Fluid Mechanics

Fluid Mechanics:
The fluid is defined as the substance which deforms continuously when subjected to a shear stress. When an external force is applied it responds to these forces, it is a substance capable of flowing.

The analysis of fluid behaviour is based on fundamental laws of mechanics as:

Conservation of mass, momentum, energy and laws of thermodynamics.

Classification of fluid flows:

• Rheological consideration
• Dilational tensor
• Temporal variations
• Spatial dimensions
• Motions characteristics
• Fluid types
The fluid is gas or liquid and they are identified by the difference of their properties which can be understood as:
1. Gases Vs liquids:
based on the molecular behaviour
2. Continuum Vs discrete fluids:
continuum – individual molecular properties are negligible. Discrete fluid- each molecule treated separately
3. Perfect Vs real fluids:
real fluids – does not slip past a solid wall
4. Newton Vs non-Newtonian fluids:
Newton μ constant for fixed fluid temperature and pressure E.g. water.Non-Newtonian – μ varies E.g. milk.
5. Compressible Vs incompressible fluids:
Compressible fluids – density changes with applied pressures.
Incompressible fluids - density not changed by external forces acting.
6. Steady Vs unsteady fluid flow:
Steady fluid flow – properties independent of time
Unsteady fluid flow – properties dependent on time

How to solve the problems on fluid flow systems?
A systematic procedure helps to solve the problems on the fluid flow systems, most of the confusion state can be avoided with few steps. Analysis and investigation methods are the key background of the solving process.
Any of the condition statement can be resolved by investigations which are of two types:
1. Theoretical investigation
2. Experimental investigation.

A theoretical investigation is based on the numerical methodology where the experimental investigation is the based on the experiments conducted in the laboratory which has the limitation of the scale up. Analytical solutions are used in the theoretical investigation.
The physical analysis is based on either force concept or energy concept. It requires the practical experience for identification and classification of the parameters of the systems; all physical variables are a collection of information regarding the system.
Mathematical analysis is based on the forces concept, energy, or dimensional analysis. All the physical analysis information becomes the raw data for the mathematical analysis.

A static condition is in which the fluid is at rest where shear stress is negligible. There will be no shearing force as in case of solid mechanics the same rules of statics are applicable to the static fluid.

The forces and stress present in the static fluid are
1. body forces – action through a distance e.g. gravity force, electromagnetic force
2. surface force – the virtue of direct contact
3. shear stress
4. stress tensor

Force between fluid and boundary act at right angles to the boundary. The following are some of the important points to be remembered:
  • Fluids flowing in pipes exhibit a velocity profile. In the laminar flow of Newtonian fluids, the velocity distribution with respect to the radius is Parabola with the apex at the centre line of the pipe
  • Bernoulli equation applies to a non-viscous and incompressible fluid which does not exchange shaft work with the surroundings.
  • The flow of gas along a pipe in the direction of decreasing pressure causes an increase in its specific volume.
  • The maximum fluid velocity obtainable in a pipe of the constant cross-sectional area is the speed of sound.
  • For a circular pipe completely filled with a liquid, the hydraulic radius is equal to the diameter of pipe divided by four.
  • A nozzle is a device that causes the interchange of internal and kinetic energies of a fluid as a result of changing cross-sectional area available for flow.
  • For subsonic flow in a converging nozzle, the velocity increases and pressure decreases as the cross-section diminishes.
  • In laminar flow, momentum is transferred as a result of the velocity gradient.
  • The expansion of a gas in a nozzle to produce a high-velocity stream is a process that coverts internal energy to kinetic energy.
  • The turbine converts the internal energy of a high-pressure stream into shaft work.
  • A throttling process does not change the temperature of ideal gases
  • For an ideal fluid flow, the Reynolds number is infinite
  • For pseudoplastic fluids increase in shear rate decreases the apparent viscosity
  • A practical attains its terminal setting velocity when the sum of the buoyancy and drag forces is equal to the gravity force.
  • The velocity of discharge of a liquid from a small orifice in the bottom or a wall of the vessel with a constant level head of liquid above the centre of the orifice in the vessel is proportional to √H
  • For a fluidized bed, with the increase in expansion of the bed up to solids carryover from the bed the pressure drop across the bed remains constant
  • A fluid A of specific gravity 1.0 and viscosity 0.001 N.s/m2 flows through a horizontal pipe of the circular cross-section. The fluid B of specific gravity 2 and viscosity 0.002 N.s/m2 flows through an identical pipe with the same average velocity as fluid A. The ratio of the pressure drop per unit length of pipe for fluid B to the pressure drop per unit length of pipe for fluid A is 2