Flow of Fluids Theory

[blank_start]Fluids[blank_end] are substances that do not permanently resist distortion and, hence, will change their shape.

[blank_start]Incompressible[blank_end] fluids are those that are inappreciably affected by changes in pressure, e.g. most liquids.

[blank_start]Compressible[blank_end] fluids are those that are appreciably affected by changes in pressure, e.g. most gases.

[blank_start]Fluid statics[blank_end] is the branch of momentum transfer concerned with fluids at rest.

[blank_start]Fluid dynamics[blank_end] is the branch of momentum transfer concerned with fluids in motion.

[blank_start]Newton’s Law of Viscosity[blank_end] roughly states that there is a linear relation between shear stress and rate of shear, and that the proportionality constant is the viscosity.

[blank_start]Kinematic viscosity[blank_end] is the ratio of viscosity to density.

[blank_start]Newtonian[blank_end] fluids are those that obey Newton’s Law of Viscosity, i.e. have constant viscosities.

[blank_start]Non-Newtonian[blank_end] fluids are those having viscosities as a function of shear rate.

Gases and low molecular weight liquids are generally [blank_start]Newtonian[blank_end] fluids.

[blank_start]Laminar[blank_end] flow is the type of flow at low velocities where the layers of fluid seem to slide by one another without eddies or swirls being present.

[blank_start]Turbulent[blank_end] flow is the type of flow at higher velocities where eddies are present giving the fluid a fluctuating nature.

The [blank_start]Reynold’s Number[blank_end] is the ratio of the kinetic or inertial forces and viscous forces.

For a straight circular pipe, values less than [blank_start]2100[blank_end] indicates laminar flow, and above [blank_start]4000[blank_end] indicates turbulent flow.

Frictional losses in the entrance region are [blank_start]larger[blank_end] than those of the same length of fully developed flow.

[blank_start]Mach[blank_end] number is the ratio of the fluid velocity to the speed of sound or acoustic velocity.

For Mach number greater than 1, flow is [blank_start]supersonic[blank_end]. If equal to 1, flow is [blank_start]critical or sonic[blank_end] and the velocity equals the local speed of sound. If less than 1, flow is [blank_start]subsonic[blank_end].

The ratio of heat capacities for air is typically [blank_start]1.4[blank_end].

[blank_start]Venturi[blank_end] meters are often used to measure flows in large lines, such as city water systems. For ordinary industrial installations, they are relatively expensive and takes considerable amount of space. The [blank_start]orifice[blank_end] meter overcomes the disadvantages of this meter but in exchange for a much larger head or power loss.

For incompressible fluids, the compressibility factor, Y is essentially equal to [blank_start]1[blank_end].

Generally, the word “[blank_start]pump[blank_end]” designates a machine or device for moving an incompressible fluid.

These are devices for moving gas (usually air).

[blank_start]Fans[blank_end] discharge large volumes of gas at low pressures of the order several hundred mm of water.

[blank_start]Blowers[blank_end] and [blank_start]compressors[blank_end] discharge gases at higher pressures.

In pumps and fans, the pressure of the fluid does not change appreciably, and [blank_start]incompressible[blank_end] flow can be assumed.

If the pressure on the liquid in the suction line drops to the vapor pressure, some of the liquid flashes into vapor. This is called [blank_start]cavitation[blank_end].

The [blank_start]reciprocating[blank_end] and [blank_start]rotary[blank_end] pumps can be used to very high pressures, whereas [blank_start]centrifugal[blank_end] pumps are limited in their head and are used for low pressures.

In general, in chemical and biological processing plants, [blank_start]centrifugal[blank_end] pumps are primarily used.

The most common method of moving small volumes of gas at low pressures is by means of [blank_start]fans[blank_end].

[blank_start]Incompressible flow[blank_end] theory can be used to calculate the power of fans.

Non-Newtonian fluids can be divided into two broad categories on the basis of their shear stress/shear rate behavior: • Shear stress is independent on time or duration of shear ([blank_start]time-independent[blank_end]) • Shear stress is dependent on time or duration of shear ([blank_start]time-dependent[blank_end])

These are the simplest because they differ from Newtonian fluids only in that their linear relationship does not go through the origin. Examples: peat slurries, margarine, chocolate mixtures, grease, soap, grain-water suspensions, toothpaste, paper pulp, and sewage sludge

The majority of non-Newtonian fluids are in this category. The apparent viscosity decreases with increasing shear rate. Examples: polymer solutions, greases, starch suspensions, mayonnaise, biological fluids, detergent slurries, and paints.

These fluids are far less common than pseudoplastics. The apparent viscosity increases with increasing shear rate. Examples: corn flour-sugar solutions, wet beach sand, starch in water, potassium silicate in water, and some solutions containing high concentrations of powder in water.

These fluids exhibit a reversible decrease in shear stress with time at a constant rate of shear.

These fluids exhibit a reversible increase in shear stress with time at a constant rate of shear.