Lumped Process with Non-interacting Balances

Suppose, the outflow (Fig. 10.3) depends on the level (laminar outflow), according to  

The general equation for a system with two non-interacting balances is  

X andy represent the states, u the manipulated inpnt variable and ti and Tz the time constants of the system. Fignre 10.5 shows the data flow diagram of this system. Sometimes, a weak connection between the balances may be present, based on the mass contents. This weak interconnection, in the data flow diagram indicated with a dashed arrow, is no real state couphng. 

From a substitution of the mass balance into the energy balance, it follows that CppAh = c,pF, T, -T) + Q,  

Consequently, the transfer function from the temperature to input flow variations becomes  

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