Fluid Mechanics Flashcards
(35 cards)
How do you find the shear stress acting on a wall?
τ=μ δu/(δx_2 )
How would you prove that flow is incompressible?
∇∙u=0
How do you prove that a flow is irrotational?
∇xu=0
What is a streamline?
It is a curve that runs parallel to the velocity field at all points.
What is a pathline?
A curve that maps the trajectory of a single particle.
What is a streakline?
A curve that connects the position of all the particles that have passed through a certain point at some time.
What condition must be met for pathlines, streamlines and streaklines to all be the same?
The flow would be steady.
What is Pascall’s Law?
In a fluid at rest, the normal stress and the stress due to hydrostatic pressure act equally and opposite in all directions.
What is bernoulli’s equation?
𝑝 + 1/2 (𝜌𝑈^2) + 𝜌𝑔𝑧 = const. Gravity term usually is neglected
Define Reynold’s Number?
The ratio of the inertial force against the viscous forces.
What can the Reynolds Number tell us about a flow?
For a flow along a wall, a boundary layer, a lower reynolds number means that there is a laminar flow whereas a higher reynolds number means a turbulent flow. The transition point is 5x10^5
How is drag related to momentum thickness?
D=ρ*U^2 *θ
What is the definition of Boundary Layer Thickness?
The distance, y, at which the flow has a velocity that is 99% of the free stream velocity.
What is the displacement thickness?
The distance that the wall would need to be moved in potential flow to get the same mass flow rate in the counterpart viscous flow. (The height, h, along the same distance as the boundary layer that would create the same area as the boundary layer).
The distance by which the external inviscid flow is displaced due to the presence of the boundary layer.
What is momentum thickness?
a measure of how much momentum flux is lost due to the presence of a boundary layer. It represents the distance by which the solid surface would need to be displaced to compensate for the loss of momentum caused by the boundary layer.
What is the shape factor of a boundary layer?
Shape factor (H) = Displacement thickness/momentum thickness.
H = 2.6 ~ Laminar
H = 1.3-1.6 ~ Turbulent
H > 3.5 ~ Flow seperation
What is the effect of pressure on a boundary layer?
Decrease in pressure - thinner boundary layer
Increase in pressure - thicker boundary layer.
What are direct numerical simulations (DNS)?
NS equations are solved at every point and capture all the details of flow.
Very accurate but very time consuming.
can only access low reynolds numbers
What causes separation of a boundary layer?
A large adverse pressure gradient (from low pressure to high pressure) will cause the flow close to the boundary to reverse and therefore separate.
What are Large Eddy Simulations (LES)?
Captures larger scale turbulences
Grid size does need to be too small
We need a model for the smaller scales as a new term in the momentum equations
Still very expensive and time consuming (need super computers with lots of memory)
What is RANS (Reynolds-averaged Navier Stokes Equations)?
Solves for the ‘mean’ flow
equations for U, V, P
This has several models
Takes the time average of each term in the navier stokes
Quicker but less accurate than the other methods.
What is the ranking of CFD models in terms of accuracy?
- DNS
- LES
- RANS
Opposite for time taken
What is the Bernoulli Theorem for incompressible flow?
p_0=p + 1/2 * (ρU^2 )=const
p_0 is the stagnation pressure and p is the static
For a subsonic flow in a diverging duct what happens to:
Pressure?
Velocity?
Mach number?
Density?
Density: increase
Flow speed: decrease
Pressure: increase
Mach number: decrease
