Continuum and Fluid Mechanics

Define the stress and strain tensors to describe the state of a deformable continuous medium.

Apply Hooke's Law for linear elastic isotropic materials and use elastic moduli.

Derive and apply the equations for bending, torsion, and buckling of beams in engineering contexts.

Derive the continuity equation for fluid flow from the principle of mass conservation.

Derive and apply Bernoulli's equation for ideal, incompressible, steady fluid flow.

Derive the Navier-Stokes equations for a viscous Newtonian fluid.

Analyze laminar flow in pipes (Poiseuille flow) and characterize flow regimes using the Reynolds number.

Solve problems involving lift and drag forces on objects in a fluid flow, including boundary layer concepts.