...
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- Fall '10