Fluids- Laminar and Turbulent Flow

Question 1

Laminar

Answer 1

Smooth streamlines and highly ordered motion

Question 2

Turbulent

Answer 2

Velocity fluctuations and highly disordered motion

Question 3

Transitional

Answer 3

The flow fluctuates between laminar and turbulent flows

Question 4

Are most flows in practice laminar or turbulent?

Answer 4

Turbulent

Question 5

What affects whether a flow is laminar or turbulent?

Answer 5

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

Question 6

Equations for Reynolds number

Answer 6

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

Question 7

What does a small or large Reynolds number mean?

Answer 7

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

Question 8

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

Answer 8

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

Question 9

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

Answer 9

Re=ρVDh/μ

Where Dh is hydraulic diameter

Question 10

What is hydraulic diameter?

Answer 10

Four times the CSA divided by the wetted perimeter.

Question 11

Does the wetted perimeter include a free surface?

Answer 11

No

Question 12

What parameter must be changed or preserved when scaling?

Answer 12

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

Question 13

What is the no slip condition?

Answer 13

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.

Question 14

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

Answer 14

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

Question 15

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

Answer 15

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

Question 16

What is a boundary layer?

Answer 16

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

Question 17

What forces influence the outer flow region?

Answer 17

Primarily inertial and pressure forces, away from boundaries

Question 18

What is boundary layer thickness?

Answer 18

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)

Question 19

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

Answer 19

It is thinner

Question 20

Formula for boundary Reynolds number

Answer 20

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

Question 21

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

Answer 21

5x10^5

Question 22

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

Answer 22

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.

Question 23

Formula for maximum velocity of flow between two plates

Answer 23

umax=(-Y^2/8μ)(dP/dx)

Where Y is the plate separation

Question 24

Formula for average velocity for flow between two plates

Answer 24

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

Question 25

What is pressure loss in relation to head loss?

Answer 25

Pressure loss=ρg x head loss

Question 26

Units of head loss

Answer 26

Meters

Question 27

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

Answer 27

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

Question 28

Formula for maximum velocity for laminar flow in a circular pipe

Answer 28

-(R^2/4μ)(dP/dx) | Minus sign is to account for pressure dropping

Question 29

Formula for head loss for laminar flow in a circular pipe

Answer 29

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

Question 30

What is turbulent flow characterised by?

Answer 30

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

Question 31

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

Answer 31

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

Question 32

What does a turbulent flow velocity profile look like?

Answer 32

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

Question 33

Wha is the viscous sublayer?

Answer 33

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

Question 34

What is the buffer layer?

Answer 34

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

Question 35

What is overlap (or transition) layer?

Answer 35

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

Question 36

What is outer (or turbulent) layer?

Answer 36

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

Question 37

Formula for shear stress at the wall of turbulent flow

Answer 37

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

Question 38

Formula for shear velocity for turbulent flow near a wall

Answer 38

u*=rt(τw/ρ) | Where τw is shear stress at wall

Question 39

Formula for viscous length

Answer 39

ν/u*

Question 40

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

Answer 40

u/umax=(1-r/R)^(1/n) | n is often 7

Question 41

Formula for friction factor for laminar flow

Answer 41

f=64μ/ρVd or 64/Re

Question 42

What is Darcy equation?

Answer 42

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

Question 43

Formula for friction factor for turbulent flow in smooth pipes

Answer 43

f=0.316/(Re^0.25)

Question 44

Symbol and units for roughness

Answer 44

Normally ε but civil use ks | Units mm

Question 45

How to use a Moody diagram

Answer 45

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.

Question 46

What is hydrodynamic entrance region?

Answer 46

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.

Question 47

What is hydrodynamic entry length, Lh?

Answer 47

The length of hydrodynamic entrance region

Question 48

What is hydrodynamically fully developed region?

Answer 48

Where both velocity profile and temperature profile remain unchanged

Question 49

Typical values of Lh/D for laminar and turbulent flow

Answer 49

0. 05Re for laminar | 1. 359Re^0.25 (usually about 10) for turbulent