Pressure Drop Calculation

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 = 1.1101x1010 (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/cm 2 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  = 4fLV2 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 R e = (ρVD) / μ

Where R e = Reynolds number  ρ = Density of steam in kg/m3 V = Velocity of steam in m/s D = Inside diameter in m 2

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  R e = (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 2(SE + P.y)

(Equation: 3: Page: 15)

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) DO-2y(Tm-A)

(Page 15)

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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