Question

A tank with 5000 kg capacity initially contains 1000 kg of water. A 50% by weight solution in ethanol is added at a rate of 500 kg / h. The solution comes out at a rate of 200 kg / h. What is the percentage of ethanol in the tank just when it is completely full?

Answer #1

Ethanol balance:

Total mass at any time in tank = 1000 + (500 - 200)t = 1000 + 300t

Let, E be concentratio of ethanol in the tank after mixing, and it be the exit concentration

(1000+300t)dE/dt = 500*0.5 - 200*E

When the tank is completely full, 1000 + 300t = 5000 thus, t= 13.333 hrs

Thus, integrating, we get

dE/(250 - 200E) = dt/(1000 + 300t)

We get at t=13.333 hrs, E = 0.8225

Thus, the tank has 82.225% Ethanol.

This result was arrived at by using Polymath. The concentration variation with time is as follows:

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 full tank with a capacity of 500 gal originally
contains water with 200lb of salt. water containing 1lb of salt per
gallon is entering at a rate of 4 gal/min and the mixture is
allowed to flow out at a rate of 6 gal/min thus the tank is
draining. how much salt is in the tank when it is half full?

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 contains 20 kg of salt dissolve in 5000 L of water. Brine
that contain 0.03 kg of salt per liter of water enters the tank at
a rate of 25 L/min. The solution is kept thoroughly mixed and
drains from the tank at the same rate. How much salt remains in the
tank after 13 minutes? (Keep three decimal places.)

A tank contains 1000 L of pure water. Brine that contains 0.05
kg of salt per liter of water enters the tank at a rate of 5 L/min.
Brine that contains 0.04 kg of salt per liter of water enters the
tank at a rate of 10 L/min. The solution is kept thoroughly mixed
and drains from the tank at a rate of 15 L/min.
(a) How much salt is in the tank after t minutes?
y=

A tank contains 1000 L of pure water. Brine that contains 0.05
kg of salt per liter of water enters the tank at a rate of 5 L/min.
Brine that contains 0.04 kg of salt per liter of water enters the
tank at a rate of 10 L/min. The solution is kept thoroughly mixed
and drains from the tank at a rate of 15 L/min.
(a) How much salt is in the tank after t minutes?
(b) How much salt...

A tank that is used to decrease flow peaks initially contains
500 kg of a 25% aqueous solution of CH3COONa (sodium acetate). The
tank operates originally in a stationary state, with feed and
discharge flows of 100 kg / h of the solution. At a given moment,
the feed to the tank changes to 130 kg / h of a solution with 30%
acetate. If the flow at the outlet of the tank is maintained at 100
kg / h...

A tank contains 50 kg of salt dissolved and thoroughly mixed in
5,000 L of water, and zero salt concentration water enters the tank
at a steady rate of 1,000 L per hour. The solution kept thoroughly
mixed and drains from the tank at the same rate. Water can be used
for gardening when salt concentration is 0.4 g/L or less. How long
will it take for water in tank to reach that

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 1000 L of brine (saltwater) with 15 kg of
dissolved salt. Pure water enters the tank at a rate of 10 L/min.
The solution is kept thoroughly mixed and drains from the tank at
the same rate. How much salt is in the tank after t minutes?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 18 minutes ago

asked 22 minutes ago

asked 28 minutes ago

asked 28 minutes ago

asked 29 minutes ago

asked 37 minutes ago

asked 41 minutes ago

asked 41 minutes ago

asked 43 minutes ago

asked 49 minutes ago

asked 1 hour ago

asked 1 hour ago