Section 1: Fluid flow, boundary layers, velocity profiles, drag (Reynolds number)

Question 1

SI base units of density

Answer 1

ρ= kg m-3

Question 2

SI base unit of velocity

Answer 2

u= m s-1

Question 3

SI base unit of acceleration

Answer 3

a= m s-1

Question 4

Newton’s first law of motion

Answer 4

Unless a force acts on a body, its velocity will not change. If F = 0 then Du = 0 provides an intuitive meaning of force: a force is that agent which changes the velocity of a body

Question 5

Newton’s second law of motion

Answer 5

The rate of change of momentum (mu) of a body, is proportional to the force that acts on it

F = m*a Force = mass x acceleration

Question 6

Newton’s third law of motion

Answer 6

For any force exerted, there is an equal force in the opposite direction

Question 7

SI base unit of viscosity

Answer 7

μ= kg m-1 s-1

Question 8

Common method for observation of fluid dynamics

Answer 8

Smoke generation in air
Dye injection into water and other fluids

Question 9

Define streamlines

Answer 9

A line that is tangential to the instantaneous velocity direction
At anyone point its tangential to the path
Fluid does not cross this line and streamlines cannot cross

Question 10

Define pathlines

Answer 10

The trajectory or path of a given fluid particle
A record of the path a fluid particle has take (its history)
Pathlines may intersect since different particles may follow different paths at different times

Question 11

Define streaklines

Answer 11

A streakline is the instantaneous locus or trace of all the fluid particles that pass through a given fixed point in space.
If we injected dye continuously from a fixed point – the dye would form a streakline as it passed down stream
Streaklines cannot intersect because two particles cannot occupy the same space at the same instant

Question 12

What occurs to the lines of movement in steady flow

Answer 12

When velocity is not changing with time (steady flow) then streamlines, pathlines and streaklines are identical

Question 13

Define timelines

Answer 13

A time line is the instantaneous location of a line of fluid particles in the flow usually the initial formed line is perpendicular to the flow boundary

Question 14

Deformed timelines

Answer 14

If one end of the line is ahead of the other, fluid is moving faster
Changes in shape of the line tells use about relative changes in velocity

Question 15

Define streamtube

Answer 15

A streamtube is an imaginary tube whose walls are streamlines. It may be envisaged as a bundle of streamlines
The boundary of the stream tube can’t be crossed
Just as streamlines cannot cross so the boundary of the streamtube cannot be crossed
Outside streamlines form duct boundary

Question 16

Key features to form turbulence

Answer 16

Disorder (irreproducible in detail)
Efficient mixing
Vorticity (irregularly distributed in 3 dimensions) - eddies on varies scales included

Question 17

What is turbulence ‘energy cascade’

Answer 17

Largest eddies have biggest kinetic energy
Continuous but irregular
Progressively decay into smaller eddies until ‘smeared out’ by viscosity
Energy reflects size of the system

Question 18

Forces dominant in a high Reynolds number world

Answer 18

Inertial forces are dominant

Question 19

Forces dominant in a low Reynolds number world

Answer 19

Viscous forces dominant

Question 20

When velocity doesn’t change, what distribution will the flow be

Answer 20

Uniform flow will have a parabolic velocity distribution

Question 21

Stress in Laminar flow

Answer 21

Viscous shear stress is transmitted through the fluid

Question 22

Stress in Turbulent flow

Answer 22

Turbulent shear stress dominates

Question 23

Define boundary layer

Answer 23

region of fluid next to the boundary across which the velocity of the fluid grades from that of the boundary to that of the unaffected part of the flow

Question 24

Define free stream

Answer 24

Unaffected part of the flow

Question 25

Define ‘no slip’ condition

Answer 25

Assumes that the speed of the fluid layer in direct contact with the boundary is identical to the velocity of this boundary

Question 26

Define birefringence

Answer 26

Rod-like particles align when sheared and create birefringence when illuminated with polarized light
Free stream: no sheer, rods aren’t aligned so no birefringence
Boundary layer: shearing due to fluid resistance along the skin

Question 27

Boundary layers always expand downstream until:

Answer 27

Flow passes an obstruction and viscous forces degrade shearing in boundary
Boundary layer meets another one growing from another surface

Question 28

Are boundary layers laminar or turbulent

Answer 28

Usually start as laminar flow but as the grow become abruptly turbulent
Once the boundary layer becomes turbulent it expands more rapidly due to mixing of turbulent boundary fluid with free stream

Question 29

Are boundary layers laminar or turbulent

Answer 29

Usually start as laminar flow but as the grow become abruptly turbulent
Once the boundary layer becomes turbulent it expands more rapidly due to mixing of turbulent boundary fluid with free stream

Question 30

Define flow separation

Answer 30

Overall pattern of flow at fairly high Re past blunt bodies or through sharply expanding channels
Near the point where the surface of the solid boundary diverges from the direction of the mean flow the boundary layer separates or breaks away from the boundary
Zone of highly turbulent fluid in a detached boundary layer (i.e. downstream of an immersed object) is called a wake

Question 31

What is pressure drag

Answer 31

Drag caused by separation bubbles that result net imbalance of pressure forces across surface

Question 32

Main source of drag over a sphere

Answer 32

Skin friction

Question 33

Flow past a sphere at increasing Reynolds numbers
0.14
1.5
24
100
10^2-^3
10^3-2x10^5

Answer 33

Re 0.14: creeping flow
Re 1.5: fore and aft symmetry lost
Re 24: small internal eddied after of sphere
Re 100: irregular eddies shed pressure drags accounts for 90% of drag, Karman Vortex street
Re 10^2-^3: Laminar wake
Re 10^3-2x10^5: Wake fully turbulent, instantaneous flow

Question 34

What is ‘drag crisis’
Before: subcritical
After: supercritical

Answer 34

The boundary layer becomes turbulent, size of wake reduces
Drag reduces by 1/3 of previous value
Main difference before and after is the delay in separation causes reduction in size of wake
Imbalance of pressure forces on the sphere surface is much smaller and pressure drag is reduced
This reduction swamps a small increase in skin-friction drag produced by the greater length of the boundary layer and its transition

Question 35

How and why reduce drag

Answer 35

Delay the separation of the boundary layer and hence reduce the size of the wake or ‘recirculation bubble’
Streamlined shapes are best for this
Larger wake increases drag

Question 36

What is the Reynolds number at which supercritical flow occurs

Answer 36

> 200,000

Question 37

High Re inertial world

Answer 37

Objects slowed by frictional resistance of water or the effects of pressure drag
A continuous application of force will lead to an increase in velocity
An episodic exertion of force can result in continuous motion

Question 38

Low Re viscous world

Answer 38

Persistent motion require the continuous action of a force
If the force ceases, then motion stops almost instantaneously

Question 39

How do bacteria get around (prokaryotes)

Answer 39

Rotation a rigidly helical flagellum by a wheel and axle