Intro Flashcards
What is the difference between liquids and gases?
Gases are highly compressible, liquids are virtually incompressible
Define viscosity
The internal resistance in a fluid
Define inviscid
Flows in which the viscosity is negligible.
What is an ideal fluid?
Flows treated as inviscid.
What is a fluid particle?
A quantity of fluid very small compared to the overall fluid flow, but very large compared to molecules.
We can think of averaging the properties of all the molecules in the fluid particle.
What does strong mixing in fluids mean?
Fluid properties, as functions of position, are continuous.
What are the properties of a fluid a function of?
A continuous function of position and time.
The divergence theorem (give meanings of symbols)
triple integral (V) ∇.F dV =
double closed integral (S) F. dS
dS = ˆn dS, with ˆn a unit vector,
V is a finite region bounded by the closed surface S, which is the peicewise smooth and has outward-pointing unit normal ^n.
Stokes’ Theorem (relationship between variables)
Double integral (S) ∇ × F. dS = closed integral (C) F. dr
S is an open surface bounded by a closed curve C, S is piecewise smooth.
The orientation of ^n, the unit normal to S, is such that C is followed in a direction given by the right-hand rule. That is, if the fingers of the right hand rule are pointing around C, then the thumb is in the ^n direction.
What direction does grad point in?
Everywhere perpendicular to the surface s = constant.
What is the Lagrangian description?
Each fluid labelled with starting position, but generally extremely hard to work out where a specific fluid particle starts.
What is the Eulerian description?
Each fluid particle labelled with current position.
The “a dot grad” operator (a · ∇)
(a · ∇)s = a · (∇s) = b∂s/∂x + c∂s/∂y + d∂s/∂z
∇.(Φu) = ?
Φ(∇.u) + (u.∇)Φ
