October 14, 2024: Chapter 3: Fluid Dynamics
Principles of Fluid Dynamics
Fluid mechanics: the study of how fluids move and the forces on them (including liquids and gases)
Fluid mechanics can be divided into fluid statics, the study of fluids at rest, and fluid dynamics, the
study if fluids in motion
Fluid dynamics: the sub-discipline of fluid mechanics dealing with fluid flow: fluids in motion
Includes: dams and levees, weather, pipe flow, hydraulic engineering, coastal and ocean engineering, naval
architecture, aerospace and automotive design, sports
Scalars and Vectors
Scalars are quantities that can be specified by giving a single number
Vectors are quantities that require not only a magnitude, but a direction to specify them completely
Vectors are often distinguished from scalar quantities either by placing a small arrow over the
quantity, or by writing the quantity in a bold font
Force
Contact force: frictional force, tension force, normal force
Non-contact force: gravitational force, electrical force, magnetic force
Representation of a force
The point at which the force acts
The line along which it acts
The sense in which it acts along this line
The size of the force
Force in equilibrium: when a body is at rest or moving uniformly in a straight line, there must be either no
force acting on it, or else the forces acting on it must balance each other
Newton’s three law of motion
Newton’s first law: every object in a state of uniform motion tends to remain in that state of motion unless an
external force is applied to it
Newton’s second law of motion: the relationship between an object’s mass m, its acceleration a, and the applied
force F is f=ma
Acceleration and force are vectors; in this law the direction of the force vector is the same as the
direction of the acceleration vector
1 newton(n) = 1kg m/s^2
Newton’s third law: for every action there is an equal and opposite reaction
Definitions and properties
Fluids: liquids and gases
A fluid is a substance that continuously deforms when subjected to a shear stress
Shear stress: a tangential force per unit area acting on a surface
, Normal stress: a normal force per unit area acting on a surface
Pressure when applied to fluid medium
Principles of fluid dynamics
Fluid dynamics: the study of physical process governing fluid motion
Extension of the notions of force balance nd newton’s second law to fluids, particularly water
Start from simple cases such as flow through a pipe or hose, but the same principles apply to flow in
streams and through soil and rocks
Both groundwater and surface-water flow are governed by the principles
Fluids differ dramatically in their viscosity
The viscosity of lava is almost a billion times that of air
Plays an important role in the nature of fluid flow
Laminar flows: flows in which viscous forces dictate the nature of flow
Turbulent: flows in which viscous forces are relatively unimportant
Most groundwater flow is laminar, while most surface-water flow is turbulent
Definitions and properties
Viscosity: a measure of a fluid's ability to resist deformation
Motion under shear stress
The rate at which fluid deformation occurs, depends not only the shear stress, but also the fluid
viscosity
The viscosity of honey is greater than the viscosity of water, which in turn is greater than the viscosity
of air
Continuum assumption
What is a point in the fluid?
Either a molecular particle or in the void space
The fluid “properties” associated with such a point would obviously depend upon the location of the
point
The fluid is idealized macroscopically as being continuous throughout its entirety
The molecules are pictured as being “smeared” or “averaged” to eliminate spaces between atomic
particles
Anything at “a point in a fluid”
Average of the quantity in a small volume surrounding the point. The volume should be
Small enough relative to the system of interest
Large compared with the average distance between the molecular
Fluid density
Principles of Fluid Dynamics
Fluid mechanics: the study of how fluids move and the forces on them (including liquids and gases)
Fluid mechanics can be divided into fluid statics, the study of fluids at rest, and fluid dynamics, the
study if fluids in motion
Fluid dynamics: the sub-discipline of fluid mechanics dealing with fluid flow: fluids in motion
Includes: dams and levees, weather, pipe flow, hydraulic engineering, coastal and ocean engineering, naval
architecture, aerospace and automotive design, sports
Scalars and Vectors
Scalars are quantities that can be specified by giving a single number
Vectors are quantities that require not only a magnitude, but a direction to specify them completely
Vectors are often distinguished from scalar quantities either by placing a small arrow over the
quantity, or by writing the quantity in a bold font
Force
Contact force: frictional force, tension force, normal force
Non-contact force: gravitational force, electrical force, magnetic force
Representation of a force
The point at which the force acts
The line along which it acts
The sense in which it acts along this line
The size of the force
Force in equilibrium: when a body is at rest or moving uniformly in a straight line, there must be either no
force acting on it, or else the forces acting on it must balance each other
Newton’s three law of motion
Newton’s first law: every object in a state of uniform motion tends to remain in that state of motion unless an
external force is applied to it
Newton’s second law of motion: the relationship between an object’s mass m, its acceleration a, and the applied
force F is f=ma
Acceleration and force are vectors; in this law the direction of the force vector is the same as the
direction of the acceleration vector
1 newton(n) = 1kg m/s^2
Newton’s third law: for every action there is an equal and opposite reaction
Definitions and properties
Fluids: liquids and gases
A fluid is a substance that continuously deforms when subjected to a shear stress
Shear stress: a tangential force per unit area acting on a surface
, Normal stress: a normal force per unit area acting on a surface
Pressure when applied to fluid medium
Principles of fluid dynamics
Fluid dynamics: the study of physical process governing fluid motion
Extension of the notions of force balance nd newton’s second law to fluids, particularly water
Start from simple cases such as flow through a pipe or hose, but the same principles apply to flow in
streams and through soil and rocks
Both groundwater and surface-water flow are governed by the principles
Fluids differ dramatically in their viscosity
The viscosity of lava is almost a billion times that of air
Plays an important role in the nature of fluid flow
Laminar flows: flows in which viscous forces dictate the nature of flow
Turbulent: flows in which viscous forces are relatively unimportant
Most groundwater flow is laminar, while most surface-water flow is turbulent
Definitions and properties
Viscosity: a measure of a fluid's ability to resist deformation
Motion under shear stress
The rate at which fluid deformation occurs, depends not only the shear stress, but also the fluid
viscosity
The viscosity of honey is greater than the viscosity of water, which in turn is greater than the viscosity
of air
Continuum assumption
What is a point in the fluid?
Either a molecular particle or in the void space
The fluid “properties” associated with such a point would obviously depend upon the location of the
point
The fluid is idealized macroscopically as being continuous throughout its entirety
The molecules are pictured as being “smeared” or “averaged” to eliminate spaces between atomic
particles
Anything at “a point in a fluid”
Average of the quantity in a small volume surrounding the point. The volume should be
Small enough relative to the system of interest
Large compared with the average distance between the molecular
Fluid density
