A tank contains 200 gallons of water that has 5 lbs of salt already in it....

A tank contains 200 gallons of water that has 5 lbs of salt already in it. A brine containing .5 lbs of salt per gallon is entering the tank at a rate of 2 gal min , and the well stirred mixture exits the tank at the same rate. What is the concentration of salt in the tank after 5 minutes?

Expert Solution

milcah answered 2 years ago

A tank contains 365 gallons of water and 50 oz of salt. Water containing a salt...

A tank contains 365 gallons of water and 50 oz of salt. Water containing a salt concentration of 1/6(1 + 1/4 sin t) oz/gal flows into the tank at a rate of 8 gal/min, and the mixture in the tank flows out at the same rate. The long-term behavior of the solution is an oscillation about a certain constant level. a) What is this level? b) What is the amplitude of the oscillation?

A tank contains 360 gallons of water and 50 oz of salt. Water containing a salt...

A tank contains 360 gallons of water and 50 oz of salt. Water containing a salt concentration of 1 6 (1 + 1 4 sin t) oz/gal flows into the tank at a rate of 8 gal/min, and the mixture in the tank flows out at the same rate. The long-term behavior of the solution is an oscillation about a certain constant level. a) What is this level? b) What is the amplitude of the oscillation? (Round your answers to...

A 200 gallon tank initial contains 100 gallons of water and 20 pounds of dissolved salt....

A 200 gallon tank initial contains 100 gallons of water and 20 pounds of dissolved salt. Brine solution begins to enter the tank at the rate of 2 gal/min with a salt concentration of 2 lb/gal. The well mixed solution leaves the tank at the rate of 1 gal/min. Find the amount of salt inside the tank 50 minutes after the process starts?

A tank is filled to capacity with 400 gallons water containing 30 lbs of salt. Brine...

A tank is filled to capacity with 400 gallons water containing 30 lbs of salt. Brine containing 2 lbs of salt per gallon is pumped into the tank at a rate of 3 gallons per minute. The well mixed solution is pumped out at rate of 3.5 gallons per minute. Determine the differential equation of the model and solve for an equation relating amount of salt in tank at time t. Determine the time until the tank is empty.

A tank contains 200 gal of water and 50oz of salt. Water containing a salt concentration...

A tank contains 200 gal of water and 50oz of salt. Water containing a salt concentration of 1/8(1+1/2 sint) oz/gal flows into the tank at a rate of 4 gal/min, the mixture flows out at the same rate. A) find the amount of salt in the tank at any moment. Q(t) = B) the amplitude of oscillation is C) level of the amplitude is

A tank contains 10 gallons of water. Salt water containing a concentration of 4t ounces per...

A tank contains 10 gallons of water. Salt water containing a concentration of 4t ounces per gallon flows into the tank at a rate of 4 gallons per minute and the mixture in the tank flows out at the same rate. (a)Construct the mathematical model for this flow process (b)Use integrating factors to solve for Q(t). (c)If the tank contains Q0 amount of salt at time t = 0, use this as an initial condition to solve for the constant...

A tank contains 400 gallons of brine (salt in solution) in which 125 pounds of salt...

A tank contains 400 gallons of brine (salt in solution) in which 125 pounds of salt has been dissolved. Freshwater (with no salt added) runs into the tank at a rate of 4 gallons per minute, and the stirred mixture is drained from the tank at the same rate. (1) Find the amount of salt in the tank after an hour. (2) How long does it take to reduce the amount of salt in the tank to 10 pounds?

A tank contains 100kg of salt and 2000L of water. Pure water enters a tank at...

A tank contains 100kg of salt and 2000L of water. Pure water enters a tank at the rate 6L/min. The solution is mixed and drains from the tank at the rate 3L/min. ) Find the concentration(kg/L) of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.)

A vat of volume 1100 gallons initially contains 4 lbs of salt. For t > 0...

A vat of volume 1100 gallons initially contains 4 lbs of salt. For t > 0 a salt brine of concentration 0.15 lbs per gallon is pumped into the vat at the rate of 5 gallons per minute; the perfectly stirred mixture is pumped out at the same flow rate. Derive a formula for the concentration of salt in the tank at any time t.

At time t = 0 a tank contains 25lb of salt dissolved in 100 gallons of...

At time t = 0 a tank contains 25lb of salt dissolved in 100 gallons of water. assume that water containing 2lb salt/gallon enters the tank at a rate of 5 gal/min and the well-stirred solution is leaving the tank at the same rate. solve for Q(t) [Amount of salt in tank at time t ]

Question