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Fluid Mechanics - Mechanical

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A Brief about
Fluid Mechanics is the study of fluid either in motion (Fluid Dynamics) or at rest (Fluid Statics) and the subsequent effects of the fluid upon the boundaries, which may be either solid surface or interface with other fluids.

From the point of view of fluid mechanics, all matter consists of only two states, fluid and solid.
A solid can resist a shear stress by static deformation; a fluid cannot. Any shear stress applied to a fluid, no matter how small, will result in motion of that fluid. The fluid moves and deforms continuously as long as shear stress applied.

There are two different point of view in analyzing problem in mechanics. The first view, appropriate to fluid mechanics, is concerned with the field of flow and is called the eulerian method of description. In the eulerian method we compute the pressure field p (x, y, z, t) of the flow pattern, not the pressure change p(t) which a particle experience as it moves through the field.
     The second method, which follows an individual particle moving through the flow, is called the lagrangian description. The lagrangian approach is more appropriate to solid mechanics.

Thermodynamic Properties of a Fluid
Pressure: Pressure is the (compression) stress at a point in static fluid.
Temperature: Temperature T is a measure of the internal energy level of a fluid.
Density: The density of fluid is its mass per unit volume.
Viscosity: When fluid is sheared, it begins to move at strain rate inversely proportional to a property called its coefficient of viscosity µ.
Consider a fluid element sheared in one plane by a single shear stress τ. The shear strain angle δθ will continuously grow with time as long as the shear stress τ is maintained, the upper surface moving at speed δu larger than lower.

From geometry,
Tan δθ
Some common fluids as water, oil, air shows a linear relation between applied shear and resulting strain rate,
τ=µ
=
So,                                                     τ=µ

Non Newtonian Fluid
Fluid which do not follow the linear law are called non Newtonian fluids.

Flow Pattern
Streamline: It is a line everywhere tangent to the velocity vector at a given instant.
Path line: It is the actual path travelled by a given fluid particle.
Streak line: It is the locus of particles which have earlier passed through a prescribed point.
Timeline: It is a set of fluid particles that forms a line at a given instant.
Streamline, streak line, and path line are identical in steady flow.

Buoyancy
·      A body immersed in a fluid experiences a vertical buoyancy force equal to the weight of displaced fluid.
·      A floating body displaces its own weight in the fluid in which it floats.

The Frictionless Flow: The Bernoulli Equation
It is closely related to the steady flow energy equation is a relation between pressure, velocity and elevation in a frictionless flow.
 = const.

Assumptions for Bernoulli Equation:
1.	Steady Flow
2.	Incompressible flow
3.	Frictionless flow
4.	Flow along a stream line
5.	No shaft work
6.	No heat transfer




Viscous Flow in Ducts

Laminar flow is characterized by smooth streamlines, and highly ordered motion. Turbulent flow is characterized by velocity fluctuation and highly disordered motion.
Reynolds Number
The transition from laminar to turbulent flow is depends on the geometry, surface roughness, flow velocity, surface temperature, type of fluid.
The ratio of inertia force to viscous force is called Reynold no.
For the flow through pipe,
  Re < 2300, laminar flow
2300 < Re< 4000 transition flow
Re> 4000   turbulent flow

Surface Tension
A liquid, being unable to expand freely, will form an interface with a secondary liquid or gas. Molecules deep within the liquid repel each other because of their close packing. Molecule at the surface are less dense and attract each other. Since half of their neighbors are missing, the mechanical effect is that the is in tension.
   If a cut of length dl is made in an interfacial surface, equal and opposite forces of magnitude Ydl are exposed to normal to cut and parallel to surface, where Y is called the coefficient of surface tension.

REFERENCES
·      Fluid Mechanics, 4th Edition- Frank M. White
·      Fluid Mechanics – Yunus A. Cengel
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