Gandhinagar Institute of Technology

Subject :- Fluid Mechanics

Prepared By – 130120119126:- Pandya Kartik

Topic :- Turbulent Flow

MECHANICAL ENGINEERING

INTRODUCTION:

Laminar Flow: In this type of flow, fluid particles moves along smooth straight parallel

paths in layers or laminas, with one layer gliding smoothly over an adjacent layer, the paths

of individual fluid particles do not cross those of neighbouring particles.

Turbulent Flow: In turbulent flow, there is an irregular random movement of fluid in

transverse direction to the main flow. This irregular, fluctuating motion can be regarded as

superimposed on the mean motion of the fluid.

Laminar

Transitional

Turbulent

Types of flow depend on the Reynold number , ρVd Re = -------- µ Re < 2000 – flow is laminar

Re > 2000 – flow is turbulent

2000 < Re < 4000 – flow changes from laminar to turbulent.

Magnitude of Turbulence : - It is the degree of turbulence, and measures how strong, violent or intence the turbulence.

- Magnitude of Turbulence = Arithmetic mean of root mean square of turbulent fluctuations

= Or =

t

dtut 0

21

t

dtut 0

21 222

31

wvu

Intensity of turbulence :

- It is the ratio of the magnitude of turbulence to the average flow velocity at a

point in the flow field

- So, Intensity of Turbulence =

222

222

31

wvu

wvu

Expression for co-efficient of friction :Darcy – Weisbach equation

From the experimental measurement on turbulent flow through pipes, it has observed

That the viscous friction associated with fluid are proportional to

(1) Length of pipe (l)

(2) Wetted perimeter (P)

(3) Vn , where V is average velocity and n is index depending on the material

(normally, commertial pipe turbulent flow n=2

f – friction factor

L – length of pipe

D – diameter of pipe

v – velocity of flow

OR

g

pph f

21

gD

lVCh f

f 2

2

Co-efficient of friction in terms of shear stress :

We know, the propelling force = (p1 - p2) Ac ---- (1)

Frictional resistance in terms of shear stress = As Where = shear stress ----(2)

By comparing both equation,

(P1 – P2) = OR

( co-efficient of frictionin terms of shear stress)

0 0

Vf 2

02

vu

dA

uvdA

dA

dFt

Shear stress in turbulent flow

In turbulent flow, fluid particles moves randomly, therefore it is impossible to trace the

Paths of the moving particles and represents it mathematically

u b

u

= mean velocity of particles moving along layer A

= mean velocity of particles moving along layer B The relative velocity of particle along layer B and with respect to layer A

= - since , >

This relative velocity is the cause of shear stress between the two layers

u au b

u a

u au b

Prandtl’s mixing length theory :

Prandtl’s assumed that distance between two layers in the transverse direction

(called mixing length l) such that the lumps of fluid particles from one layer could reach the other

Layer and the particles are mixed with the other layer in such a way that the momentum of the

Particles in the direction of x is same, as shown in below figure :

Total shear

where , (Viscosity)

n = 0 for laminar flow. For highly turbulent flow, .

tv

2

22

dy

duyk

dy

du

dy

du

dy

du

dy

du

dy

du

22 yk

Hydrodynamically Smooth andRough Pipe Boundaries

Hydronamically smooth pipe : The hight of roughness of pipe is less than thickness of

laminar sublayer of flowing fluid.

ɛ < δ′

Hydronamically rough pipe : The hight of roughness of pipe is greater than the

thickness of laminar sublayer of flowing fluid.

ɛ > δ′

From Nikuradse’s experiment

Criteria for roughness:

Hydrodynamically

smooth pipe

Hydrodynamically

rough pipe

Transiton region

region in a pipe

In terms of Reynold number

1. If Re → Smooth boundary

2. If Re ≥100→Rough boundary

3. If 4<Re <100 →boundary is in transition stage.

625.0

25.0

6

4

Velocity Distribution for turbulentflow

Velocity Distribution

in a hydrodynamically

smooth pipe

Velocity Distribution

in a hydrodynamically

Rough Pipes

y

V

ve

log5.25.8*

R

V

ve

log5.275.4*

Velocity Distribution for turbulentflow in terms of average Velocity (V)

Velocity Distribution

in a hydrodynamically

smooth pipe

Velocity Distribution

in a hydrodynamically

Rough Pipes

RV

V

Ve

*5.275.1

*log

R

V

Ve

log5.275.4*

THANK YOU….