Ongoing Fluid Mechanics Billy Flashcards
what is incompressible?
liquid are incompressible and fluids are compressible
ρ ?
Density, ρ(r , t)
p ?
Pressure p(r , t)
ū ?
Fluid Density ū=ū(r, t)
Define a Streamline
An imaginary line in a flow which is everywhere tangential to the fluid density ū.
Imagine a freeze frame rather than following particle
1.1
Equations for streamlines
dx/u = dy/v = dz/w (=k)
Define a Stagnation point
places where the velocity is zero.
1.2
Equations for particle paths, with dr/dt = ū(r,t).
dx/dt=u
dy/dt=v
dz/dt=w
when is a flow steady ?
when ðu/ðt = 0
Define a streakline
imagine injecting dye into a flow at a specific location for all time.
Suffix Notation.
δ_pq ?
{ 1 if p=q
{ 0 if p≠q
Suffix Notation.
ε_pqr ?
{ +1 cyclic 123, 231, 312
{ -1 anticyclic 321, 213, 132
{ 0 otherwise
D/Dt ?
D/Dt = ð/ðt + u·ð/ðx + v·ð/ðy + w·ð/ðz
D/Dt = ð/ðt + ū·∇
Dρ/Dt ?
D/Dt = ðρ/ðt + ū·(∇ρ)
Dū/Dt ?
D/Dt = ðū/ðt + (ū·∇)ū
what is the mass of an enclosed area V
∭ρdV
what is the rate of change mass in enclosed area V
∭ðρ/ðt dV
what is the rate of mass flow out of boundary S of V.
∬ρṉ·ūdS
Equation 1.14a
the equation of conservation of mass ?
ðρ/ðt + ∇(ρū) =0
Equations 1.14b
?
ðρ/ðt + ū·∇ρ + ρ∇·ū =0
or
Dρ/Dt + ρ∇·ū = 0
Equation 1.15
Density does not change equation?
Dρ/Dt =0
therefore for liquids ∇·ū=0
what are External forces ?
body forces. external forces that are acting on the fluid. we usually only consider gravity, unless told
what are internal forces ?
?
for inviscid fluids, what is the only force acting on the fluid
the notes dont say. please find out. but i do know its always in the direction of -normal. (minus the normal)
δf = -pṉδs
what is hydrostatic equilibrium ?
when the fluid is at rest
Equation 1.16
the hydrostatic equilibrium equation ?
ρF = ∇p
total linear momentum ?
Ƥ= ∭ρūdV
Rate of change if total linear momentum ?
∭ð(ρū)/ðt dV =
∭ρF -∇p dV - ∬ρū(ū·ṉ) dS
General form of the Divergence Theorem?
∭ðǿ/ð(x_p) dV = ∬ǿn_p dS
what are the three forms of the divergence theorem?
- ∭∇·F dV = ∬F·ṉ dS
- ∭∇ǿ dV = ∬ǿṉ dS
- ∭∇xū dV = ∬ṉxū dS
Equation 1.17
don’t know its name yet ?
ρ( ðū/ðt + (ū·∇)ū ) = ρF-∇p
or mass x acceleration = force
lecture 9 please fill in
lecture 9 please fill in
lecture 9 please fill in
lecture 9 please fill in
lecture 9 please fill in
lecture 9 please fill in
whats vorticity ?
ῶ = ∇xū
what is a vortex line ?
is an imaginary line in a fluid, which is anywhere tangential to the vorticity.
Equation 3.1
what is the velocity at point ṟ on a rigid body.
āxṟ. where ā is the angular velocity
Equation 3.2
stupid, fill out later
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