A fluid is defined as any substance that continuously deforms under shear stress and requires a container to be stored. Fluids can be classified as viscous or inviscid depending on whether frictional effects are significant. Fluid flows can be internal, occurring within bounded surfaces like pipes, or external, over unbounded surfaces. Incompressible flow assumes the fluid density remains constant, while compressible flow allows density to change. Laminar flow is smooth and layered, while turbulent flow is irregular with velocity fluctuations. Forced flow is driven by external means like pumps, while natural flow occurs due to buoyancy effects. Steady flow does not change over time at a point, while uniform flow does not change with location in a

1. DEFINITION
 “A fluid, such as water or air, deforms
continuously when acted on by shearing or
tangential stress of any magnitude.”
 Solids resist the deformation when acted upon
shear or tangential stress
 For this reason fluids need container walls for
storage where as no such requirement for solids
 There are exceptions both in solids and in fluids
and one should be aware of them
Definition of a Fluid

2. Viscous vs Inviscid Region of Flow
Flows in which the frictional effects are significant are
called viscous flows. Neglecting the viscous terms in
such inviscid flow regions greatly simplifies the
analysis without much loss in accuracy.
Classification of Fluid Flows

3. The flow of an unbounded fluid over a surface such as a
plate, a wire, or a pipe is external flow. The flow in a
pipe or duct is internal flow if the fluid is completely
bounded by solid surfaces.
Internal and External Flow

4. Incompressibility is an approximation, and a flow is said
to be incompressible if the density remains nearly
constant throughout. Therefore, the volume of every
portion of fluid remains unchanged over the course of its
motion when the flow (or the fluid) is incompressible.
Compressible versus Incompressible Flow
𝐷𝜌
𝐷𝑡
= 0
𝐷𝜌
𝐷𝑡
=
𝜕𝜌
𝜕𝑡
+ 𝑢
𝜕𝜌
𝜕𝑥
+ 𝑣
𝜕𝜌
𝜕𝑦
+ 𝑤
𝜕𝜌
𝜕𝑧
=
𝜕𝜌
𝜕𝑡
+V∙ 𝛁𝝆

5. The highly ordered fluid motion characterized by smooth
layers of fluid is called laminar. The highly disordered
fluid motion that typically occurs at high velocities and is
characterized by velocity fluctuations is called turbulent.
Laminar versus Turbulent Flow

6. In forced flow, a fluid is forced to flow over a surface or
in a pipe by external means such as a pump or a fan. In
natural flows, any fluid motion is due to natural means
such as the buoyancy effect, which manifests itself as the
rise of the warmer (and thus lighter) fluid and the fall of
cooler (and thus denser) fluid.
Natural (or Unforced) versus
Forced Flow

7. The term steady implies no change at a point with time. The
opposite of steady is unsteady. The term uniform implies
no change with location over a specified region.
Steady versus Unsteady Flow

8. No change with the location over a specified region
Uniform Flow Vs Nonuniform flow

9.  A continuum is a body that can be continually sub-divided
into infinitesimal elements with properties being those of
the bulk material.
 Molecules in all solid or fluid, are
 discretely spread
 in continuous motion
CONTINUUM
 Physical variable at a point in space is the averaged
value of the variable in a small sphere
 How small the volume should be
 Measure a property say
density in a fluid volume
 Report density of fluid as
fluid volume is decreased