• Darcy -Weisbach equation use to calculate pressure drop/head loss through pipe.

• Head Loss= f (L/D)(V2/2g)• Head Loss= p1-p2/ρg• p= Δ f (L/D)(ρV2/2)

• Where f =Friction factorL= length of pipe

D= dia. Of pipeV= Velocity of liquidρ= density of liquid

Friction Factor and Reynolds no• Friction factor (f ) is decided by flow of fluid.• Reynolds no decide type of flow.

1. Re<= 2100 then f =64/Re2. 2100<Re<=4000 use Churchill Equation3. Re>4000 use Colebrook-White Equation

• We can use Moody’s chart also to estimate friction factor.

• For that we need value of pipe roughness.

Churchill Equation

ε: Pipe Roughness

• Colebrook-White Equation

• Also we can use following equations to estimate approximate value of friction factor

Moody chart

Pipe roughness

Material Roughness (mm)Drawn Tubing, Glass, Plastic 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 0.03Wrought Iron (New) 0.045Carbon Steel (New) 0.02-0.05

Carbon Steel (Slightly Corroded) 0.05-0.15Carbon Steel (Moderately Corroded) 0.15-1

Carbon Steel (Badly Corroded) 1-3Carbon Steel (Cement-lined) 1.5

Asphalted Cast Iron 0.1-1Cast Iron (new) 0.25

Cast Iron (old, sandblasted) 1

Sheet Metal Ducts (with smooth joints) 0.02-0.1

Galvanized Iron 0.025-0.15Wood Stave 0.18-0.91

Wood Stave, used 0.25-1Smooth Cement 0.5

Concrete – Very Smooth 0.025-0.2Concrete – Fine (Floated, Brushed) 0.2-0.8

Concrete – Rough, Form Marks 0.8-3Riveted Steel 0.91-9.1

Water Mains with Tuberculations 1.2Brickwork, Mature Foul Sewers 3

Methods to Calculate head loss/pressure loss from fittings

•3K method•2K method•Equivalent length method

3K Method

Chemsys Process Engineering P. LtdFitting Types K1 K∞ Kd (in0.3) Kd (mm0.3)

90° Elbow, ThreadedStandard Radius (R/D =

1) 800 0.14 4 10.6

Long Radius (R/D = 1.5) 800 0.071 4.2 11.1

90° Elbow, Flanged or Welded

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

90° Elbow, Mitered1 weld 90° 1000 0.27 4 10.62 welds 45° 800 0.068 4.1 10.83 welds 30° 800 0.035 4.2 11.1

45° Elbow, ThreadedStandard Radius (R/D =

1) 500 0.071 4.2 11.1

Long Radius (R/D = 1.5) 500 0.052 4 10.6

45° Elbow, Mitered 1 weld 45° 500 0.086 4 10.62 welds 22.5° 500 0.052 4 10.6

180° Bend

threaded, close-return (R/D = 1) 1000 0.23 4 10.6

flanged (R/D = 1) 1000 0.12 4 10.6all types (R/D = 1.5) 1000 0.1 4 10.6

Tee Through-branch as an Elbow

threaded (r/D = 1) 500 0.274 4 10.6threaded (r/D = 1.5) 800 0.14 4 10.6

flanged (r/D = 1) 800 0.28 4 10.6stub-in branch 1000 0.34 4 10.6

Tee Run-throughthreaded (r/D = 1) 200 0.091 4 10.6flanged (r/D = 1) 150 0.05 4 10.6stub-in branch 100 0 0 0

Angle valve45°, full line size, β = 1 950 0.25 4 10.6

90° full line size, β = 1 1000 0.69 4 10.6Globe valve standard, β = 1 1500 1.7 3.6 9.5

Plug valvebranch flow 500 0.41 4 10.6

straight through 300 0.084 3.9 10.3three-way (flow

through) 300 0.14 4 10.6Gate valve standard, β = 1 300 0.037 3.9 10.3Ball valve standard, β = 1 300 0.017 3.5 9.2

Diaphragm dam type 1000 0.69 4.9 12.9Swing check valve Vmin = 35[ρ (lbm/ft3)]

−1/2 1500 0.46 4 10.6

Lift check valve Vmin = 40[ρ (lbm/ft3)]−1/2 2000 2.85 3.8 10

Head Loss= K( V2/2g)

2K Method Chemsys Process Engineering P. Ltd

Fitting Type K1 K∞

90° Elbow Curved

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

90° Elbow Mitered R/D 1.5

1 Weld (90° Angle) 1000 1.152 Weld (45° Angle) 800 0.353 Weld (30° Angle) 800 0.3

4 Weld (22.5° Angle) 800 0.275 Weld (18° Angle) 800 0.25

45° ElbowAll Types, SR (R/D = 1) 500 0.2

All Types LR (R/D = 1.5) 500 0.15

45° Elbow Mitered 1 Weld (45° Angle) 500 0.252 Welds (45° Angle) 500 0.15

180°

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

Tee, used as elbow

Screwed, SR (R/D = 1) 500 0.7

Screwed, LR 800 0.4Flanged/Welded, SR (R/D =

1) 800 0.8

Stub-in-tpye Branch 1000 1

Tee, Run ThroughScrewed 200 0.1

Flanged/Welded 150 0.05Stub-in-type Branch 100 0

Valves, Gate/Ball/Plug

Full Line Size, Beta = 1 300 0.1

Reduced Trim, Beta = 0.9 500 0.15

Reduced Trim, Beta = 0.8 1000 0.25

Valves

Globe, Standard 1500 4Globe, Angle 1000 2

Diaphragm, dam type 1000 2

Butterfly 800 0.25

Check ValvesLift 2000 10

Swing 1500 1.5Tiliting-disk 1000 0.5

•D:Internal diameter of pipe (Inches) •K :Resistance Coefficient •K1:Resistance Coefficient for fitting at Re=1•K∞:Resistance Coefficient for large fitting at Re=∞ •Re: Reynolds number

Equivalent length MethodFitting Types (L/D)eq

90° Elbow Curved, ThreadedStandard Radius (R/D = 1) 30

Long Radius (R/D = 1.5) 16

90° Elbow Curved, Flanged/Welded

Standard Radius (R/D = 1) 20

Long Radius (R/D = 2) 17

Long Radius (R/D = 4) 14

Long Radius (R/D = 6) 12

90° Elbow Mitered1 weld (90°) 602 welds (45°) 153 welds (30°) 8

45° Elbow Curved. ThreadedStandard Radius (R/D = 1) 16

Long Radius (R/D = 1.5)

45° Elbow Mitered 1 weld 45° 152 welds 22.5° 6

180° Bendthreaded, close-return (R/D = 1) 50

flanged (R/D = 1) all types (R/D = 1.5)

Tee Through-branch as an Elbowthreaded (r/D = 1) 60

threaded (r/D = 1.5) flanged (r/D = 1) 20stub-in branch

Tee Run-throughthreaded (r/D = 1) 20flanged (r/D = 1) stub-in branch

Angle valve45°, full line size, β = 1 55

90° full line size, β = 1 150Globe valve standard, β = 1 340

Plug valvebranch flow 90

straight through 18three-way (flow through) 30

Gate valve standard, β = 1 8Ball valve standard, β = 1 3

Diaphragm dam type Swing check valve Vmin = 35[ρ (lbm/ft3)]−1/2 100

Lift check valve Vmin = 40[ρ (lbm/ft3)]−1/2 600Hose Coupling Simple, Full Bore 5

1. Calculate Equivalent length with reference to given chart.

2. Add this length to straight length and calculate head loss/pressure drop.

Z1 Z110

LZ2

L*Sin10

• 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.

• Example 2. Calculation of Pressure Loss: if fittings are present.(3K)• Pipe Size: DN100 (4") • Pipe Diameter (Nominal): 4" • Pipe Internal Diameter:102.3 mm • Pipe Length: 50 m Fittings: 3 x 90° long radius (R/D = 2) • flanged elbows Fluid Velocity: 3 m/s • Fluid Density: 1000 kg/m3 • Reynolds Number:306,900 • Friction Factor: 0.018 • Gravitational Acceleration:9.81 m/s

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Thanks