Momentum and Fluid Transport


  • Momentum transport (Fluid Transport) is based on the principle of conservation of momentum (Newton’s second law of motion).
  • The property we follow is the flux of momentum (quantity of momentum transferred per unit time per area, τyz)
  • We use a transport law to relate the flux to the gradient of momentum (Newton’s Law of Viscosity)
  • We combine momentum conservation with the transport law to calculate velocity fields

The Navier-Stokes equation is the most used form of momentum balance:

ρ((du/dt)+u*∇u-f)-µ∇^2u+∇p = 0

The first line represents the conservation of momentum—basically, the Newton's second law—in terms of fluid velocity vector u and pressure p. The second line represents the conservation of mass. The body force f is frequently absent, and the remaining parameters—fluid density and viscosity—are often constant. In spite of their simple form, the Navier-Stokes equations are capable of producing an astounding variety of fluid flows.

Fluid Transport

The analysis of fluid transport is fundamental in the design and control of a industrial process. Different fluids have different resistances to flow, this property is known as a viscocity.

The conservation of momentum says that the sum of momentum of all atoms before the collision must be equal that after the collision.

Newton's Law:

τxy = µ(dvx/dy)


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