Reynold's number Flashcards
What is the difference between laminar flow and turbulent flow
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
What are the 3 different flow regimes
- laminar
- transitional
- turbulent
what forces makes flow laminar what forces makes flow turbulent
laminar flow: viscous forces
turbulent flow:inertial forces
What is a viscous force
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)
What is the inertial force
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
At low velocity what type of flow do we have
laminar flow, streamline past object
At high velocity what type of flow do we have
turbulent flow, greater the density , higher chance of turbulence
What are the factors that drive turbulence
- length of object
- density of fluid
- velocity of fluid
Why does turbulence increase when the characteristic length is longer
-longer characteristic length, the greater the surface area the fluid has to flow across the greater time for turbulence to build up
What is the factor that will drive laminar flow
viscosity and the fluids ability to stick together
What is the formula for Reynold’s number
R.N = F_i / F_v = p * S * v^2 / ( u * S * v/l)
= p * v * l / u = v * l / (kinematic viscosity )
What is kinematic viscosity
viscosity/ density
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
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
What does a low Re imply
viscous forces are dominant
laminar flow
What does a high Re imply
inertial forces are dominant
turbulent flow
What is a vortex
region where fluid flow moves around a central axis
Describe rotation in a solid body
object ROTATES around the axis. The tangential velocity is proportional to the radius from the center. velocity proportional to radius v/r = constant
Describe the rotation in a spinning fluid
- has a rotational core (v/r = constant) and an irrotational periphery (v* r = constant)
explain what happens in an irrotational periphery of a vortex
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
Describe why there is a transition from rotational core to irrotational periphery in the fluid
- 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)
What features do animals at low Re have
hairy appendages
What happens to the bristles at low Re
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
What happens to bristles at low Re number and then you INCREASE the velocity
the semi -stagnant fluid layer between hairs will be disrupted such that water flows past the bristles
What is leakiness
volume per unit time of fluid passing between hairs / volume per unit time of fluid passing WITHOUT hairs
What factor affects the leakiness of hair appendages
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
Explain how a water boatman functions
- 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
Why are some insects capable of flight despite having no wings but hair appendages instead
operate at low Re number and their wing appendages have fine meshes such that their wings act as paddle ( not leaky)
How do silk mouths change their antennas into sieves to detect the phermones
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 )
What is scallop theorem
At high Re drag is proportional to V^2* time.
At low Re drag is proportional to v*t
What is the consequence of the scallop theorem for organisms living in low Re
cannot have reciprocal motion
- can take on corkscrew motion
Explain the actions of a rotifer
- 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
