Question

We want to control the concentration of solute in the well-mixed blending tank of diameter 1m shown in Figure 3. The outlet flowrate and volume of liquid in the tank can be assumed to be constant, and variations of stream densities with composition may be neglected. The steady state operating conditions are: F?1 = 200 L/min F?2 = 300 L/min C?1 = 0.5 mole/L C?2 = 0.25 mole/L Liquid level at steady state: H? = 1.28 m Questions: • Identify state variable, input variables, and parameters • Derive the differential equation that describes the dynamics of the concentration in the tank under the assumption that the volume of liquid in the tank is constant • Calculate the outlet flowrate and concentration at steady state F1(t) C1(t) F2(t) C2(t) H D F(t) C(t) Repeat Problem 3 from this tutorial but under the new conditions that the inlet concentration C1(t) starts at its steady-state value C?1 = 8 g/l and then steadily increases at a rate of 0.2g/l-min. • Identify the system parameters, input variables and state variables • Derive an ODE for the deviation of the outlet concentration C3(t) • There is a danger that precipitation of solute will occur if the mixer concentration exceeds 7g/l. Will this occur? • Derive an expression for the mixer concentration over time but do not solve the time at which this concentration exceeds 7g/l. Use Laplace transforms, partial fractions to solve this problem. • Confirm your solution satisfies the initial condition and the governing ODE

          We want to control the concentration of solute in the well-mixed blending tank of diameter 1m shown in Figure 3. The outlet flowrate and volume of liquid in the tank can be assumed to be constant, and variations of stream densities with composition may be neglected. The steady state operating conditions are:

F?1 = 200 L/min
F?2 = 300 L/min
C?1 = 0.5 mole/L
C?2 = 0.25 mole/L
Liquid level at steady state: H? = 1.28 m

Questions:
• Identify state variable, input variables, and parameters
• Derive the differential equation that describes the dynamics of the concentration in the tank under the assumption that the volume of liquid in the tank is constant
• Calculate the outlet flowrate and concentration at steady state

F1(t)
C1(t)
F2(t)
C2(t)
H
D
F(t)
C(t)

Repeat Problem 3 from this tutorial but under the new conditions that the inlet concentration C1(t) starts at its steady-state value C?1 = 8 g/l and then steadily increases at a rate of 0.2g/l-min.

• Identify the system parameters, input variables and state variables
• Derive an ODE for the deviation of the outlet concentration C3(t)
• There is a danger that precipitation of solute will occur if the mixer concentration exceeds 7g/l. Will this occur?
• Derive an expression for the mixer concentration over time but do not solve the time at which this concentration exceeds 7g/l. Use Laplace transforms, partial fractions to solve this problem.
• Confirm your solution satisfies the initial condition and the governing ODE

$We want to control the concentration of solute in the well-mixed blending tank of diameter 1m shown in Figure 3. The outlet flowrate and volume of liquid in the tank can be assumed to be constant, and variations of stream densities with composition may be neglected. The steady state operating conditions are: F?1 = 200 L/min F?2 = 300 L/min C?1 = 0.5 mole/L C?2 = 0.25 mole/L Liquid level at steady state: H? = 1.28 m Questions: • Identify state variable, input variables, and parameters • Derive the differential equation that describes the dynamics of the concentration in the tank under the assumption that the volume of liquid in the tank is constant • Calculate the outlet flowrate and concentration at steady state F1(t) C1(t) F2(t) C2(t) H D F(t) C(t) Repeat Problem 3 from this tutorial but under the new conditions that the inlet concentration C1(t) starts at its steady-state value C?1 = 8 g/l and then steadily increases at a rate of 0.2g/l-min. • Identify the system parameters, input variables and state variables • Derive an ODE for the deviation of the outlet concentration C3(t) • There is a danger that precipitation of solute will occur if the mixer concentration exceeds 7g/l. Will this occur? • Derive an expression for the mixer concentration over time but do not solve the time at which this concentration exceeds 7g/l. Use Laplace transforms, partial fractions to solve this problem. • Confirm your solution satisfies the initial condition and the governing ODE$

Added by Ricardo C.

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