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University Year 1 > Fluids- Laminar and Turbulent Flow > Flashcards

Fluids- Laminar and Turbulent Flow Flashcards

1
Q

Laminar

A

Smooth streamlines and highly ordered motion

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2
Q

Turbulent

A

Velocity fluctuations and highly disordered motion

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3
Q

Transitional

A

The flow fluctuates between laminar and turbulent flows

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4
Q

Are most flows in practice laminar or turbulent?

A

Turbulent

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5
Q

What affects whether a flow is laminar or turbulent?

A

Mean velocity of fluid, size of pipe, density of fluid, viscosity of fluid

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6
Q

Equations for Reynolds number

A 
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
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7
Q

What does a small or large Reynolds number mean?

A

Small means viscous forces dominate and flow is laminar. Large means inertial forces dominate and flow is turbulent

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8
Q

What are typical critical Reynolds number for flow between parallel plates, inside a rough-walled pipe, in an extremely smooth pipe?

A

Parallel plates=1500
Rough-walled pipe=2300
Extremely smooth pipe=40000

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9
Q

What is the equation for Reynolds number for any geometry pipe?

A

Re=ρVDh/μ

Where Dh is hydraulic diameter

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10
Q

What is hydraulic diameter?

A

Four times the CSA divided by the wetted perimeter.

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11
Q

Does the wetted perimeter include a free surface?

A

No

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12
Q

What parameter must be changed or preserved when scaling?

A

To keep Re the same, adjust velocity or viscosity to replicate the turbulence. Mach number should also be preserved.

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13
Q

What is the no slip condition?

A

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.

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14
Q

What does the velocity profile of a fluid flowing through a cylindrical pipe look like?

A

Parabola symmetrical either side of centre line to the edges. Maximum velocity in the centre. Average velocity is half maximum for laminar flow.

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15
Q

What are the two regions of flow in a wall/walls?

A

Outer flow region which is inviscid. Inner flow region called a boundary layer.

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16
Q

What is a boundary layer?

A

A very thin region of flow near a solid wall where viscous forces and rotationality cannot be ignored.

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17
Q

What forces influence the outer flow region?

A

Primarily inertial and pressure forces, away from boundaries

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18
Q

What is boundary layer thickness?

A

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)

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19
Q

What does a higher free-stream speed, V, mean for the boundary layer?

A

It is thinner

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20
Q

Formula for boundary Reynolds number

A

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

21
Q

What is the critical boundary Reynolds number for transition generally taken to be?

A

5x10^5

22
Q

How does a boundary layer develop over distance travelled along the surface?

A

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.

23
Q

Formula for maximum velocity of flow between two plates

A

umax=(-Y^2/8μ)(dP/dx)

Where Y is the plate separation

24
Q

Formula for average velocity for flow between two plates

A

Vavg=Y^2ΔP/12μl
Where Y is plate separation
l is length of flow
ΔP is frictional pressure loss

25
Q

What is pressure loss in relation to head loss?

A

Pressure loss=ρg x head loss

26
Q

Units of head loss

A

Meters

27
Q

Formula for velocity at any radial position for laminar flow in a circular pipe

A

umax(1-r^2/R^2)
Where r is vertical distance from centre line
R is maximum radius

28
Q

Formula for maximum velocity for laminar flow in a circular pipe

A

-(R^2/4μ)(dP/dx)

Minus sign is to account for pressure dropping

29
Q

Formula for head loss for laminar flow in a circular pipe

A

32μlV/ρgd^2
Where l is distance gone along pipe
d is diameter
μ is dynamic viscosity

30
Q

What is turbulent flow characterised by?

A

Disorderly and rapid fluctuations of swirling regions of fluid, called eddies, throughout the flow

31
Q

What do eddies mean for mixing of flow and transfer of mass, momentum, heat?

A

They enhance the mixing of the flow meaning much greater transfer of mass, momentum and heat

32
Q

What does a turbulent flow velocity profile look like?

A

More squashed parabola than laminar. Much higher velocity gradient at the walls to meet no slip condition.

33
Q

Wha is the viscous sublayer?

A

Very thin layer next to wall. Viscous effects are dominant. Velocity profile nearly linear.

34
Q

What is the buffer layer?

A

Turbulent effects becoming significant but flow is still dominated by viscous effects

35
Q

What is overlap (or transition) layer?

A

Also called inertial sublayer. Turbulent effects are much more significant but still not dominant.

36
Q

What is outer (or turbulent) layer?

A

The remaining part of the flow in which turbulent effects dominate over viscous effects.

37
Q

Formula for shear stress at the wall of turbulent flow

A

τw=μu/y
Where w is subscript
u is velocity
y is distance distance from wall

38
Q

Formula for shear velocity for turbulent flow near a wall

A

u*=rt(τw/ρ)

Where τw is shear stress at wall

39
Q

Formula for viscous length

A

ν/u*

40
Q

What is power-law velocity profile equation for turbulent flow?

A

u/umax=(1-r/R)^(1/n)

n is often 7

41
Q

Formula for friction factor for laminar flow

A

f=64μ/ρVd or 64/Re

42
Q

What is Darcy equation?

A

hloss=flV^2/2gd
Where f is friction factor
Works for laminar and turbulent flow

43
Q

Formula for friction factor for turbulent flow in smooth pipes

A

f=0.316/(Re^0.25)

44
Q

Symbol and units for roughness

A

Normally ε but civil use ks

Units mm

45
Q

How to use a Moody diagram

A

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.

46
Q

What is hydrodynamic entrance region?

A

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.

47
Q

What is hydrodynamic entry length, Lh?

A

The length of hydrodynamic entrance region

48
Q

What is hydrodynamically fully developed region?

A

Where both velocity profile and temperature profile remain unchanged

49
Q

Typical values of Lh/D for laminar and turbulent flow

A
  1. 05Re for laminar

1. 359Re^0.25 (usually about 10) for turbulent

University Year 1 (44 decks)

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