One of the most important elements in the pneumatic circuits is the pressure reducer which is commonly used to keep a constant downstream pressure, whatever the value of the upstream one. In fact the downstream pressure would anyway vary, but it could be considered to operate with a sufficient accuracy if its outlet. pressure varies within a zone of ±5% of its nominal value. That is why every pressure reducer, after being manufactured then assembled; must be tested to verify its function, and whether it works in the prescribed tolerance. The testing bench consists of several pressurized air bottles, branches to the pressure reducer, downstream of which there mounted a short pipe of inner diameter: dpipe ; nozzled at its outlet end witha diameter: dn. In the present research, a complete mathematical model is developed to find out the optimum nozzle diameter of the testing section which is necessary to identify the function of certain reducer.