Fluid Dynamics

Question 1

What does ‘ρ’ and ‘p’ represent?

Answer 1

ρ - density

p - pressure

Question 2

What variable is commonly used to denote velocity?

Answer 2

u = (u,v,w)

Question 3

Define a steady flow

Answer 3

A flow is said to be steady if the velocity is independent of time
u = u(x) only

Question 4

Define an unsteady flow

Answer 4

If the flow varies with time, the flow is said to be unsteady
u = u(x, t)

Question 5

Define a stagnation point

Answer 5

A stagnation point is a location, x = x*

at which u(x*) = 0

Question 6

What is ∇p perpendicular to?

Answer 6

The level surfaces

Question 7

What equations does the Continuity Eqn result from?

Answer 7

A fundamental law of Newtonian dynamics,

conservation of mass

Question 8

Define flux

Answer 8

The flux of a quantity through a surface is the rate of flow of the quantity through the surface,
or
the amount of quantity that flows through the surface per unit time.
(The quantity could be mass, heat, particles, magnetic fields, …)

Question 9

Equivalent term to vector field

Answer 9

vector function

Question 10

For scalar field f(x,y,z), describe the direction and magnitude of vector field ∇f

Answer 10

perpendicular to the level surfaces of f ( f = const)
pointing in the direction of increasing f
with a magnitude equal to the rate of change of f in this direction.

Question 11

What is the divergence of a vector field?

Answer 11

div F = ∇• F

Question 12

What is divergence of a vector field in context?

Answer 12

The divergence measures the rate of ‘expansion’ or ‘stretching’ of the vector field

Question 13

How are the 2 categories of exact solutions to the Navier-Stokes eqns determined?

Answer 13

Those for which the nonlinear term u · ∇u vanishes
(e.g. Couette flow, Poiseuille flow)
and those for which it doesn’t
(e.g. stagnation point flow, flow in convergent and divergent channels, flow over a porus wall)

Question 14

What does μ represent in the Navier-Stokes eqn?

Answer 14

coefficient of viscosity

Question 15

What can be assumed if there is no flow?

Answer 15

The fluid doesn’t move

The velocity = 0 (zero vector)

Question 16

What is the concept of a free surface of a fluid?

Answer 16

The free surface of a liquid just means the surface that is in contact with air.

Question 17

What is pressure dependent on?

Answer 17

p = p(x,y,z,t)
i.e. space AND time.
Don’t forget to include this ‘t’ when solving for p.

Question 18

Define streamwise

Answer 18

In the direction of flow (u vector)

Question 19

What is body force of a fluid?

Answer 19

Body force is a force that is felt throughout the whole volume of the fluid, i.e. gravity

Question 20

Explain the no-slip boundary conditions

Answer 20

In fluid dynamics, the no-slip condition for viscous fluids assumes that at a solid boundary, the fluid will have zero velocity relative to the boundary.

Question 21

How are streamlines defined?

Answer 21

dx1/u = dx2/v = dx3/w

Question 22

Relationship between velocity and streamlines?

Answer 22

Velocity is tangent to the streamlines

Question 23

Thinking about the eqn for the deformation matrix, what do eij and ξij represent in terms of physical properties of the fluid?

Answer 23

eij - represents local straining

ξij - represents rotation

Question 24

What is a material volume?

Answer 24

A material volume is a set of particles within a closed material surface, and therefore contains the same set of particles for all time.

Question 25

Define an isotropic fluid

Answer 25

has no preferred direction

Question 26

What’s the difference between Fundamental and Derived units?

Answer 26

Fundamental - standard reference units e.g. cm

Derived - obtained by using the definitions of the physical quantities involved e.g. speed cm/s