Exam flashcards

Question 1

What is the Lorentz factor?

Answer 1

1/γ = sqrt(1-v²/c²)

Question 2

What is the relativistic kinetic energy?

Answer 2

-m₀c²/γ

Question 3

What is the equation for rotational kinetic energy?

Answer 3

Iω²/2

Question 4

How do we determine conserved quanties?

Answer 4

If a coordinate does not appear in the Lagrangian, its associated momentum is conserved
(Noether’s Theorem)

Question 5

Why can µ not be neglected in the NS equation?

Answer 5

Outside boundary flow is inviscid
Sharp velocity gradient

Question 6

What is the density for an incompressible flow?

Answer 6

Constant
Not a function of x or y

Question 7

What is ∇×(∇φ)?

Answer 7

0

Question 8

What is the identity for ∇²φ?

Answer 8

∇²φ = ∇⋅(∇φ)

Question 9

What is the velocity for a viscous flow?

Answer 9

Constant
∂v/∂t = 0

Question 10

What is the boundary condition for a potential flow?

Answer 10

u_⊥ = 0
So 0 = u_r

Question 11

What potentials have radial directions?

Answer 11

Coulomb
Gravity

Question 12

What are the momenta for the E-L equation?

Answer 12

p_x = ∂L/∂ẋ

Question 13

How do we integrate?

Answer 13

∫a(s)ds = ∫b(t)dt

Question 14

How do we get the differential equation for the streamline?

Answer 14

dr×v = 0
dr = dλv

Question 15

What is the |∇|?

Answer 15

L₀^-1

Question 16

What is the |∇²|?

Answer 16

L₀^-2

Question 17

What is the inertial term of the NS eqn?

Answer 17

ρ(v ·∇)v

Question 18

What is the viscous term of the NS eqn?

Answer 18

µ∇²v

Question 19

What are the directions of the oscillations and speed for vortex shedding?

Answer 19

Perpindicular