Chapter 6

Question 1

What is translation?

Answer 1

When a fluid particle simply moves from one position to another. Laminar flow, no rotation. Draw diagrams.

Question 2

What is rotation?

Answer 2

In rotation, fluid particles rotate in any direction and create angular velocity. By this mechanism a VORTEX is created in the fluid motion. Source of turbulence. Diagram.

Question 3

What is linear deformation?

Answer 3

The sides of the square containing the fluid particle stretch or contract in any direction, total area remains unchanged. Diagram.

Question 4

What is angular deformation?

Answer 4

The angles between the sides change. Shear stress and strain of flow would be dominant. Generate shear stress/force. Diagram.

Question 5

Derive translation formulas?

Answer 5

Du/Dt = u(∂u/∂x) + v(∂u/∂y) + w(∂u/∂z) + ∂u/∂t
Dv/Dt = u(∂v/∂x) + v(∂v/∂y) + w(∂v/∂z) + ∂v/∂t
Dw/Dt = u(∂w/∂x) + v(∂w/∂y) + w(∂w/∂z) + ∂w/∂t

Question 6

What are the three fluid rotation equations?

Answer 6

Ωx = 0.5(∂w/∂y - ∂v/∂z)
Ωy = 0.5(∂u/∂z - ∂w/∂x)
Ωz = 0.5(∂v/∂x - ∂u/∂y)

Question 7

What are the angular deformation (AD) equations?

Answer 7

AD in xy plane = ∂v/∂x + ∂u/∂v
AD in yz plane = ∂w/∂y + ∂v/∂z
AD in zx plane = ∂u/∂z + ∂w/∂x

Question 8

Linear Deformation (LD) equations?

Answer 8

LDx = ∂u/∂x
LDy = ∂v/∂y
LDz = ∂w/∂z

Question 9

What is it called if adding all of the LD’s together = 0?

Answer 9

Same as mass conservation for incompressible flow, called VOLUME DILATION