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Darcy -Weisbach -Weisbach equation use to calculate pressure drop/head drop/head loss through pipe. Head Loss= f Loss= f (L/D)( V2/2g) Head Loss= p1-p2/ρ p1-p2/ ρg Δp= Δp= f (L/D)( ρV2/2) •
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Where f Where f =Friction =Friction factor factor
L= length of pipe D= dia. Of pipe V= Velocity of liquid ρ= density of liquid
Friction Factor and Reynolds no •
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Friction factor ( f ) is decided by flow of fluid. Reynolds no decide type of flow. 1. Re<= 2100 then f =64/Re 2. 21004000 use Colebrook-White Equation
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We can use Moody’s chart also to estimate friction factor.
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For that we need value of pipe roughness.
Churchill Equation
ε: Pipe Roughness
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Colebrook-White Equation
Also we can use following equations to estimate approximate value of friction factor
Moody chart
Pipe roughness Material Drawn Tubing, Glass, Plastic
Roughness (mm) 0.0015-0.01
Drawn Brass, Copper, Stainless Steel (New)
>0.0015-0.01
Flexible Rubber Tubing - Smooth
0.006-0.07
Flexible Rubber Tubing - Wire Reinforced
0.3-4
Stainless Steel Wrought Iron (New) Carbon Steel (New)
0.03 0.045 0.02-0.05
Carbon Steel (Slightly Corroded)
0.05-0.15
Carbon Steel (Moderately Corroded)
0.15-1
Carbon Steel (Badly Corroded) Carbon Steel (Cement-lined) Asphalted Cast Iron Cast Iron (new) Cast Iron (old, sandblasted)
1-3 1.5 0.1-1 0.25 1
Sheet Metal Ducts (with smooth joints)
0.02-0.1
Galvanized Iron Wood Stave Wood Stave, used Smooth Cement Concrete – Very Smooth
0.025-0.15 0.18-0.91 0.25-1 0.5 0.025-0.2
Concrete – Fine (Floated, Brushed)
0.2-0.8
Concrete – Rough, Form Marks Riveted Steel Water Mains with Tuberculations Brickwork Mature Foul Sewers
0.8-3 0.91-9.1 1.2 3
Methods to Calculate head loss/pressure loss from fittings •
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3K method 2K method Equivalent length method
Chemsys Process Engineering P. Ltd Fitting
3K Method
90° Elbow, Threaded
90° Elbow, Flanged or Welded
90° Elbow, Mitered
45° Elbow, Threaded
Head Loss= K( V2/2g)
45° Elbow, Mitered
180° Bend
Tee Through-branch as an Elbow
Tee Run-through
Angle valve Globe valve Plug valve Gate valve Ball valve Diaphragm Swing check valve
K1
K∞
Kd (in0.3)
Kd (mm0.3)
800
0.14
4
10.6
Long Radius (R/D = 1.5)
800
0.071
4.2
11.1
Standard Radius (R/D = 1)
800
0.091
4
10.6
Long Radius (R/D = 2)
800
0.056
3.9
10.3
Long Radius (R/D = 4)
800
0.066
3.9
10.3
Long Radius (R/D = 6)
800
0.075
4.2
11.1
1 weld 90° 2 welds 45° 3 welds 30° Standard Radius (R/D = 1)
1000 800 800
0.27 0.068 0.035
4 4.1 4.2
10.6 10.8 11.1
500
0.071
4.2
11.1
Types Standard Radius (R/D = 1)
Long Radius (R/D = 1.5)
500
0.052
4
10.6
1 weld 45° 2 welds 22.5° threaded, close-return (R/D = 1) flanged (R/D = 1)
500 500
0.086 0.052
4 4
10.6 10.6
1000
0.23
4
10.6
1000
0.12
4
10.6
all types (R/D = 1.5)
1000
0.1
4
10.6
threaded (r/D = 1)
500
0.274
4
10.6
threaded (r/D = 1.5)
800
0.14
4
10.6
flanged (r/D = 1) stub-in branch
800 1000
0.28 0.34
4 4
10.6 10.6
threaded (r/D = 1)
200
0.091
4
10.6
flanged (r/D = 1) stub-in branch
150 100
0.05 0
4 0
10.6 0
45°, full line size, β = 1
950
0.25
4
10.6
90° full line size, β = 1
1000
0.69
4
10.6
standard, β = 1 branch flow straight through three-way (flow through) standard, β = 1 standard, β = 1 dam type Vmin = 35[ρ (lbm/ft3)]−1/2 Vmin = 40[
1500 500 300
1.7 0.41 0.084
3.6 4 3.9
9.5 10.6 10.3
300
0.14
4
10.6
300 300 1000
0.037 0.017 0.69
3.9 3.5 4.9
10.3 9.2 12.9
1500
0.46
4
10.6
2K Method
Chemsys Process Engineering P. Ltd Fitting
90° Elbow Curved
90° Elbow Mitered R/D 1.5
Type
K1
K∞
Threaded, SR (R/D = 1)
800
0.4
Flanged/Welded, SR (R/D = 1)
800
0.25
All Types, LR (R/D = 1.5)
800
0.2
1 Weld (90° Angle) 2 Weld (45° Angle) 3 Weld (30° Angle) 4 Weld (22.5° Angle) 5 Weld (18° Angle)
1000 800 800 800 800
1.15 0.35 0.3 0.27 0.25
All Types, SR (R/D = 1)
500
0.2
All Types LR (R/D = 1.5)
500
0.15
1 Weld (45° Angle) 2 Welds (45° Angle)
500 500
0.25 0.15
Screwed, SR (R/D = 1)
1000
0.6
Flanged/Welded, SR (R/D = 1)
1000
0.35
All Types, LR (R/D = 1.5)
1000
0.3
Screwed, SR (R/D = 1)
500
0.7
Screwed, LR Flanged/Welded, SR (R/D = 1) Stub-in-tpye Branch Screwed Flanged/Welded Stub-in-type Branch
800
0.4
800
0.8
1000 200 150 100
1 0.1 0.05 0
Full Line Size, Beta = 1
300
0.1
Reduced Trim, Beta = 0.9
500
0.15
Reduced Trim, Beta = 0.8
1000
0.25
Globe, Standard Globe, Angle
1500 1000
4 2
Diaphragm, dam type
1000
2
Butterfly Lift
800 2000
0.25 10
45° Elbow
45° Elbow Mitered
180°
Tee, used as elbow
D:Internal diameter of pipe (Inches) K :Resistance Coefficient K 1:Resistance Coefficient for fitting at Re=1 K ∞:Resistance Coefficient for large fitting at Re=∞ Re: Reynolds number •
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Tee, Run Through
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Valves, Gate/Ball/Plug
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Valves
Equivalent length Method Fitting
Types
(L/D)eq
Standard Radius (R/D = 1)
30
Long Radius (R/D = 1.5)
16
Standard Radius (R/D = 1)
20
Long Radius (R/D = 2)
17
Long Radius (R/D = 4)
14
Long Radius (R/D = 6)
12
1 weld (90°) 2 welds (45°) 3 welds (30°)
60 15 8
Standard Radius (R/D = 1)
16
90° Elbow Curved, Threaded
1. Calculate Equivalent length with reference to given chart. 2. Add this length to straight length and calculate head loss/pressure drop.
90° Elbow Curved, Flanged/Welded
90° Elbow Mitered
45° Elbow Curved. Threaded Long Radius (R/D = 1.5) 45° Elbow Mitered
180° Bend
Tee Through-branch as an Elbow
Tee Run-through
1 weld 45° 2 welds 22.5°
15 6
threaded, close-return (R/D = 1)
50
flanged (R/D = 1) all types (R/D = 1.5) threaded (r/D = 1) threaded (r/D = 1.5) flanged (r/D = 1) stub-in branch threaded (r/D = 1) flanged (r/D = 1) stub-in branch
60 20 20
45°, full line size, β = 1
55
90° full line size, β = 1
150
standard, β = 1 branch flow straight through
340 90 18
three-way (flow through)
30
Gate valve Ball valve Diaphragm
standard, β = 1 standard, β = 1 dam type
8 3
Swing check valve
Vmin = 35[ρ (lbm/ft3)]−1/2
100
Lift check valve
Vmin = 40[ρ (lbm/ft3)]−1/2
600
Angle valve Globe valve Plug valve
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Example 1. Oil, with ρ= 900kg/m3 and kinematic coefficient of viscosity γ= 0.00001m2/s, flows at Q= 0.2m3/s through 500 m of 200-mm diameter cast-iron pipe. Determine (a) the head loss and (b) the pressure drop if the pipe slopes down at 10 in the flow direction.
Z1
Z1 10
L*Sin10 L Z2
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Example 2. Calculation of Pressure Loss: if fittings are present.(3K)
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Pipe Size: DN100 (4")
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Pipe Diameter (Nominal): 4"
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Pipe Internal Diameter:102.3 mm
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Pipe Length: 50 m Fittings: 3 x 90° long radius (R/D = 2)
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flanged elbows Fluid Velocity: 3 m/s
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Fluid Density: 1000 kg/m 3
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Reynolds Number:306,900
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Friction Factor: 0.018
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Gravitational Acceleration:9.81 m/s
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