Ongoing Fluid Mechanics Billy

Question 1

what is incompressible?

Answer 1

liquid are incompressible and fluids are compressible

Question 2

ρ ?

Answer 2

Density, ρ(r , t)

Question 3

p ?

Answer 3

Pressure p(r , t)

Question 4

ū ?

Answer 4

Fluid Density ū=ū(r, t)

Question 5

Define a Streamline

Answer 5

An imaginary line in a flow which is everywhere tangential to the fluid density ū.

Imagine a freeze frame rather than following particle

Question 6

1.1

Equations for streamlines

Answer 6

dx/u = dy/v = dz/w (=k)

Question 7

Define a Stagnation point

Answer 7

places where the velocity is zero.

Question 8

1.2

Equations for particle paths, with dr/dt = ū(r,t).

Answer 8

dx/dt=u
dy/dt=v
dz/dt=w

Question 9

when is a flow steady ?

Answer 9

when ðu/ðt = 0

Question 10

Define a streakline

Answer 10

imagine injecting dye into a flow at a specific location for all time.

Question 11

Suffix Notation.

δ_pq ?

Answer 11

{ 1 if p=q

{ 0 if p≠q

Question 12

Suffix Notation.

ε_pqr ?

Answer 12

{ +1 cyclic 123, 231, 312
{ -1 anticyclic 321, 213, 132
{ 0 otherwise

Question 13

D/Dt ?

Answer 13

D/Dt = ð/ðt + u·ð/ðx + v·ð/ðy + w·ð/ðz

D/Dt = ð/ðt + ū·∇

Question 14

Dρ/Dt ?

Answer 14

D/Dt = ðρ/ðt + ū·(∇ρ)

Question 15

Dū/Dt ?

Answer 15

D/Dt = ðū/ðt + (ū·∇)ū

Question 16

what is the mass of an enclosed area V

Answer 16

∭ρdV

Question 17

what is the rate of change mass in enclosed area V

Answer 17

∭ðρ/ðt dV

Question 18

what is the rate of mass flow out of boundary S of V.

Answer 18

∬ρṉ·ūdS

Question 19

Equation 1.14a

the equation of conservation of mass ?

Answer 19

ðρ/ðt + ∇(ρū) =0

Question 20

Equations 1.14b

?

Answer 20

ðρ/ðt + ū·∇ρ + ρ∇·ū =0
or
Dρ/Dt + ρ∇·ū = 0

Question 21

Equation 1.15

Density does not change equation?

Answer 21

Dρ/Dt =0

therefore for liquids ∇·ū=0

Question 22

what are External forces ?

Answer 22

body forces. external forces that are acting on the fluid. we usually only consider gravity, unless told

Question 23

what are internal forces ?

Answer 23

?

Question 24

for inviscid fluids, what is the only force acting on the fluid

Answer 24

the notes dont say. please find out. but i do know its always in the direction of -normal. (minus the normal)
δf = -pṉδs

Question 25

what is hydrostatic equilibrium ?

Answer 25

when the fluid is at rest

Question 26

Equation 1.16

the hydrostatic equilibrium equation ?

Answer 26

ρF = ∇p

Question 27

total linear momentum ?

Answer 27

Ƥ= ∭ρūdV

Question 28

Rate of change if total linear momentum ?

Answer 28

∭ð(ρū)/ðt dV =

∭ρF -∇p dV - ∬ρū(ū·ṉ) dS

Question 29

General form of the Divergence Theorem?

Answer 29

∭ðǿ/ð(x_p) dV = ∬ǿn_p dS

Question 30

what are the three forms of the divergence theorem?

Answer 30

1. ∭∇·F dV = ∬F·ṉ dS
2. ∭∇ǿ dV = ∬ǿṉ dS
3. ∭∇xū dV = ∬ṉxū dS

Question 31

Equation 1.17

don’t know its name yet ?

Answer 31

ρ( ðū/ðt + (ū·∇)ū ) = ρF-∇p

or mass x acceleration = force

Question 32

lecture 9 please fill in

Answer 32

lecture 9 please fill in

Question 33

lecture 9 please fill in

Answer 33

lecture 9 please fill in

Question 34

lecture 9 please fill in

Answer 34

lecture 9 please fill in

Question 35

whats vorticity ?

Answer 35

ῶ = ∇xū

Question 36

what is a vortex line ?

Answer 36

is an imaginary line in a fluid, which is anywhere tangential to the vorticity.

Question 37

Equation 3.1

what is the velocity at point ṟ on a rigid body.

Answer 37

āxṟ. where ā is the angular velocity

Question 38

Equation 3.2

stupid, fill out later

Answer 38

?