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This paper describes the methodology of combining experimental measurements with mathematical–physics analyses in the investigation of flow in the aperture and nozzle. The aperture and nozzle separate the differentially pumped chamber from the specimen chamber in an environmental scanning electron microscope (ESEM). Experimental measurements are provided by temperature and pressure sensors that meet the demanding conditions of cryogenic temperature zones and low pressures. This aperture maintains the required pressure difference between the chambers. Since it separates the large pressure gradient, critical flow occurs on it and supersonic gas flow with the characteristic properties of critical flow in the state variables occurs behind it. As a primary electron beam passes through the differential pumped chamber and the given aperture, the aperture is equipped with a nozzle. The shape of the nozzle strongly influences the character of the supersonic flow. The course of state variables is also strongly influenced by this shape; thus, it affects the number of collisions the primary beam's electrons have with gas molecules, and so the resulting image. This paper describes experimental measurements made using sensors under laboratory conditions in a specially created experimental chamber. Then, validation using mathematical–physical analysis in the Ansys Fluent system is described. [ABSTRACT FROM AUTHOR]