Real Flow Through Pipes
In real flow through pipes the friction must be considered
Main Parameters:
(in any stream line. )
1- Energy difference.
2- Flow rate ( rate of discharge)
3- Pipe Configuration.
( diameter, length and material of pipe.)
Can be obtained from Bernoulli’s and continuity
equations.
1
Can be obtained from Bernoulli’s and continuity
equations.
E1  E 2  h loss12
hL
Q  V1A1  V2 A 2
hLoss : is due to friction or
the formation of vortex.
A
z1
2
z2
Losses in Pipes
Major Losses
Losses due to friction
Laminar Flow
Turbulent Flow
Minor Losses
Secondary Losses
Change in Sections
Fittings: Bends, Elbows and Valves…etc.
3
Flow of Real Fluid Through Pipes or Ducts.
No slip boundary conditions
y(r)
u = 0.99 Uo
δ : Boundary layer thickness
δ
Flat plate
U L
 Re 
ν
u
Pipe
4
U D
 Re 
ν
u
Laminar
Turbulent
time
Losses in Pipe
y(r)
Due to friction
Laminar Flow
Turbulent Flow
hLoss : In laminar flow is due to friction between the
Fluid layers.
hLoss : In turbulent flow is due to friction between the
Fluid and the wall boundary or the formation of vortex
5due to the change of pipe cross-section.
u
Friction Losses due to Laminar Flow
du
τμ
dy
Fluid layer
Fluid layer
dy
u
du
o
PA  (P  dP) A  τ o πDdx
 dPA  τ o πDdx
πD
 dP
 τ o πDdx
4
2
6
Laminar
u+du
P
P+dP
dx
  dP  D
τo  

 dx  4

P1  P2  D P1  P2  D
τo 

dx 4
4L
ΔP f
V
 ρ
L D
2
2
7
Where:
Darcy equation
f : is friction coefficient
Friction Loss Head of Laminar Flow
32 μuL 64 L V
hf 

γd
Re d 2 g
2
Friction Loss Head of Turbulent Flow
2
2
LV
V
hf  f
k
d 2g
2g
8
9
Example-1
10
Secondary Losses in
Pipes
11
Secondary Losses in Pipes
1- Losses in Pipe Entrance:
Fluid
2
V
h in  0.5
2g
12
H
2- Losses in Sudden Enlargement:
Po
1
V2
V1
P2
P1
13
2
Eddies
2- Losses in Sudden Enlargement:
Po
1
2
V2
V1
P2
P1
Eddies
P1A1 - Po (A1–A2) – P2A2 = ρA2V2 (V2-V1)
Experimentally
14
P1= Po
(P1-P2)A2 = ρA2V2 (V2-V1)
(P1-P2) = ρV2 (V2-V1)
P2  P1  V22 V1V2




ρg
g
(1)
g
Applying Energy equation between section 1 and section 2
2
1
2
2
P1 V
P2 V
 


 h losses
ρg 2 g ρg 2 g
From equations 1 and 2

V1  V2 

2
 h losses
15
2g
(2)
3- Losses in Sudden Contraction:
1
2
V1
V2
Eddies
Vena
Contracta
Due to the Vena Contracta
Ac=CcA

Vc  V 

2
16
 h losses
2g
AcVc = AV
 h losses
A


V  V 
Ac



2g
2
2
 h losses
A2
A1
17
 1
 V2
V2
 
 1
K
2g
 Cc  2 g
0.1
0.3
0.5
0.7
1.0
Cc
0.61
0.632
0.673
0.73
1.0
K
0.41
0.34
0.24
0.14
0.0
3- Losses in Pipe Fitting : (bends and valves)
 h losses
2
V
K
2g
Eddies
Where : K is the fitting losses coefficient.
18
Fitting
Losses Coefficient
Gate Valve ( 75% open)
Globe valve
Spherical plug valve
Pump foot valve
Return valve
90o elbow
45o elbow
Large radius 90o bend
Tee junction
Sharp pipe entry
Sharp
pipe exit
19
0.25 – 2.5
10
0.1
1.5
2.2
0.9
0.4
0.6
1.8
0.5
0.5