Fluid Dynamics Flashcards
What does ‘ρ’ and ‘p’ represent?
ρ - density
p - pressure
What variable is commonly used to denote velocity?
u = (u,v,w)
Define a steady flow
A flow is said to be steady if the velocity is independent of time
u = u(x) only
Define an unsteady flow
If the flow varies with time, the flow is said to be unsteady
u = u(x, t)
Define a stagnation point
A stagnation point is a location, x = x*
at which u(x*) = 0
What is ∇p perpendicular to?
The level surfaces
What equations does the Continuity Eqn result from?
A fundamental law of Newtonian dynamics,
conservation of mass
Define flux
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, …)
Equivalent term to vector field
vector function
For scalar field f(x,y,z), describe the direction and magnitude of vector field ∇f
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.
What is the divergence of a vector field?
div F = ∇• F
What is divergence of a vector field in context?
The divergence measures the rate of ‘expansion’ or ‘stretching’ of the vector field
How are the 2 categories of exact solutions to the Navier-Stokes eqns determined?
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)
What does μ represent in the Navier-Stokes eqn?
coefficient of viscosity
What can be assumed if there is no flow?
The fluid doesn’t move
The velocity = 0 (zero vector)
What is the concept of a free surface of a fluid?
The free surface of a liquid just means the surface that is in contact with air.
What is pressure dependent on?
p = p(x,y,z,t)
i.e. space AND time.
Don’t forget to include this ‘t’ when solving for p.
Define streamwise
In the direction of flow (u vector)
What is body force of a fluid?
Body force is a force that is felt throughout the whole volume of the fluid, i.e. gravity
Explain the no-slip boundary conditions
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.
How are streamlines defined?
dx1/u = dx2/v = dx3/w
Relationship between velocity and streamlines?
Velocity is tangent to the streamlines
Thinking about the eqn for the deformation matrix, what do eij and ξij represent in terms of physical properties of the fluid?
eij - represents local straining
ξij - represents rotation
What is a material volume?
A material volume is a set of particles within a closed material surface, and therefore contains the same set of particles for all time.
Define an isotropic fluid
has no preferred direction
What’s the difference between Fundamental and Derived units?
Fundamental - standard reference units e.g. cm
Derived - obtained by using the definitions of the physical quantities involved e.g. speed cm/s
