Fluid Mechanics #13 - Kinetic Energy Theorem & Power of Internal Forces | Real Fluids

Description: In this new video of the "Real Fluids" series, we take a major step towards the formulation of the Total Mechanical Energy Theorem. Before tackling the fourth integral theorem, we must establish the Kinetic Energy Theorem and, crucially, determine the expression for the power developed by the internal forces. This session focuses on the mathematical derivation of these two essential concepts. In this video: Derivation of the Kinetic Energy Theorem: We start from Newton's second law applied to a material point and generalize it to a system of particles, showing that the time derivative of total kinetic energy equals the sum of the powers of external and internal forces. Focus on Internal Forces: We explain why the internal forces term (the double sum) is not zero for deformable systems like fluids, unlike rigid bodies. This term is the major difference compared to the Momentum Theorem. Power of Internal Forces: Using the divergence theorem, we transform surface integrals into volume integrals to isolate the expression of Wint. Viscous Stresses and Dissipation: We decompose the stress tensor into a static pressure part and a viscous part, highlighting the role of the dissipation function Φ, which measures the mechanical energy degraded by friction. Special Case: We show how the expression simplifies for an incompressible fluid, where the dilatation term vanishes. This theoretical foundation is essential for understanding energy transfers and losses in real fluid flows. Who is this for? This session is intended for undergraduate science students, preparatory class students, or engineering students who want to master the fundamental theorems of fluid mechanics. Useful Links: Previous Session (Fluid Mechanics #12 – Momentum Equations):    • Fluid Mechanics #12 - Momentum Equations: ...   Watch the Full Playlist on "Incompressible Fluid Mechanics" here:    • 5. Incompressible Fluid Mechanics   Keywords: Fluid Mechanics, Real Fluids, Kinetic Energy Theorem, Internal Forces, Power, Viscous Stresses, Dissipation Function, Stress Tensor, Euler Equations, Incompressible Flow, Engineering, Physics. Hashtags: #FluidMechanics #RealFluids #KineticEnergy #InternalForces #Viscosity #Engineering #Physics