These equations state that changes in momentum of fluid particles depend only on the external pressure and internal viscous forces acting on the fluid.

These equations state that changes in momentum of fluid particles depend only on the external pressure and internal viscous forces acting on the fluid.

• A. Lagrangian Equations
• B. Navier - Stokes Equations
• C. Reynolds Equations
• D. Torricelli Equations

Answer: (B)

Momentum balance in a fluid is described by the Navier–Stokes equations, which express how the momentum of a fluid element changes due to the forces acting on it. For a Newtonian fluid, the rate of change of momentum (the material derivative of velocity times density) equals the sum of forces per unit volume: the pressure gradient, which represents external pressure driving or resisting motion, and the viscous stresses, which capture the internal friction between fluid layers. In mathematical form, this is ρ(Du/Dt) = -∇p + μ∇^2u + body forces, where Du/Dt is the material derivative of velocity, ∇p is the pressure gradient, and μ∇^2u represents the viscous effects. This framework precisely describes how pressure forces and internal viscous forces govern the evolution of fluid motion. Other options don’t fit this description. Lagrangian equations pertain to individual particle motion in classical mechanics rather than the continuous momentum balance of fluids. Reynolds equations are simplified or averaged forms used in specific thin-film lubrication contexts. Torricelli equations deal with efflux velocity from an orifice and do not express the momentum balance for a fluid element.

Momentum balance in a fluid is described by the Navier–Stokes equations, which express how the momentum of a fluid element changes due to the forces acting on it. For a Newtonian fluid, the rate of change of momentum (the material derivative of velocity times density) equals the sum of forces per unit volume: the pressure gradient, which represents external pressure driving or resisting motion, and the viscous stresses, which capture the internal friction between fluid layers. In mathematical form, this is ρ(Du/Dt) = -∇p + μ∇^2u + body forces, where Du/Dt is the material derivative of velocity, ∇p is the pressure gradient, and μ∇^2u represents the viscous effects. This framework precisely describes how pressure forces and internal viscous forces govern the evolution of fluid motion.

Other options don’t fit this description. Lagrangian equations pertain to individual particle motion in classical mechanics rather than the continuous momentum balance of fluids. Reynolds equations are simplified or averaged forms used in specific thin-film lubrication contexts. Torricelli equations deal with efflux velocity from an orifice and do not express the momentum balance for a fluid element.