at t=0,a tank contains Q0 g of the salt dissolved in 100L of water, assume that...

at t=0,a tank contains Q0 g of the salt dissolved in 100L of water, assume that water containing 1/4g of salt per L in entering the tank at a rate of r L/min. at the same time, the well-mixed mixture is draining from the tank at the same rate.

a) set up the differential equation and initial condition for the salt amount Q as a function of time.

b)find the amount of salt in the tank as a function of time t, Q(t), by solving the differential equation in the above problem.

c) when t->infinit , meaning after a long time, what is the limt amount Qlimit?

Expert Solution

Colby Messinger 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 ]

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 2 liter tank of water contains 3 grams of salt at time t = 0...

A 2 liter tank of water contains 3 grams of salt at time t = 0 (in minutes). Brine with concentration 3t grams of salt per liter at time t is added at a rate of one liter per minute. The tank is mixed well and is drained at 1 liter per minute. At what positive time is there a minimum amount of salt and what is that amount?

A tank contains 40 lb of salt dissolved in 400 gallons of water. A brine solution...

A tank contains 40 lb of salt dissolved in 400 gallons of water. A brine solution is pumped into the tank at a rate of 4 gal/min; it mixes with the solution there, and then the mixture is pumped out at a rate of 4 gal/min. Determine A(t), the amount of salt in the tank at time t, if the concentration of salt in the inflow is variable and given by cin(t) = 2 + sin(t/4) lb/gal. A(t) =

A tank contains 9,000 L of brine with 11 kg of dissolved salt. Pure water enters...

A tank contains 9,000 L of brine with 11 kg of dissolved salt. Pure water enters the tank at a rate of 90 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. (a) How much salt is in the tank after t minutes? (b) How much salt is in the tank after 10 minutes? (Round your answer to one decimal place.)

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 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 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 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 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...

Question