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Computational fluid dynamics is used to calculate flows in the time-pressure dispenser. The analysis of different factors such as the yield stress, the power-law constants, the needle length, etc. will be useful in understanding the dispensing mechanism and thus allow for performance improvement. The numerical solution can provide more information about the wall shear stress and the pressure drop caused by a sudden contraction. The approximation error associated with the analytical method can be understood through comparison with the numerical results. Thus, an approximation compensation model may be derived for the analytical method to improve modeling accuracy.