Reynold's number

Question 1

What is the difference between laminar flow and turbulent flow

Answer 1

Laminar: 
-reversible and reproducible
-no mixing 
-ordered flow 
-even velocity gradient (velocity changes uniformly)
Turbulent:
-mixing
-disordered flow
-irreproducible and non-reversible 
-vorticity 
-velocity gradients are unsteady

Question 2

What are the 3 different flow regimes

Answer 2

• laminar
• transitional
• turbulent

Question 3

what forces makes flow laminar what forces makes flow turbulent

Answer 3

laminar flow: viscous forces

turbulent flow:inertial forces

Question 4

What is a viscous force

Answer 4

fluid slides over the surface of the plate and exerts a force due to
- viscosity
-shearing
-velocity gradient associated with it
uSv/l ( S = area od plate, u = viscosity , v velocity of fluid , l length of plate)

Question 5

What is the inertial force

Answer 5

fluid collides with the plate area 
force is exerted due to 
-density
- velocity of fluid
- surface area of plate 
F_i = p *S * v^2

Question 6

At low velocity what type of flow do we have

Answer 6

laminar flow, streamline past object

Question 7

At high velocity what type of flow do we have

Answer 7

turbulent flow, greater the density , higher chance of turbulence

Question 8

What are the factors that drive turbulence

Answer 8

1. length of object
2. density of fluid
3. velocity of fluid

Question 9

Why does turbulence increase when the characteristic length is longer

Answer 9

-longer characteristic length, the greater the surface area the fluid has to flow across the greater time for turbulence to build up

Question 10

What is the factor that will drive laminar flow

Answer 10

viscosity and the fluids ability to stick together

Question 11

What is the formula for Reynold’s number

Answer 11

R.N = F_i / F_v = p * S * v^2 / ( u * S * v/l)

= p * v * l / u = v * l / (kinematic viscosity )

Question 12

What is kinematic viscosity

Answer 12

viscosity/ density

Question 13

What happens to Re when you compare between air and water ( given a fixed speed and shape) ? What is the Re difference between air and water in real life

Answer 13

because Re = p* v* l/ u because water is denser it will have a greater Re than air. The Re in real life between air and water is roughly the same because the velocity of objects in water is slower

Question 14

What does a low Re imply

Answer 14

viscous forces are dominant

laminar flow

Question 15

What does a high Re imply

Answer 15

inertial forces are dominant

turbulent flow

Question 16

What is a vortex

Answer 16

region where fluid flow moves around a central axis

Question 17

Describe rotation in a solid body

Answer 17

object ROTATES around the axis. The tangential velocity is proportional to the radius from the center. velocity proportional to radius v/r = constant

Question 18

Describe the rotation in a spinning fluid

Answer 18

• has a rotational core (v/r = constant) and an irrotational periphery (v* r = constant)

Question 19

explain what happens in an irrotational periphery of a vortex

Answer 19

the object translates around the periphery. angular momentum needs to be conserved this means that mvr = constant. an increase in r decreases v. this is due to fluids being able to shear past each other

Question 20

Describe why there is a transition from rotational core to irrotational periphery in the fluid

Answer 20

• you need energy to shear fluid past one another so as you go closer to the core the energy needed to shear the fluid becomes greater until we no longer have that energy and so viscous forces start to dominate
• if no energy is added, viscous shearing will cause the vortex to grind to a halt
• at low Re viscous forces dominate ( and can have large rotational cores)

Question 21

What features do animals at low Re have

Answer 21

hairy appendages

Question 22

What happens to the bristles at low Re

Answer 22

They have a thick layer of semi stagnant fluid that adheres to the hairs causing it to act like a paddle
- fluid does not see the gaps between the paddle

Question 23

What happens to bristles at low Re number and then you INCREASE the velocity

Answer 23

the semi -stagnant fluid layer between hairs will be disrupted such that water flows past the bristles

Question 24

What is leakiness

Answer 24

volume per unit time of fluid passing between hairs / volume per unit time of fluid passing WITHOUT hairs

Question 25

What factor affects the leakiness of hair appendages

Answer 25

The Reynold’s number and the gap width / hair diameter

• the finer the mesh the lower the leakiness ( more paddle like0
• the higher the Re the more leaky

Question 26

Explain how a water boatman functions

Answer 26

• operates at intermediate Re ( inertial forces matter)
• at high Re, the drag experienced by the paddle is proportionate to v^2
• thrust is greater during the backward stroke then the slow recovery stroke
• flattening of the hairs during the recovery reduces the area and drag during the recovery stroke

Question 27

Why are some insects capable of flight despite having no wings but hair appendages instead

Answer 27

operate at low Re number and their wing appendages have fine meshes such that their wings act as paddle ( not leaky)

Question 28

How do silk mouths change their antennas into sieves to detect the phermones

Answer 28

It increases the speed of the appendages to increase the Re number, they also sample a greater cross sectional area ( because of the higher speed and the principle of continuity )

Question 29

What is scallop theorem

Answer 29

At high Re drag is proportional to V^2* time.

At low Re drag is proportional to v*t

Question 30

What is the consequence of the scallop theorem for organisms living in low Re

Answer 30

cannot have reciprocal motion

- can take on corkscrew motion

Question 31

Explain the actions of a rotifer

Answer 31

• operates at low Re
• able to create rotational core vortices that can bring fluids from afar closer
• because fluid is viscous ,sections of water are pulled together