Existing analytical flow models for predicting flow rate at microscale seal displacements are limited to two separate domains. The first assumes a small channel length to height aspect ratio at relatively large seal displacements. The second assumes a large channel length to height aspect ratio at relatively small seal displacements. A piecewise analytical model for compressible flow is developed here to enable predicting flow rates in valves with fluid pathways of any aspect ratio. The new model is validated by numerical studies and experiment. The results are applicable to flat valve seals having a cylindrical seal boss feature with fluid passage length to height aspect ratios ranging from 3.3 to 800. The new model is particularly useful for the design of microvalves and macro-scale valves with small actuator displacements.

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