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.

Expert Solution

milcah answered 2 years ago

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 ]

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?

A) A 50 gallon tank initially contains 10 gallons of fresh water. At t = 0...

A) A 50 gallon tank initially contains 10 gallons of fresh water. At t = 0 t = 0 a brine solution containing 1 pound of salt per gallon is poured into the tank at the rate of 4 gal/min., while the well-stirred mixture leaves the tank at the rate of 1 gal/min. Find the amount of salt in the tank at the moment of overflow. B) A tank contains 100100 g of salt and 400400 L of water. Water...

A vat with 500 gallons of beer contains 3% alcohol (by volume). Beer with 7% alcohol...

A vat with 500 gallons of beer contains 3% alcohol (by volume). Beer with 7% alcohol is pumped into the vat at a rate of five gal/min and the mixture is pumped out at the same rate. What is the percentage of alcohol after an hour? How long will it take to have a beer with 6.5% alcohol?

A 100 gallon tank initially contains 10 gallons of fresh water. At t=0 a brine solution...

A 100 gallon tank initially contains 10 gallons of fresh water. At t=0 a brine solution containing 1 pound of salt per gallon is poured into the tank at the rate of 4 gal/min., while the well-stirred mixture leaves the tank at the rate of 2 gal/min. Find the amount of salt in the tank at the moment of overflow. Enter answer as numerical decimal correct to two decimal places. pounds.

A tank initially contains 300 gallons of a salt solution made by dissolving 30 pounds of...

A tank initially contains 300 gallons of a salt solution made by dissolving 30 pounds of salt in water. A solution containing 0.6 pounds of salt per gallon enters the tank at a rate of 5 gallons per minute. A drain is opened at the bottom of the tank through which the well stirred solution leaves the tank at the same rate of 5 gallons per minute. Let y(t) denote the amount of salt (in pounds) which is in the...

4. Consider a mixing tank with a volume of 50 gallons which is initially filled with...

4. Consider a mixing tank with a volume of 50 gallons which is initially filled with 10 gallons of fresh water. Suppose there is an inflow pipe which pumps in a 1 lb/gallon brine (salt/water) mixture at a rate of 4 gallons per minute, and there is an outflow pipe which removes the mixture from the tank at a rate of 2 gallons per minute. (a) Use the given information to derive an initial value problem which models the amount...

At time t=0 a tank holds 550 gallons of water with 100 pounds of dissolved salt....

At time t=0 a tank holds 550 gallons of water with 100 pounds of dissolved salt. An input pipe brings in solution at 8 gallons per minute at a concentration of 2 pounds per gallon. An output pipe carries away solution at 2 gallons per minute. Find how much salt is in the tank after 45 minutes.

determine the volume in gallons of 15.6 lbs of oil. the oil has a density of...

determine the volume in gallons of 15.6 lbs of oil. the oil has a density of 0.880 g/ml.

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.

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