Flow of Fluids Theory

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are substances that do not permanently resist distortion and, hence, will change their shape.

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fluids are those that are inappreciably affected by changes in pressure, e.g. most liquids.

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fluids are those that are appreciably affected by changes in pressure, e.g. most gases.

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is the branch of momentum transfer concerned with fluids at rest.

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is the branch of momentum transfer concerned with fluids in motion.

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roughly states that there is a linear relation between shear stress and rate of shear, and that the proportionality constant is the viscosity.

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is the ratio of viscosity to density.

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fluids are those that obey Newton’s Law of Viscosity, i.e. have constant viscosities.

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fluids are those having viscosities as a function of shear rate.

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Gases and low molecular weight liquids are generally fluids.

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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.

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flow is the type of flow at higher velocities where eddies are present giving the fluid a fluctuating nature.

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The is the ratio of the kinetic or inertial forces and viscous forces.

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For a straight circular pipe, values less than indicates laminar flow, and above indicates turbulent flow.

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Frictional losses in the entrance region are than those of the same length of fully developed flow.

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number is the ratio of the fluid velocity to the speed of sound or acoustic velocity.

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For Mach number greater than 1, flow is . If equal to 1, flow is and the velocity equals the local speed of sound. If less than 1, flow is .

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The ratio of heat capacities for air is typically .

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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 meter overcomes the disadvantages of this meter but in exchange for a much larger head or power loss.

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For incompressible fluids, the compressibility factor, Y is essentially equal to .

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Generally, the word “” designates a machine or device for moving an incompressible fluid.

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These are devices for moving gas (usually air).

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discharge large volumes of gas at low pressures of the order several hundred mm of water.

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and discharge gases at higher pressures.

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In pumps and fans, the pressure of the fluid does not change appreciably, and flow can be assumed.

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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 .

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The ❌ and ❌ pumps can be used to very high pressures, whereas ❌ pumps are limited in their head and are used for low pressures.

reciprocating

rotary

centrifugal

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In general, in chemical and biological processing plants, pumps are primarily used.

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The most common method of moving small volumes of gas at low pressures is by means of .

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theory can be used to calculate the power of fans.

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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 (❌)
• Shear stress is dependent on time or duration of shear (❌)

time-independent

time-dependent

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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

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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.

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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.

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

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

Flow of Fluids Summary

Flow of Fluids Theory

are substances that do not permanently resist distortion and, hence, will change their shape.

fluids are those that are inappreciably affected by changes in pressure, e.g. most liquids.

fluids are those that are appreciably affected by changes in pressure, e.g. most gases.

is the branch of momentum transfer concerned with fluids at rest.

is the branch of momentum transfer concerned with fluids in motion.

roughly states that there is a linear relation between shear stress and rate of shear, and that the proportionality constant is the viscosity.

is the ratio of viscosity to density.

fluids are those that obey Newton’s Law of Viscosity, i.e. have constant viscosities.

fluids are those having viscosities as a function of shear rate.

Gases and low molecular weight liquids are generally fluids.

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.

flow is the type of flow at higher velocities where eddies are present giving the fluid a fluctuating nature.

The is the ratio of the kinetic or inertial forces and viscous forces.

For a straight circular pipe, values less than indicates laminar flow, and above indicates turbulent flow.

Frictional losses in the entrance region are than those of the same length of fully developed flow.

number is the ratio of the fluid velocity to the speed of sound or acoustic velocity.

For Mach number greater than 1, flow is . If equal to 1, flow is and the velocity equals the local speed of sound. If less than 1, flow is .

The ratio of heat capacities for air is typically .

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 meter overcomes the disadvantages of this meter but in exchange for a much larger head or power loss.

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 (❌)
• Shear stress is dependent on time or duration of shear (❌)

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.