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This report details the development of a numerical model named DUCT, which analyzes unsteady flows in laboratory ductwork systems. The analysis is based on the method of characteristics, analogous to liquid piping systems. Damper opening and/or closing initiate time-variable boundary conditions at hood inlets. Minor losses and ductwork friction are included, as well as interaction with fans. Extensive data was obtained from three university laboratory systems for purposes of code verification: two at Georgia Institute of Technology and one at Michigan State University. Comparisons between experiments and simulations demonstrate the accuracy and versatility of DUCT. The report also demonstrates the significance of system inertia.