Question

A pond contains V gallons of water and M grams of pollutant. Polluted water, containing ρ...

A pond contains V gallons of water and M grams of pollutant. Polluted
water, containing ρ grams per gallon of the pollutant, enters the pond at the rate of a gallons per hour. The mixture flows out at the same rate of a gallons per hour, and we assume that the pollutant is always perfectly mixed with the water in the pond (that is, equal volumes of water contain the equal amount of pollutant everywhere in the pond). Write the differential equations for the amount of pollutant in the pond, as a function of time, and investigate the long-time behavior of the solution.
Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A tank initially contains 100 pounds of salt dissolved in 500 gallons of water. Saltwater containing...
A tank initially contains 100 pounds of salt dissolved in 500 gallons of water. Saltwater containing 5 pounds of salt per gallon enters the tank at the rate of 2 gallons per minute. The mixture (kept uniform by stirring) is removed at the same rate of 2 gallons per minute. How many pounds of salt are in the tank after an hour?
A 2000 gallon tank initially contains a mixture of 750 gallons of water and 100 gallons...
A 2000 gallon tank initially contains a mixture of 750 gallons of water and 100 gallons of salt. Water is added at a rate of 8 gallons per minute, and salt is added at a rate of 2 gallons per minute. At the same time, a well mixed solution of "brine" is exiting at a rate of 5 gallons per minute. What percentage of the mixture is salt when the tank is full?
Consider a 400-gallon capacity tank of water that contains 200 gallons of water in which 10...
Consider a 400-gallon capacity tank of water that contains 200 gallons of water in which 10 pounds of salt are dissolved. Suppose that water with a salt concentration of 2 pounds per gallon enters the tank at a rate of 6 gallons per minute, is well-stirred, and the mixture leaves the tank at 9 gallons per minute. Set up and solve the initial value problem to get the amount of salt as a function of time. Use this function to...
Consider a 2500-gallon capacity tank of water that contains 100 gallons of water in which 10...
Consider a 2500-gallon capacity tank of water that contains 100 gallons of water in which 10 pounds of salt are dissolved. Suppose that water with a salt concentration of 2 pounds per gallon enters the tank at a rate of 6 gallons per minute, is well-stirred, and the mixture leaves the tank at 5 gallons per minute. (a) Set up and solve the initial value problem to find the amount of salt in the tank as a function of time....
A tank contain 200 gallons of water. Five gallons of brine per minute flow into the...
A tank contain 200 gallons of water. Five gallons of brine per minute flow into the tank, each gallon of brine containing 1 pound of salt. Five gallons of water flow out of the tank per minute. Assume that the tank is kept well stirred. Find a differential equation for the number of pounds of salt in the tank (call it y) Assuming the tank intially contains no salt, solve this differential equation. At what time will there be 100...
A 50-gallon tank initially contains 10 gallons of fresh water. At t = 0, a brine...
A 50-gallon tank initially contains 10 gallons of fresh water. At t = 0, a brine solution containing 2 pounds of salt per gallon is poured into the tank at a rate of 5 gal/min. The well-stirred mixture drains from the tank at a rate of 3 gal/min. Find the amount of salt in the tank at the moment of overflow. Please use differential equations to solve this problem and please put the answer in decimal form. I did this...
initially, a large tank with a capacity of 250 gallons contains 125 gallons of clean water....
initially, a large tank with a capacity of 250 gallons contains 125 gallons of clean water. A saline solution with a concentration of 4 pounds per gallon flows into the tank at a rate of 20 gallons per minute. the solution mixes perfectly well while drawing at a rate of 10 gallons per minute. Find: 1) the amount of salt in the tank at the time it fills up (in pounds) 2) the rate at which the salt comes out...
A tank contains 300-gallon of pure water. At time t = 0, a solution containing 2...
A tank contains 300-gallon of pure water. At time t = 0, a solution containing 2 lb of salt per gallon flows into the tank at a rate of 1 gallon per minute, and the well-stirred mixture flows out at a rate of 2 gallons per minute. Find the amount(in lb) of salt Q in the solution as a function of t in minutes. please show work and explain thank you
A 24 gallon tank is filled with pure water. Water which has a concentration of 6g...
A 24 gallon tank is filled with pure water. Water which has a concentration of 6g of salt per gallon flows into the tank at a rate of 2 gallons/min, and the mixture is stirred to a uniform concentration. Water also leaks from the tank at the same rate, 2 gallons/min. Find a differential equation describing the rate of change of salt in the tank. Hint: The concentration of salt in the tank is S(t)/24, where S(t) is the total...
A 100 gallon tank is filled with brine solution containing 50 pounds of salt. Pure water...
A 100 gallon tank is filled with brine solution containing 50 pounds of salt. Pure water enters the tank a rate of 10 gal per hour. Well mixed solution leaves the first tank at the same rate (10 gal/hr) and enters a second 100 gallon tank initially containing 10 pounds of salt. How much salt is in tank 2 at any time?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT