Solution Found!
Mixing. Suppose a brine containing 0.2 kg of salt per
Chapter 2, Problem 35E(choose chapter or problem)
Mixing. Suppose a brine containing 0.2 kg of salt per liter runs into a tank initially filled with 500 L of water containing 5 kg of salt. The brine enters the tank at a rate of 5 L/min. The mixture, kept uniform by stirring, is flowing out at the rate of 5 L/min (see Figure 2.6). (a) Find the concentration, in kilograms per liter, of salt in the tank after 10 min. [Hint: Let A denote the number of kilograms of salt in the tank at t minutes after the process begins and use the fact thatrate of increase in A = rate of input = rate of exit.A further discussion of mixing problems is given in Section 3.2.](b) After 10 min, a leak develops in the tank and an additional liter per minute of mixture flows out of the tank (see Figure 2.7). What will be the concentration, in kilograms per liter, of salt in the tank 20 min after the leak develops? [Hint: Use the method discussed in 31 and 32.]
Questions & Answers
QUESTION:
Mixing. Suppose a brine containing 0.2 kg of salt per liter runs into a tank initially filled with 500 L of water containing 5 kg of salt. The brine enters the tank at a rate of 5 L/min. The mixture, kept uniform by stirring, is flowing out at the rate of 5 L/min (see Figure 2.6). (a) Find the concentration, in kilograms per liter, of salt in the tank after 10 min. [Hint: Let A denote the number of kilograms of salt in the tank at t minutes after the process begins and use the fact thatrate of increase in A = rate of input = rate of exit.A further discussion of mixing problems is given in Section 3.2.](b) After 10 min, a leak develops in the tank and an additional liter per minute of mixture flows out of the tank (see Figure 2.7). What will be the concentration, in kilograms per liter, of salt in the tank 20 min after the leak develops? [Hint: Use the method discussed in 31 and 32.]
ANSWER:Solution:Step 1In this problem we need to find the concentration of salt in the tank in part (a). In part (b) we are asked to find the concentration of the salt in the tank if after 10 min, a leak develops in the tank and an extra liter per minute of salt and water flows out of the tank.