Introduction to Fluid Mechanics Chapter 2 Fundamental Concepts

Main Topics Fluid as a Continuum Velocity Field Stress Field Viscosity Surface Tension Description and Classification of Fluid Motions

Fluid as a Continuum This molecular structure is one in which the mass is not continuously distributed in space, but is concentrated in molecules that are separated by relatively large regions of empty space. For very small volumes, the density varies greatly, but above a certain volume, the density becomes stable, the volume now encloses a huge number of molecules.

Velocity Field Velocity is a vector it indicates the velocity of a fluid particle that is passing through the point x , y , z at time instant t it can be written in terms of its three scalar components

One-, Two-, and Three-Dimensional Flows A flow is classified as one-, two-, or three-dimensional depending on the number of space coordinates required to specify the velocity field 1-D flow 2-D flow

Timelines, Pathlines, Streaklines, and Streamlines Timelines - lines formed by adjacent fluid particles at a given instant Pathlines - path or trajectory traced out by a moving fluid particle Streaklines - lines joining different articles passing through a point Streamlines - lines that at a given instant are tangent to the direction of flow at every point in the flow field In a steady flow, pathlines, streaklines, and streamlines are identical lines

Stress Field What kinds of forces act on fluid particles? surface forces (pressure, friction) and body forces (gravity and electromagnetic)

Viscosity Shear stresses arise due to viscous flow Newtonian Fluids Most of the common fluids (water, air, oil, etc.) “Linear” fluids

Viscosity Fluids in which shear stress is not directly proportional to deformation rate Non-Newtonian Fluids Special fluids (e.g., most biological fluids, toothpaste, some paints, etc.) “Non-linear” fluids

Viscosity Non-Newtonian Fluids

Surface Tension Whenever a liquid is in contact with other liquids or gases an interface develops that acts like a stretched elastic membrane, creating surface tension.

Description and Classification of Fluid Motions