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Unformatted text preview: School of Chemical Engineering CEIC3000 Process Modelling and Analysis Brief Solution to Tutorial 1 1. Using the cylinder surge tank example discussed in class to explain what is a mathe matical dynamic model and the concepts of input, output and state variables. What are the steps involved in developing a process model? Solution: A surge tank can be modelled in different ways with different state, input and output variables. For example, if we are interested in knowing how would the outlet volumetric ﬂow rate F o ( t ) is affected by the inlet volumetric ﬂow rate F i ( t ), we have: ρA dh ( t ) dt = ρF i ( t ) ρk √ h ( t ) (1) F o ( t ) = k √ h ( t ) (2) where k is the valve coeﬃcient. In this case, h ( t ) is the state variable, F i ( t ) is the input variable and F o ( t ) is the output variable. If the we want to know how would the liquid level be affected by the inlet ﬂow rate, then we have the output variable h ( t ), which is also the state variable....
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 Linear Algebra, Eigenvalue, eigenvector and eigenspace, SCHOOL OF CHEMICAL ENGINEERING

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