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```					                     Frictional losses in piping system
2
V1 p1                       p2 V22
Extended Bernoulli' s equation,           z1  hA  hE  hL           z2
 2g                              2g
p1  p2 p
       hL  frictional head loss
P1                                           
P2    R: radius, D: diameter
L: pipe length
Consider a laminar, fully developed circular pipe flow      w: wall shear stress

[ p  ( p  dp)](R 2 )   w (2R)dx,
w       Pressure force balances frictional force
2 w
p                    P+dp    dp          dx, integrate from 1 to 2
R
p       p1  p2         4 F I F IF I
L     L
V          2
Darcy’s Equation:



 hL  w
HK HK2g J
GK
g D
 f
H
D
F IFV I where f is defined as frictional factor characterizing
f       2
w         G
HK 2 Jpressure loss due to pipe wall shear stress
4 H K
When the pipe flow is laminar, it can be shown (not here) that
64                              VD
f       , by recognizing that Re        , as Reynolds number
VD                               
64
Therefore, f       , frictional factor is a function of the Reynolds number
Re
Similarly, for a turbulent flow, f = function of Reynolds number also
f  F(Re). Another parameter that influences the friction is the surface

roughness as relativeto the pipe diameter       .
D
F  I: Pipe frictional factor is a function of pipe Reynolds
Such that f  F Re,
H DK
number and the relative roughness of pipe.
This relation is sketched in the Moody diagram as shown in the following page.
The diagram shows f as a function of the Reynolds number (Re), with a series of
F I.

parametric curves related to the relative roughness
HK
D

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 views: 1 posted: 9/17/2012 language: English pages: 3