What equation is used to determine the cylinder rod's buckling load?

The buckling load of a cylinder rod is determined using Euler's equation, which describes the critical load at which a slender, long column will buckle under axial compression. This equation takes into account factors such as the length of the rod, the moment of inertia of its cross-section, and the material properties, notably the modulus of elasticity.

Euler's equation provides a fundamental understanding of how instability occurs in structural elements subjected to compressive forces. It illustrates that as the load increases, there is a point at which the rod can no longer remain straight and begins to deform sideways, leading to buckling. This understanding is crucial in hydraulic applications where cylinder rods are often used, as engineers must ensure that the design of these components can withstand the operational loads without failing.

The other choices reflect different principles used in fluid mechanics and dynamics but do not relate to the specific phenomenon of buckling in columns. Bernoulli’s equation pertains to fluid flow and the relationships between pressure and velocity in fluids, while Pascal’s principle deals with the transmission of pressure in incompressible fluids. Newton's second law relates to the motion of objects based on force and mass, which does not specifically address buckling behavior in structural members. Thus, the reliance on Euler's equation is essential