Which formula is NOT used to calculate pipe wall thickness in a hydraulic mechanism?

The Joukowsky formula is not used to calculate pipe wall thickness in a hydraulic mechanism; instead, it is primarily associated with the analysis of water hammer in fluid dynamics. The formula helps to determine the pressure rise caused by a sudden change in fluid velocity within a pipeline, specifically dealing with transient flow conditions.

In contrast, the other options listed are critical in calculating the wall thickness of pipes based on various factors such as internal pressure, material properties, and dimensions. The Boardman formula, for instance, is often used in determining wall thickness requirements for pipes subjected to internal pressure. The Barlow formula also plays a similar role, allowing engineers to calculate the required wall thickness for pipes based on the material strength and internal pressure. The Lamé formula, deriving from the theory of elasticity, can also be applied to determine stresses in thick-walled cylinders, which is relevant for wall thickness calculations in pipelines.

Thus, the Joukowsky formula does not relate to the structural assessment of pipes in terms of determining wall thickness, making it the correct answer in this context.