Fundamental descriptions of flow-fields

Question 1

What is the difference between Eulerian and Lagrangian flow descriptions?

Answer 1

Eulerian: Observes fluid at a fixed point; simpler, more commonly used.
Lagrangian: Follows individual particles; complex but informative.

Question 2

True or False: The Eulerian description tracks individual fluid particles

Answer 2

False

Question 3

The Lagrangian method considers the motion of individual __________.

Answer 3

fluid particles

Question 4

What is the 2D mass continuity equation for incompressible flow?

Answer 4

∂u/∂x + ∂w/∂z = 0

Question 5

What is the full 3D incompressible continuity equation?

Answer 5

∂u/∂x + ∂v/∂y + ∂w/∂z = 0

Question 6

Match these quantities with their meanings:
- u, v, w
- x, y, z

Answer 6

• u, v, w = Velocity components in the x, y, z directions
• x, y, z = Spatial coordinates

Question 7

True or False: If the fluid is incompressible, net flow through any control volume must be non-zero.

Answer 7

False

Question 8

In a 2D flow-field, rotation through an angle is related to __________ of velocity components.

Answer 8

gradients (i.e., partial derivatives)

Question 9

What is vorticity (Ω)?

Answer 9

A measure of the local rotation of a fluid element.

Question 10

What is the angular velocity about the y-axis in 2D?

Answer 10

ω_z = ½ (∂w/∂x − ∂u/∂z)

Question 11

Express vorticity in 3D vector form.

Answer 11

Ω⃗ = ∇ × u⃗

Question 12

Match the term “Irrotational Flow” with its defining property.

Answer 12

A flow with zero vorticity (∇ × u⃗ = 0)