Environmental Fluid Mechanics - Week 1

what is a fluid

loosely bound particles that are continuously and permanently distorted by external forces

continuous distortion

change shape after force is applied

permanent distortion

do not return to original form after force is lifted

is chemical composition enough to know if a substance is a fluid

no

is glass fluid or solid?

a low shearing rate makes glass fluid, but a high shearing rate makes glass solid

fluid mechanics

energy and forces, and their effect on fluids, as well as practical applications of these mechanics

outline the “tree” of mechanics

Mechanics; statics, dynamics: kinematics, kinetics: thermodynamics, N3L, N2L

fluid statics

when the sum of forces acting upon the fluid must be equal to 0, the fluid is at rest or moving with constant velocity without deforming

fluid dynamics

describes how the forces and velocities in fluids change

what equation is associated with thermodynamics

W=Fd

what is the fluid version of the N2L

Navier-Stokes equation

what are the applications of environmental fluid mechanics

air and water; buoyancy; complex topography/geometry; air/water quality and chemistry; Earth’s rotation; turbulence

what forces are fluids to subjected to

pressure, gravity (buoyancy), viscosity (molecular), Coriolis(pseudo-forces), magnetic, inertial force, surface tension/capillary forces

which relevant forces are fluids to subjected to

pressure, gravity (buoyancy), viscosity (molecular), inertial forces

when inertial forces are lower than viscous forces, we have what type of flow

laminar

when inertial forces are higher than viscous forces, we have what type of flow

turbulent

is a turbulent flow good or bad in environmental fluid mechanics

mostly good, for mixing

what are two methods to apply Newton’s 2nd Law to a fluid?

discrete fluids and continuum mechanics

which method for applying Newton’s 2nd Law to fluids is generally preferred?

continuum mechanics

when we are finding the wind speed of a fluid, what are we doing

taking the average speed of each particle

when we are finding the air mass of a fluid, what are we doing

taking the sum of each particle mass

how do we look at a fluid in the continuum mechanics framework

a continuous field of matter with properties derived from individual particles

for extensive properties, we are taking the

sum

for intensive properties, we are taking the

average

do we need a large or small amount of molecules to make our continuum assumptions

large

how does the velocity of particles change as the volume of the box they are in is increased

It appears to oscillate due to experimental uncertainty, then stabilizes once an adequate sample size is reached

how does the mass of particles change as the volume of the box they are in is increased

it increases in a pseudo-stepwise fashion

how can we apply continuum mechanics to a real building

we assume a large amount of molecules bump into the building to maintain a smooth flow

how do we know if we have enough molecules to assume continuum mechanics

if the physical length scale is much much larger that the distance between the particles

how do we make assumptions for gases in continuum mechanics

Knudsen number

What is the equation for the Knudsen number

Kn = λ/L

λ

mean free path

L

physical length scale

Kn

average distance covered by particle before collision with other particles

when the Knudsen number is less than 0.01,

L is greater than 1000λ, so our assumption is valid

when the Knudsen number is greater than or equal to 1

L is less than or equal to λ, so our assumption is invalid

what are situations where we cannot make the continuum assumption

outer bounds of atmosphere (exosphere), soot particulates in troposphere, flow of water in clay filtration system, nanofluids

field

physical quantity defined at every point in space or time

scalar

parameter with a magnitude

vector

magnitude with one orientation

gradients of scalars

show how fast a scalar changes in each scalar direction

gradient vector

direction of greatest change

second-order tensor

gradient of a vector

how many directions and components does a second-order tensor have

two directions and nine components

the order/rank of tensor indicates what

the number of distinct indicies it has