Midterm 2: Lecture 10-20 Flashcards
What is inviscid flow?
flow that moves without drag/friction – no energy needed to be put into the fluid to get it to move past other fluid particles and overcome its internal friction
What is a no-slip condition?
fluid adjacent to a surface is stuck and cannot move
What is a stagnation point?
point at which fluid stops moving (v = 0)
What is laminar flow?
velocity changes uniformly away from pipe wall
- ordered flow – shape of flow is predictable
- reversible and reproducible – can predict where fluid will start or end up
- no mixing
What is turbulent flow?
velocity changes are unsteady
- disordered flow – shape of flow is unpredictable
- non-reversible and irreproducible
- efficient mixing
- vorticity
Flow through pipes is observed to adopt 3 different flow regimes. What are these types of flows?
laminar → transitional → turbulent
What is Reynold’s number?
ratio of inertial force to viscous force that predicts transition from laminar to turbulent flow
- viscous force (Fv): makes flow laminar
- inertial force (Fi): makes flow turbulent
What is viscous force?
fluid slides over (parallel) the surface of the plate, which is so thin that no fluid collides with its leading edge
fluid exerts force on the plate of area S due to its viscosity and the shearing in velocity gradient (v/l) associated with it
How is a velocity gradient formed in fluid?
fluid touching side of the plate is not moving, which slows down fluid flowing next to it, etc.
What is inertial force?
fluid collides with plate area
fluid exerts force against the plate (due to momentum)
Why does increasing fluid density drive flowing fluids towards becoming turbulent?
greater inertia, more likely to separate from surface and generate turbulence
Why does increasing velocity drive flowing fluids towards becoming turbulent?
fluid stream begins to break away from surface, disrupting laminar flow
Why does increasing characteristic length / flow path (l) drive flowing fluids towards becoming turbulent?
more surface area to flow across, therefore more time for turbulence to develop
What is viscosity?
tendency of fluid to flow due to external forces acting on it
What is kinematic viscosity?
tendency of fluid to flow due to gravitational forces acting on it – ratio of viscosity to density
What is the relationship between viscosity and resistance?
increase viscosity → increase resistance (to moving around when force is applied)
What is a vortex?
region within fluid where flow moves around a central axis
Spinning Solids
linear relationship between distance from centre (r) and tangential velocity
What is a solid-body rotation?
rotates (360º turn every cycle) around central axis
Spinning Fluids (Vortex)
ROTATIONAL CORE: (inner) solid-body rotation
IRROTATIONAL PERIPHERY: (outer) translation, NO rotation – because shear rate is increasing towards axis of rotation
- fluids can move past other bits of fluids
- particles closest to axis of rotation is always being pushed faster than particles further out, causing it to circle/turn in the fluid faster (but still maintaining its orientation)
- closer to axis of rotation → tangential velocity increases with radius for some time, then decreases
What is translation?
holds its orientation (no 360º turns) in a circle around central axis
Spinning Solids vs. Spinning Liquids
all parts of a solid are in fixed relation to all other parts of the solid – NOT the case for fluids
What is shear rate?
the gradient in velocity – the difference in velocity between the two surfaces containing the fluid, divided by the distance between them
Sieve (for filtering)
need leaky appendage – want high Re
Paddle (for swimming/locomotion)
need non-leaky appendage – want low Re
can push air around in the same way that a solid membrane is required to do at high Re
Re «_space;1: viscous forces dominate – low velocity, low Re
- viscosity of fluid stops the fluid moving
- dissipated forces will overcome any momentum the fluid has and will slow it down and cause it to stop
- fluid in contact with bristles will be stuck because of the fluid’s viscosity relative to its inertia
- if you move the hairy appendage through a fluid, the fluid trapped between bristles does not get dislodged – its viscosity is too great relative to the inertia
- fluid moving around appendage literally flows around it (does not go between bristles)
Re ~10: inertial forces dominate – high velocity, high Re
- dislodges fluid between bristles to get fluid passing between appendages
- if you move bristly appendages through water faster, at some point the inertial forces will increase relative to viscous forces, and you start to get fluid beginning to flow through bristles
What is leakiness?
volume/time of fluid passing between hairs divided by volume/time without hairs
What is gap width / hair diameter?
how much space there is relative to bristles
Scallop Theorem – Swimming
swims by closing shell, pushing water out from between the two closing shells to push itself forward
at high Re: drag (Fd) ∝ v2 x time (Fi = ⍴Sv2)
at low Re (< 1): drag (Fd) ∝ v x time (Fv = μ(v/l)S)
- can no longer swim forward – each stroke (regardless of speed) cancels out the previous movement as the drag produced is equal in both directions
- will move forward slightly when trying to swim, but as soon as it reopens shell to refill it with water for the next push, it will move it right back to where it began (regardless of how fast it opens/closes shell)
Scallop Theorem – Swimming
at very low Re («_space;1)
any organism with only 1 articulation cannot travel when Re «_space;1, since the swimming motion will always repeat itself in reverse
flows are completely reversible – therefore motion is too
Dynamic scaling works as long as…
there are no fluid/fluid interfaces, and fluid velocity is subsonic
What happens if Re in two different situations is the same (ie. model vs. real-life)?
character of their fluid flows will also be the same, even if the scales are very different
ratio of inertial and viscous forces are the same ∴ the way the fluid moves around the same-shaped object will be the same, regardless of the scale
