Fluids- Laminar and Turbulent Flow Flashcards
Laminar
Smooth streamlines and highly ordered motion
Turbulent
Velocity fluctuations and highly disordered motion
Transitional
The flow fluctuates between laminar and turbulent flows
Are most flows in practice laminar or turbulent?
Turbulent
What affects whether a flow is laminar or turbulent?
Mean velocity of fluid, size of pipe, density of fluid, viscosity of fluid
Equations for Reynolds number
Re=ρVd/μ=Vd/ν Where Vxd are the inertial forces and ν are the viscous forces V is mean velocity d is diameter of pipe μ is dynamic viscosity ν is kinematic viscosity
What does a small or large Reynolds number mean?
Small means viscous forces dominate and flow is laminar. Large means inertial forces dominate and flow is turbulent
What are typical critical Reynolds number for flow between parallel plates, inside a rough-walled pipe, in an extremely smooth pipe?
Parallel plates=1500
Rough-walled pipe=2300
Extremely smooth pipe=40000
What is the equation for Reynolds number for any geometry pipe?
Re=ρVDh/μ
Where Dh is hydraulic diameter
What is hydraulic diameter?
Four times the CSA divided by the wetted perimeter.
Does the wetted perimeter include a free surface?
No
What parameter must be changed or preserved when scaling?
To keep Re the same, adjust velocity or viscosity to replicate the turbulence. Mach number should also be preserved.
What is the no slip condition?
The fluid particles near any solid boundary are held by the wall and do not slip past it. In a viscous fluid, this restricts the motion of fluid particles in the next adjacent layer, and the next, and so on.
What does the velocity profile of a fluid flowing through a cylindrical pipe look like?
Parabola symmetrical either side of centre line to the edges. Maximum velocity in the centre. Average velocity is half maximum for laminar flow.
What are the two regions of flow in a wall/walls?
Outer flow region which is inviscid. Inner flow region called a boundary layer.
What is a boundary layer?
A very thin region of flow near a solid wall where viscous forces and rotationality cannot be ignored.
What forces influence the outer flow region?
Primarily inertial and pressure forces, away from boundaries
What is boundary layer thickness?
Symbol δ
Defined as the distance away from the wall at which the velocity component parallel to the wall is 99% of the fluid speed outside the boundary layer (free stream velocity)
What does a higher free-stream speed, V, mean for the boundary layer?
It is thinner
Formula for boundary Reynolds number
Rex=ρVx/μ=Vx/ν
Where x in Rex is subscript but not otherwise
V is free stream velocity
x is length of plate in flow direction
What is the critical boundary Reynolds number for transition generally taken to be?
5x10^5
How does a boundary layer develop over distance travelled along the surface?
Starts on the surface as laminar and grows upwards like root x curve until critical value of x when transition region begins. Upper limit of boundary layer is wobbly but generally a bit steeper than just before transition region. Then enters turbulent and line is still wobbly but is steeper than in transition. There is an overlap layer, a buffer layer and a viscous sublayer going down to the wall.
Formula for maximum velocity of flow between two plates
umax=(-Y^2/8μ)(dP/dx)
Where Y is the plate separation
Formula for average velocity for flow between two plates
Vavg=Y^2ΔP/12μl
Where Y is plate separation
l is length of flow
ΔP is frictional pressure loss
What is pressure loss in relation to head loss?
Pressure loss=ρg x head loss
Units of head loss
Meters
Formula for velocity at any radial position for laminar flow in a circular pipe
umax(1-r^2/R^2)
Where r is vertical distance from centre line
R is maximum radius
Formula for maximum velocity for laminar flow in a circular pipe
-(R^2/4μ)(dP/dx)
Minus sign is to account for pressure dropping
Formula for head loss for laminar flow in a circular pipe
32μlV/ρgd^2
Where l is distance gone along pipe
d is diameter
μ is dynamic viscosity
What is turbulent flow characterised by?
Disorderly and rapid fluctuations of swirling regions of fluid, called eddies, throughout the flow
What do eddies mean for mixing of flow and transfer of mass, momentum, heat?
They enhance the mixing of the flow meaning much greater transfer of mass, momentum and heat
What does a turbulent flow velocity profile look like?
More squashed parabola than laminar. Much higher velocity gradient at the walls to meet no slip condition.
Wha is the viscous sublayer?
Very thin layer next to wall. Viscous effects are dominant. Velocity profile nearly linear.
What is the buffer layer?
Turbulent effects becoming significant but flow is still dominated by viscous effects
What is overlap (or transition) layer?
Also called inertial sublayer. Turbulent effects are much more significant but still not dominant.
What is outer (or turbulent) layer?
The remaining part of the flow in which turbulent effects dominate over viscous effects.
Formula for shear stress at the wall of turbulent flow
τw=μu/y
Where w is subscript
u is velocity
y is distance distance from wall
Formula for shear velocity for turbulent flow near a wall
u*=rt(τw/ρ)
Where τw is shear stress at wall
Formula for viscous length
ν/u*
What is power-law velocity profile equation for turbulent flow?
u/umax=(1-r/R)^(1/n)
n is often 7
Formula for friction factor for laminar flow
f=64μ/ρVd or 64/Re
What is Darcy equation?
hloss=flV^2/2gd
Where f is friction factor
Works for laminar and turbulent flow
Formula for friction factor for turbulent flow in smooth pipes
f=0.316/(Re^0.25)
Symbol and units for roughness
Normally ε but civil use ks
Units mm
How to use a Moody diagram
Relative roughness is ε/d (both mm). Calculate Re. Follow a line for relative roughness until reach are calculated. Read off left y axis to find friction factor.
What is hydrodynamic entrance region?
The region from the pipe inlet to the point at which the profile is constant. Normally taken to be until wall shear stress reaches within about 2% of fully developed value.
What is hydrodynamic entry length, Lh?
The length of hydrodynamic entrance region
What is hydrodynamically fully developed region?
Where both velocity profile and temperature profile remain unchanged
Typical values of Lh/D for laminar and turbulent flow
- 05Re for laminar
1. 359Re^0.25 (usually about 10) for turbulent
