Head Loss Calculations: The total friction loss Hs Consist of: Hs
Hs1 + Hs2
=
Where:
Hs1 Hs2
…………………………………………………….…… (1) : Friction loss Inside pipes : Friction loss inside fittings
Linear friction loss equation: Hs =
J . L …………………………………… ……………………………………... .... (2)
J = l . V² / ( 2 g D ) ………..…………………………………………………………….. (3) Where:
J L l V g D
: linear loss factor : length Of the pipe (m.) : friction loss factor (COLBROOK-WHITE formula) : velocity of water (m/s) : gravity acceleration (9.81 m/s²) : pipe inside diameter (m.)
COLBROOK WHITE formula:……………………………………………………………….. ( 4 ) 1 sqr(l)
= - 2 x log [
Where:
K D RE
k 3.7 x D
+
2.51 Re x sqr( l )
: pipe inside Surface roughness (m.) : pipe inside diameter (m.) : REYNOLD’S no. is given as follows: (1/1)
RE = V x D / n …………………………………………………………………………. ( 5 ) Where:
V = Q/A
n V D
: water viscosity= ( n = 1E-06 : velocity of water (m/s) : pipe inside diameter (m.)
m2/s)
………………………………………...………………………………………. ( 6 )
Where:
Q A
Data for the first pipe :
: flow rate (m³/s) : cross section are of the pipe (m²) 4" GI 114.3 mm 6.02 mm
D = K =
0.1023 m 0.0001 m
Pipe type & size 4" Out side diameter (mm) Wall thickness (mm) : pipe inside diameter (m.) : pipe inside Surface roughness (m.)
)
Project : AGRICULTURE BANK AL EHSAA
Flow :
Page ( 2 )
Q = 340.0 GPM = 21.42 l/s = 0.02142 2 A = px D /4 =
V = Q/A = Re = V x D / n = 1 sqr(l)
m³/sec
3.14 x 0.102 ² / 4 = 0.00821 m²
2.608 m/s 2.608 x 0.1023 / 0.000001 = 266700.48 0.0001 3.7 x 0.102
= - 2 log [
+
2.51 x sqr( l ) 266700.5
]
By solving above equation : l=
0.02061 0.02061 x 2.6081 x 2.608 2 x 9.81 x 0.1023
J = l . V² / ( 2 g D ) = Loss m per 100 m = J x 100 =
0.06988 x 100 m = 6.988
= 0.06988 m/m m / 100m
Pipe length L = 1.0 m dh(1) Liner loss = J x L = 0.06988 x 1.0 = 0.07 m Local losses equation is given as follows: HS2
=
SUM ZE . V ² / ( 2 . G ) …..…………………………………………………….. (7) : Gravity acceleration (9.81 m/s²) : Velocity of water (m/s) : Sum of local loss factors
Where:
G V SUM ZE
SUM ZE =
gate valve Flexible Globe valve check valve elbow ( 45 leg.) elbow ( 90 leg.) tee reducer Strainer discharge outlet Total local factors
HS2
SUM ZE . V ² / ( 2 . g )
=
HS(2) = SUM ZE.x V² / ( 2 g ) =
1 0 0 1 0 1 1 0 1 0
5.4 x
x x x x x x x x x x
0.2 0.2 8 2 0.2 0.3 0.9 0.5 2 1 =
= = = = = = = = = =
2.6081 X 2.6081 2 x 9.81
0.2 0 0 2 0 0.3 0.9 0 2 0 5.40
= 1.8721 m
DH Total loss = HS1 + HS2 = 0.07 + 1.872 = 1.942 m Total heal (DH+GH) / pipe
= Static head + Friction losses ………………………. ( 8 ) = 0.0 + 1.942 = 1.942 m
Project : AGRICULTURE BANK AL EHSAA
Data for the second pipe :
D = K = Flow :
Page ( 3 )
4" GI 114.3 mm 6.02 mm
Pipe type & size 4" Out side diameter (mm) Wall thickness (mm)
2.608 m/s 2.608 x 0.1023 / 0.000001 = 266700.48 0.0001 3.7 x 0.102
= - 2 log [
By solving above equation :
l=
+
2.51 x sqr( l ) 266700.5
0.02061
0.02061 x 2.6081 x 2.608 2 x 9.81 x 0.1023
J = l . V² / ( 2 g D ) = Loss m per 100 m = J x 100 =
]
0.06988 x 100 m = 6.988
= 0.06988 m/m m / 100m
Pipe length L = 4.0 m dh(1) Liner loss = J x L = 0.06988 x 4.0 = 0.28 m Local losses equation is given as follows: HS2
=
SUM ZE . V ² / ( 2 . G )
SUM ZE =
gate valve Flexible Globe valve check valve elbow ( 45 leg.) elbow ( 90 leg.) tee reducer Strainer discharge outlet Total local factors
HS2
SUM ZE . V ² / ( 2 . g )
=
HS(2) = SUM ZE.x V² / ( 2 g ) =
0 0 0 0 0 2 0 1 0 0
1.1 x
x x x x x x x x x x
0.2 0.2 8 2 0.2 0.3 0.9 0.5 2 1 =
= = = = = = = = = =
2.6081 X 2.6081 2 x 9.81
0 0 0 0 0 0.6 0 0.5 0 0 1.10
= 0.3814 m
DH Total loss = HS1 + HS2 = 0.28 + 0.381 = 0.661 m Total heal (DH+GH) / pipe
= Static head + Friction losses = 0.0 + 0.661 = 0.661 m
Total Head for pipe 1 & 2 = 1.942 + 0.661 = 2.603 m Other pipes are calculated same as above, All data and results are arranged in the following table :
