Question

In: Advanced Math

Consider a tank containing at time t = 0, 100 gallons of brine. Assume that water...

Consider a tank containing at time t = 0, 100 gallons of brine. Assume that water containing 1/4 lb of salt per gallon is entering the tank at a rate of 3 gallons per minute, and that the well stirred solution is leaving the tank at the same rate. Find a differential equation for the amount of salt A(t) in the tank at time t > 0

**PLEASE SHOW ALL STEPS CLEARLY SINCE I REALLY WANT TO UNDERSTAND THE WHOLE PROCESS** **If possible please type the solution?***

Thank you!

Solutions

Expert Solution


Related Solutions

Consider a tank containing at time t = 0, 100 gallons of brine. Assume that water...
Consider a tank containing at time t = 0, 100 gallons of brine. Assume that water containing 1/4 lb of salt per gallon is entering the tank at a rate of 3 gallons per minute, and that the well stirred solution is leaving the tank at the same rate. Find a differential equation for the amount of salt A(t) in the tank at time t > 0 **PLEASE SHOW ALL STEPS CLEARLY SINCE I REALLY WANT TO UNDERSTAND THE WHOLE...
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.
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.
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.
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) 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 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?
5. (Mixing Problem) A very large tank is initially filled with 100 gallons of water containing...
5. (Mixing Problem) A very large tank is initially filled with 100 gallons of water containing 5 pounds of salt. Beginning at time t = 0, a brine solution with a concentration of 1 pound of salt per gallon flows into the top of the tank at 3 gallons per second, the mixture is stirred, and the mixture flows out of the bottom of the tank at 2 gallons per second. (a) Letting w = pounds of salt in the...
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...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT