Gravity-flow tank

The gravity-flow tank that we considered in Chap. 1 and later in Example 2.9 makes a nice simple system to start our simulation examples. The force balance on the outlet line gave us the nonlinear ODE 

To describe the system completely a total continuity equation on the liquid in the tank is also needed. 

We have to pick a specific numerical case to solve these two coupled ordinary diiferential equations. Equation (5.1) is nonlinear because of the term. Physical dimensions, parameter values, and steadystate flow rate and liquid height are given in Table 5.1. 

Using the relationship F = vAp and substituting the numerical values of parameters into Eqs. (S.l) and (5.2) give 

TWO CASES ARE RUN. AT TIME EQUAL ZERO THE FEED FI.OW RATE tS INCREASEn TO 1005t OF THE DESIGN FLOW RATE (15,700 GPM). CASE NO.l STARTS FROM 67% OF DESIGN FLOW RATE CASE N0.2 STARTS FROM 50% OF DESIGN FLOW RATE DATA VI,H1/.1.40,2.0,5/ 

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Example 2.9. The gravity-flow tank system described in Chap. 1 provides a simple example of the application of the equations of motion to a macroscopic system. Referring to Fig. 1.1, let the length of the exit line be L (ft) and its cross-sectional area be A, The vertical, cylindrical tank has a cross-sectional area of A,... 

Example 6.4. onsider the nonlinear ordinary differential equation for the gravity-flow tank of Example 2.9. 

Figure 2 Dynamic responses of gravity-flow tank...

EXAMPLE 2.4. Consider the nonlinear ordinary differential equation (ODE) for a gravity-flow tank, which is derived from a momentum balance around the exit pipe. 

The gravity-flow tank discussed in Chapter 1 is described by two nonlinear ODEs ... 

Maximum Level in a Gravity-Flow Tank in Transient Conditions... 

A gravity-flow tank consists of a vessel receiving an inlet flow and a pipeline or other devices to allow the flow exit (Luyben, 1996). When the inflow of the vessel is modified, a new steady-state condition with a different level is achieved after a certain time, during which the level changes. It is easy to calculate the diameter of the pipe to obtain a certain holdup level at steady-state conditions. 

The following equations govern the gravity-flow tank described by Luyben (1996) ... 

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