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27 Nov 2019

A 1700L tank contains 850L of water with a salt concentration of8g/L. Water with a salt concentration of 51g/L flows into the tankat a rate of 86g/min. The fluid mixes instantaneously, and ispumped out at a specified rate R(out) . Let y(t) denote thequantity of salt in the tank at time t .

Assume . R(out)=36 L/min

a)Set up and solve the differential equation for y(t)

b) What is the salt concentration when the tank overflows?

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Related questions

The mixing tank in Figure 7.24 initially holds 500 L of a brine solution with a salt concentration of 0.2 kg/L. For the first 10 min of operation, valve A is open, adding 12 L/min of brine containing a 0.4 kg/L salt concentration. After 10 min, valve B is switched in, adding a 0.6 kg/L concentration at 12 L/min. The exit valve C removes 12 L/min, thereby keeping the volume constant. Find the concentration of salt in the tank as a function of time.

The answer is 0.04-0.02e^(-3/125)+0.02u(t-10)[1-e^{-3(t-10)/125}]

Show transcribed image text

In Section, we looked at mixing problems in which the volume of fluid remained constant and saw that such problems give rise to separable differentiable equations. (See Example 6 in that section) If the rates of flow into and out of the system are different, then the volume is not constant and the resulting differential equation is linear but not separable.

A tank contains 100 L of water. A solution with a salt concentration of 0.4 kg/L is added at a rate of 5L/min. The solution is kept mixed and is drained from the tank at a rate of 3 L/min. If y(t) is the amount of salt (in kilograms) after t minutes, show that y satisfies the differential equation 

 

Solve this equation and find the concentration after 20 minutes.

 

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