Midterm 2: Lecture 10-20

Question 1

What is inviscid flow?

Answer 1

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

Question 2

What is a no-slip condition?

Answer 2

fluid adjacent to a surface is stuck and cannot move

Question 3

What is a stagnation point?

Answer 3

point at which fluid stops moving (v = 0)

Question 4

What is laminar flow?

Answer 4

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

Question 5

What is turbulent flow?

Answer 5

velocity changes are unsteady

• disordered flow – shape of flow is unpredictable
• non-reversible and irreproducible
• efficient mixing
• vorticity

Question 6

Flow through pipes is observed to adopt 3 different flow regimes. What are these types of flows?

Answer 6

laminar → transitional → turbulent

Question 7

What is Reynold’s number?

Answer 7

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

Question 8

What is viscous force?

Answer 8

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

Question 9

How is a velocity gradient formed in fluid?

Answer 9

fluid touching side of the plate is not moving, which slows down fluid flowing next to it, etc.

Question 10

What is inertial force?

Answer 10

fluid collides with plate area

fluid exerts force against the plate (due to momentum)

Question 11

Why does increasing fluid density drive flowing fluids towards becoming turbulent?

Answer 11

greater inertia, more likely to separate from surface and generate turbulence

Question 12

Why does increasing velocity drive flowing fluids towards becoming turbulent?

Answer 12

fluid stream begins to break away from surface, disrupting laminar flow

Question 13

Why does increasing characteristic length / flow path (l) drive flowing fluids towards becoming turbulent?

Answer 13

more surface area to flow across, therefore more time for turbulence to develop

Question 14

What is viscosity?

Answer 14

tendency of fluid to flow due to external forces acting on it

Question 15

What is kinematic viscosity?

Answer 15

tendency of fluid to flow due to gravitational forces acting on it – ratio of viscosity to density

Question 16

What is the relationship between viscosity and resistance?

Answer 16

increase viscosity → increase resistance (to moving around when force is applied)

Question 17

What is a vortex?

Answer 17

region within fluid where flow moves around a central axis

Question 18

Spinning Solids

Answer 18

linear relationship between distance from centre (r) and tangential velocity

Question 19

What is a solid-body rotation?

Answer 19

rotates (360º turn every cycle) around central axis

Question 20

Spinning Fluids (Vortex)

Answer 20

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

Question 21

What is translation?

Answer 21

holds its orientation (no 360º turns) in a circle around central axis

Question 22

Spinning Solids vs. Spinning Liquids

Answer 22

all parts of a solid are in fixed relation to all other parts of the solid – NOT the case for fluids

Question 23

What is shear rate?

Answer 23

the gradient in velocity – the difference in velocity between the two surfaces containing the fluid, divided by the distance between them

Question 24

Sieve (for filtering)

Answer 24

need leaky appendage – want high Re

Question 25

Paddle (for swimming/locomotion)

Answer 25

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

Question 26

Re &laquo_space;1: viscous forces dominate – low velocity, low Re

Answer 26

• 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)

Question 27

Re ~10: inertial forces dominate – high velocity, high Re

Answer 27

• 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

Question 28

What is leakiness?

Answer 28

volume/time of fluid passing between hairs divided by volume/time without hairs

Question 29

What is gap width / hair diameter?

Answer 29

how much space there is relative to bristles

Question 30

Scallop Theorem – Swimming

Answer 30

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)

Question 31

Scallop Theorem – Swimming

at very low Re (&laquo_space;1)

Answer 31

any organism with only 1 articulation cannot travel when Re &laquo_space;1, since the swimming motion will always repeat itself in reverse

flows are completely reversible – therefore motion is too

Question 32

Dynamic scaling works as long as…

Answer 32

there are no fluid/fluid interfaces, and fluid velocity is subsonic

Question 33

What happens if Re in two different situations is the same (ie. model vs. real-life)?

Answer 33

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