Dynamic Balances Homework Due October 29, 2001

• The first two problems only ask you to derive the transient balance equations. 
• You must find analytical solutions to problems 3, 4 and 5 
• You may use Maple or another computer program to solve problems 3, 4 and 5.

1. Consider the conical water tank shown in Figure 1 below. Write the dynamic material balance equation if the flowrate out of the tank is proportional to the square root of the height of the water in the tank, i.e.

List state variables, input variables and parameters. (Hint: Use h as a state variable).

Figure 1

2. Model the mixing tank with two feedstreams as shown in Figure 2. Assume that each feedstream has two liquid components A and B. Model the following cases:

1. Constant liquid volume, constant liquid density.
2. Variable volume, constant liquid density.
3. Variable volume, liquid density varies linearly with concentration.

Figure 2

3. A car tire has a slow leak. The flowrate of air out of the tire is proportional to the pressure of air in the tire (we are using gauge pressure). The initial pressure is 30 psig and after five days the pressure is down to 20 psig. How long will it take to reach 10 psig?

    

    

4. A car tire has a slow leak. The flowrate of air out of the tire is proportional to the square root of the air pressure in the tire (we are using gauge pressure). The initial pressure is 30 psig and after five days the pressure is down to 20 psig. How long will it take to reach 10 psig? Compare your results with problem 3.

5. Problem 11.13 (from Felder & Rousseau).