This document discusses turbulent flow and provides definitions and equations related to turbulent flow characteristics. It defines laminar and turbulent flow, noting that turbulent flow involves irregular random movement transverse to the main flow. The type of flow depends on the Reynolds number, with laminar flow below 2000 and turbulent flow above. Turbulent flow magnitude and intensity are defined using root mean square equations. Equations are also provided for friction factor in turbulent pipe flow involving length, diameter, velocity. Prandtl's mixing length theory is described for modeling turbulent shear stress. Boundaries can be hydrodynamically smooth or rough depending on roughness height compared to the laminar sublayer thickness. Velocity distributions in smooth and rough pipes are shown using logarithmic equations involving thickness and

1. Gandhinagar Institute of Technology
Subject :- Fluid Mechanics
– 130120119126:- Pandya Kartik
Topic :- Turbulent Flow
MECHANICAL
ENGINEERING

2. 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.

3. Laminar
Transitional
Turbulent

5.  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.

6.  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
dtu
t 0
21
  
t
dtu
t 0
21
      222
3
1
wvu 

7.  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
3
1
wvu
wvu



8. 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

9. f – friction factor
L – length of pipe
D – diameter of pipe
v – velocity of flow
OR
g
pp
hf

21


gD
lVC
h
f
f
2
2


10. 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
V
f 2
0
2

 vu
dA
uvdA
dA
dF
t


 



11. 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

12. ub
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
uaub
ua
uaub

13. 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 :

15. Total shear
where , (Viscosity)
n = 0 for laminar flow.
For highly turbulent flow, .
 tv 
2
22













dy
du
yk
dy
du














dy
du
dy
du













dy
du
dy
du

22
yk 

16. Hydrodynamically Smooth and
Rough 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′

17. 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

18. Velocity Distribution for turbulent
flow
 Velocity Distribution
in a hydrodynamically
smooth pipe
 Velocity Distribution
in a hydrodynamically
Rough Pipes








y
V
v
e
log5.25.8
*








R
V
v
e
log5.275.4
*

19. Velocity Distribution for turbulent
flow in terms of average Velocity (V)
 Velocity Distribution
in a hydrodynamically
smooth pipe
 Velocity Distribution
in a hydrodynamically
Rough Pipes








RV
V
V
e
*
5.275.1
*
log








R
V
V
e
log5.275.4
*

20. THANK YOU….