## Fluid Mechanics and continuum mechanics

__Fluid Mechanics:__**Fluid**is defined as a substance that deforms under a shear stress, no matter how big the magnitude.

There are some variables that need to be defined in order to find observe a fluid and its environment.

Sheer Stress-> When the shape of a material is subjected to change

Sheer strain-> would be the ratio of deformation of a material compared to its original proportions

Rate of Flow-> Quantity of fluid running through a pipe or channel in a certain period of time

Porosity-> measure of empty spaces in material

Density-> Mass per unit of volume

There are 3 different ways to express density in fluid mechanics

1. Mass density -> r is the mass of the fluid per unit volume

2. Specific weight (w)-> can be expressed in a similar way to weight= mass x gravity.

i. w= pg

3. Relative Density (specific gravity, S)-> ratio of fluid density (specific weight) to the fluid density (specific weight) of a standard reference fluid

a. Reference Fluid being for water fluid at 4 degrees Celsius

Viscosity-> Fluid property that determines the relationship between fluid strain rate and applied shear stress. It may be see as a quantitative measure of the fluid’s resistance to the flow.

Dynamic viscosity-> Ratio between the applied shear stress and the rate of shear. This is the common viscosity we defined above

Apparent viscosity -> slope of shear stress versus shear strain rate curve

· Newton’s Viscosity Law:

o After several experiments Newton discovered a linear relationship between fluids like: water, oil and air.

o Any fluid that fits into Newton’s relationship (stated as an equation) is considered a Newtonian fluid.

Time-> this would be the amount of time a fluid is put under stress.

Pressure-> atmospheric pressure may alter viscosity

Velocity-> Rate of change of position of an object showing the direction.

Body Force-> A force that acts all over the volume of the object

Temperature-> environment temperature may alter viscosity

Fluid Mechanics is a topic that has many branches, these are:

· Fluid statics-> study of fluids at rest

· Fluid dynamics-> study of the effects of forced on fluids

· Fluid kinematic-> study of fluids in motion

Fluid mechanics can best be defined as: The study of the physics of continuous materials which deform when subjected to a force.

The ones we will focus on are Fluid dynamics and fluid kinematic as during the experiment our liquid as always in motion.

Fluid mechanics takes for granted that every type of fluid obey three basic laws:

1. Conservation of Mass

2. Conservation of Energy

3. Conservation of Momentum

There is a fourth assumption that may be very useful. We may assume a fluid is incompressible, which means that the density of the

fluid doesn’t change.

Fluid mechanics is also a branch of continuum mechanics, which we will also be defining and explaining.

Fluid Kinematic:

· Describes the way fluids move without making reference to the forces that act upon it

· The main question would be: How a fluid flows?

Fluid Dynamics:

· Similar to fluids kinematic but at this time we take the forces on the fluid into consideration

· This would be the behavior of the fluid analyzed from the standpoint of Newton’s second law of motion

Non-Newtonian fluids:

· Fluids which the shear stress are not linearly related to the shear strain

· These use apparent viscosity rather than dynamic viscosity

· They are classified into groups

o Pseudo Plastics

o Dilatants

o Plastics

o Thixotropic fluid

o Rheopectic fluid

· These types of liquids don’t take the shape of the container they are poured into.

· Change their viscosity under stress.

Sheer strain-> would be the ratio of deformation of a material compared to its original proportions

Rate of Flow-> Quantity of fluid running through a pipe or channel in a certain period of time

Porosity-> measure of empty spaces in material

Density-> Mass per unit of volume

There are 3 different ways to express density in fluid mechanics

1. Mass density -> r is the mass of the fluid per unit volume

2. Specific weight (w)-> can be expressed in a similar way to weight= mass x gravity.

i. w= pg

3. Relative Density (specific gravity, S)-> ratio of fluid density (specific weight) to the fluid density (specific weight) of a standard reference fluid

a. Reference Fluid being for water fluid at 4 degrees Celsius

Viscosity-> Fluid property that determines the relationship between fluid strain rate and applied shear stress. It may be see as a quantitative measure of the fluid’s resistance to the flow.

Dynamic viscosity-> Ratio between the applied shear stress and the rate of shear. This is the common viscosity we defined above

Apparent viscosity -> slope of shear stress versus shear strain rate curve

· Newton’s Viscosity Law:

o After several experiments Newton discovered a linear relationship between fluids like: water, oil and air.

o Any fluid that fits into Newton’s relationship (stated as an equation) is considered a Newtonian fluid.

Time-> this would be the amount of time a fluid is put under stress.

Pressure-> atmospheric pressure may alter viscosity

Velocity-> Rate of change of position of an object showing the direction.

Body Force-> A force that acts all over the volume of the object

Temperature-> environment temperature may alter viscosity

Fluid Mechanics is a topic that has many branches, these are:

· Fluid statics-> study of fluids at rest

· Fluid dynamics-> study of the effects of forced on fluids

· Fluid kinematic-> study of fluids in motion

Fluid mechanics can best be defined as: The study of the physics of continuous materials which deform when subjected to a force.

The ones we will focus on are Fluid dynamics and fluid kinematic as during the experiment our liquid as always in motion.

Fluid mechanics takes for granted that every type of fluid obey three basic laws:

1. Conservation of Mass

2. Conservation of Energy

3. Conservation of Momentum

There is a fourth assumption that may be very useful. We may assume a fluid is incompressible, which means that the density of the

fluid doesn’t change.

Fluid mechanics is also a branch of continuum mechanics, which we will also be defining and explaining.

Fluid Kinematic:

· Describes the way fluids move without making reference to the forces that act upon it

· The main question would be: How a fluid flows?

Fluid Dynamics:

· Similar to fluids kinematic but at this time we take the forces on the fluid into consideration

· This would be the behavior of the fluid analyzed from the standpoint of Newton’s second law of motion

Non-Newtonian fluids:

· Fluids which the shear stress are not linearly related to the shear strain

· These use apparent viscosity rather than dynamic viscosity

· They are classified into groups

o Pseudo Plastics

o Dilatants

o Plastics

o Thixotropic fluid

o Rheopectic fluid

· These types of liquids don’t take the shape of the container they are poured into.

· Change their viscosity under stress.

T= shear stress

Ty= finite stress supported

Ty= finite stress supported

= slope of shear stress versus shear strain rate curve du/dy= velocity gradient.

Newtonian Fluids

· Fluids that under shear stress is linear proportional to the velocity magnitude in the direction perpendicular to the plane of shear.

· These take the shape of the container they are poured into.

Newtonian Fluids

· Fluids that under shear stress is linear proportional to the velocity magnitude in the direction perpendicular to the plane of shear.

· These take the shape of the container they are poured into.

Continuum Mechanics as we said, is the general topic that includes fluid mechanics. So it is important that we define what it is. This topic studies the behavioral of materials as a continuous mass rather than divided in particles. In other words, they study the bouncing of the molecules in materials as a continuous behavior, not as separate sections.