Mach number is the ratio of the speed of a moving fluid to the speed of sound in the fluid.

• It helps determine if flow can be treated as incompressible

• low Mach # (<.3) usually represents fluid @incompressible flow

Pressure typically ranges from 0-infinity because we cannot have tension in a gas/fluid.

• Gas molecules are too far apart on average for the intermolecular fores to support the tensile stress and maintain cohesion
• liquid should in theory be able to support a tensile stress becase of its strong molecular forces. However, liquid boils as the pressure on liquid decreases to the vapor pressure--vapor pockets prevent liquid from being in tension

molecular mean free path  =  λ

some representative physical length  =  d

• helps determine the best method of description (continuum vs. non-continuum)
• if Kn# is close to 1: λ is close to length and we cannot use continuum method: must use Molecular Model

Body: long range & volumetric by nature.

• Acts ON the element's mass (ie EXTERNAL)

Surface: Short range & interfacial areal by nature.

• Exerted by pressure or shear through physical contact between element and its surroundings

• The flow is the same at every location in the pipe
• Velocity field does not change in flow direction

Bulk Modulus measures a substance's resistance to uniform compression

Δpressure

Δvolume

Stress Vector (Σ) can be used to calculate surface Force, but not to describe the state of stress in fluid, because it depends on orientation.

There are an infinite # of possible surface orientations for one point on the interior of a fluid.

Therefore Σ is not unique to a point in fluid.

Stress Tensor (σ) is orientation free so can uniquely describe a point in a fluid.

Sea level atmospheric pressure represents the weight of the column of air directly above a m^2 of Earth's surface.

The total weight of air in the Earth's atmosphere would be the sea level atmospheric pressure * Surface Area of the Earth.

Internal E is primarily of function of T, mostly concerned with ΔU.

Kinetic E = mv^2

Higher U-->Higher  T-->Higher Molecular V-->Higher KE

Helps us to find the net surface tension acing on the contact line because we don't know the surface tension between air and the surface of a solid

If Θ>90: not wetted

If Θ<90: wetted by liquid

If Θ=0: perfectly wetted

Laminar: smooth flow, paths of each particle never interfere with each other. Velocity of fluid is constant at all points

Turbulent: irregular flow that is characterized by roughness and tiny whirlpool regions

AT REST: Fluid has no shear stresses (only normal)

Σ=-pn + 0

IN MOTION: Fluid exerts normal (pressure) and tangential stress on a surface

Σ=σn + τ

Fluid that obeys Newton's law of viscosity: τ=μdγ/dt

(shear stress is proportional to shear strain rate)

stress vs. strain rate = linear relationship w/ constant=μ

example: water & air

When Newton's 2nd Law is written in its inertial form

Σforces - d/dt mv=0

the product "-d/dt mv" is called the inertial force because it has units of F.

It is in the non-accelerating inertial reference frame

Ep=M*p/ρ=pV

P/ρ represents the per-unit-mass form of pressure-potential energy

ability of a fluid to perform mechanical work at high pressure

underlying molecular structure of a fluid is ignored-->deliberate ommission in mathematical model

considers macroscopic properties at a point in the fluid as averages instead of individual molecules

assumes all properties are continuous flow

mean free path<<physical length

(almost always works in liquid b/c distance b/w molecules is small)

the response to shear stress which is tangential Force/Area

FLUID: Resists but cannot prevent deformation due to shear. continues to deform as long as shear is applied.

SOLID: Can prevent deformation. Quickly returns to rest and retains its new shape

Inviscid Fluid: means the fluid has viscosity=0

(no fluids technically exist)

Inviscid Flow: While fluid may have viscosity, the viscous effects are negligable (ex. boundary layer)

No shear stresses acting on a fluid at rest

states of stress is influenced by body forces

purley compressive forces and characterized by hydrostatic pressure distribution

 effect of viscosity

layer around plate

velocity changes smoothly and continuously from 0 on the plate to free stream value.

Thickness increases down the length from the leading edge

flow changes from laminar to turbulent

close to plate: fluid does not move

Σ=n·σ

take the dot product of the normal vector for plane and the stress tensor

n denotes the orientation of a surface element

n points at the fluid or the source of the force

plays a key role in description of surface forces

CLOSED: always points away from the interieor

OPEN: points from surface toward agent responsible for force

Pitot-tube can give Nose Pressure (Pn) or measures velocity in a fluid

Connected to a manometer

INCOMPRESSIBLE FLUIDS: density of the fluid is constant (Impossible to assume)

INCOMPRESSIBLE FLOW: density of a fluid particle doesnt change its density as it moves

Mechanical: Represented and measured as p=F/A (almost always measurable)

Thermodynamic: macroscopic model describing molecules colliding. Can only be measured in fluid is @ equilibrium

Signifcant when fluids with complex molecula structure undergo compression/expansion

Responsible for a viscous loss of energy when it occus rapidly

ie: interior of a shock wave: ultrasound

Response to compressive stress

Fixed amount of liquid occupies the same volume under most conditions-->difficult to compress (large force=small dV)

Distance b/w molecules of gas is greater and variable so a small force=large dV

A device flled with mercury or water that is used to measure atmospheric pressure.

used by meterologist to forecast short-term changes in weather

Re=ρVL/mu

The ration between inertial forces and viscous forces

measures the importance of inertial forces

Tells if the flow is laminar or turbulent

high reynolds #: dominance and turbular flow

low reynolds #: are laminar flows (viscous)

1) chemical composition of surface

2) temperature

3) charge on surface

compounds/acting agents that lower the surface tension of a liquid/interfacial tension

ex detergents, wetting agents, pulmonary surfactants