PRESSURE DROP CALCULATION

1. FOR WATER LINE

Hazen Williams’s formula

The equation in SI units

∆P = 1.1101x10 10 (Q/C) 1.85

D4.87

Where

∆P = Frictional pressure drop in kPa/m

Q = Flow rate in m3/hr

C = Hazen-Williams roughness coefficient factor, dimensionless

D =Inside diameter in mm

Example:

Q = 15 m3/hr

C = As per Table A (smooth pipe)

D = 53.1mm (outer diameter 60.3 x thickness 5.54)

Then,

∆P = 1.1101x10 10 (15/140) 1.85

53.14.87

= 0.705 kPa/m

Assume length is 250m

= 176.25 kPa

= 1.79 kg/cm2

The equation in U.S customary units

∆P = 4.524 (Q/C) 1.85

D4.87

Where

∆P = Frictional pressure drop in psi per ft of pipe length

Q = Flow rate in gal/min

C = Hazen-Williams roughness coefficient factor, dimensionless

D =Inside diameter in inch

Example:

Q = 66.04 gal/min

C = As per Table A (smooth pipe)

D = 2.09 inch (outer diameter 60.3 x thickness 5.54)

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Then,

∆P = 4.524 (66.04/140) 1.85

2.094.87

= 0.0310 psi/ft

Assume length is 820.21 ft (250 m)

= 25.50 psi

= 175.81 kPa

= 1.79 kg/cm2

Table A - Hazen-Williams C Factor Table

Pipe material C factor

Smooth pipes (all metal) 130-140

Cast iron (old) 100

Cast iron (unlined new) 120

Iron (worn/pitted) 60-80

Polyvinyl chloride 150

Brick 100

Smooth wood 120

Smooth masonry 120

Vitrified clay 110

Plastic 150

2. FOR STEAM LINE & AIR LINE

Darcy equation

hf = 4fLV 2

2gD

Where

hf = Head loss to friction in m

f = Friction factor

V = Velocity of flow in m/s

g = Acceleration due to gravity in m/s

D = Inside diameter of pipe in m

Re = (ρVD) / μ

Where

Re = Reynolds number

ρ = Density of steam in kg/m3

V = Velocity of steam in m/s

D = Inside diameter in m

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μ = Dynamic viscosity in kg/m-s

Example:

V = 28.28 m/s

g = 9.81 m/s

D = 97.18 mm (outer diameter 114.3 mm & thickness 8.56 mm)

ρ = 19.86 kg/m3

μ = 25.96 x 10-6 from steam table temp 426°C and pressure 59.6 bar

Re = (19.88 x 28.28 x 0.09718)

25.96 x 10-6

= 2107027.302

= 2.107 x 10-6

As per below figure (pipe size 4’’ and Reynolds number 2.107 x 10-6 )

f = 0.0185

hf = 1677.81 m

∆P = ρgh

∆P = P1– P2

= (19.86 x 9.81 x 1677.81)

= 326882.11 N/m2

P1– P2 = 3.77 kg/cm2

If P1 = 60 kg/cm2

Then, P2 = 56.23 kg/cm2

Similar type of calculation for air line.

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3. PIPE WALL THICKNESS CALCULATION AS PER ASME 31.1 2004

Tm = (P x Do) + A (Equation: 3: Page: 15) 2(SE + P.y)

P = Design Pressure

Do = Outer diameter of pipe

SE = Allowable stress (Refer Table A-1 page 99, Table A-2 page 111)

A = Corrosion allowance

1.5 mm for steam & 2 mm for water

y = Coefficient having values as given in table 104.2.1(A)

Bending Tolerance in percentage = Tn – Tm x 100 Tm

Main steam line

1. Outer diameter in mm (DO) = 114.3

2. Pipe thickness provided in mm = 8.56

3. Operating pressure in Kg/cm2 (P) = 60

4. Operating temperature in oc = 426

5. Design pressure in Kg/cm2 (P) = 70

6. Design temperature in oc = 436

7. Pipe material = SA 335 Gr. P11

8. Allowable stress in Kg/cm2 (SE) for design condition = 1002.57

Design condition

Tm = (70x114.3) + 1.5 2(1002.57+ (70 x 0.4))

Minimum thickness required in mm (Tm) = 5.38mm

Tolerance 12.5% as per ASME = 5.38 x 0.125

= 0.6725mm

Then thickness (Tm) = 6.05mm

Bending Tolerance in percentage = 8.56 – 6.05 x 100 6.05

= 41.42%

Minimum thickness required is 6.05 mm and provided thickness is 8.56mm.

Hence it is acceptable

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Design pressure shall not exceed

P = 2SE(Tm-A) (Page 15) DO-2y(Tm-A)

Tm = Provided thickness shall be taken for calculation

P = 82.53 Kg/cm2

ADDITIONAL ALLOWANCES BEYOND 12.5% WALL DEVIATION FOR:

BENDING will reduce safe working pressure by the following amounts: 6 D= 6%, 5 D= 8%,

4D= 14%, 3 D = 25%. More information in ASME B 31.1 paragraph 102.4.5.

THREADING you need to make allowance for the depth of the thread. More information in

ASME B 31.1 paragraph 102.4.2.

CORROSION factors need to be addressed if the pipe is exposed to a corrosive environment.

The additional wall thickness needs to be calculated such that over the desired life of the system

that there remains sufficient wall thickness throughout the pipe's life. More information in

ASME B31.1 paragraph 102.4.1. Future articles will deal with organic coatings that will mitigate

this issue at a cost significantly lower than stainless steel. If you have current needs for organic

coatings--call.

ACTUAL WALL THICKNESS can positively influence pressure ratings. Theses are specified in

ASME B31.1 paragraph 102.4.4. Section Do. This paragraph allows for actual wall thickness and

outside diameter to be used in calculating working pressure without relying on 12.5% wall

deviations. You will realize extra value when you use actual wall thickness to calculate safe

working pressure. Our measurement capabilities plus our stock of pipe will allow us to assist you

in getting the best pipe for your systems.

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