Process Design of Piping

Table of Contents

The process design of piping is a balance between the size or diameter of the pipe and the pressure drop in the pipe.

For a particular flow rate of fluid, if we select a larger pipe, it gives a lesser pressure drop, but it increases the fixed cost of the pipe. On the other hand, a lower pressure drop means lower power consumption or lower operating cost.

Lower pressure drop may reduce the size of the fluid-moving device (e.g. pump, fan, blower), so it may reduce the fixed cost of the pump.

So, the fixed cost of the pipe increases with diameter while the pumping cost decreases with the diameter of the pipe.

So, here we need to make a balance between pipe diameter and pressure drop in the pipe and find the optimum value of the pipe diameter.

Optimum Pipe Diameter

The optimum pipe diameter depends on the current cost of material, cost of power, and rate of interest at a particular place and at a particular time. It changes with place and time.

Equation (1) is used to find the optimum diameter of the Carbon Steel Pipe.

This equation is valid for the turbulent flow of an incompressible fluid

(1) $\begin{equation*} d_{optimum}=293\; G^{0.53} \; \rho^{-0.37} \end{equation*}$

Where, d_optimum = Optimum pipe size, (mm)

G = Mass flow rate, (kg/s)

ρ = Density of fluid, (kg/m³)

Equation (2) is used to find the optimum diameter of Stainless Steel Pipe

This equation is valid for the turbulent flow of an incompressible fluid

(2) $\begin{equation*} d_{optimum}=260\; G^{0.52} \; \rho^{-0.37} \end{equation*}$

where, d_optimum = Optimum pipe size, (mm)

G = Mass flow rate, (kg/s)

ρ = Density of fluid, (kg/m³)

Standard Pipes

All standard pipes are available from 3 mm (1/8 in) to 600 mm (24 in) size.

Standard pipes are specified with three different diameters,

Inside Diameter,
Outside Diameter
Nominal Diameter.

For standard pipes having a diameter of more than 300 mm (12 in), Nominal Diameters are equal to the actual Outside Diameter. Still, for smaller pipes, there is no relation between Nominal Diameter and Inside Diameter or Outside Diameter.

Standard Pipe Size Chart

Wall Thickness of the Standard Pipe

The schedule number indicates it as per the US standards.

(3) $\begin{equation*} SCH = \frac{p_{sf}\times 1000}{\sigma_s} \end{equation*}$

where, p_sf = Safe working pressure, N/mm²

σ_s = Safe allowable stress, N/mm²

The thickness of standard pipe increases with increases in schedule number.

Seamless standard pipes do not have welding joints.

Fabricated pipes are fabricated by rolling the plates followed by joining the ends of the plate by welding which are also known as Electric Resistance Welded (ERW) pipes.

Using the following equation the thickness of the pipe, subjected to internal pressure.

$t=\frac{p \; r_i}{\sigma E - 0.6p}+CA=\frac{p \; r_o}{\sigma E + 0.4p}+CA$

where, t = Thickness of pipe, mm

p = Internal design pressure, N/m²

r_i = Inside radius of pipe, mm

r_o = Outside radius of pipe, mm

σ = Allowable stress of pipe material at design temperature, N/m²

E = Joint efficiency; for seamless standard pipe, E = 1

CA = Corrosion allowance, mm

Suggested Fluid Velocities in Pipe

These are only for approximate calculations of pipe diameter. It can be used for the quick calculation of short-distance pipelines or for estimating pipe size as a starting point for pressure drop calculations.

Table 1: Suggested Fluid Velocities in Pipe

Fluid	Service	Suggested Velocity (m/s)
Water	Pump suction line	0.3 to 1.5
	Pump discharge line	2 to 3
	Average service	1 to 2.5
	Gravity flow	0.5 to 1
Steam	0 to 2 atm g, saturated	20 to 30
	2 to 10 atm g, saturated	30 to 50
	Superheated below 10 atm g	20 to 50
	Superheated above 10 atm g	30 to 75
	Vacuum lines	100 to 125
Air	0 to 2 atm g	20
	> 2 atm g	30
Ammonia/refrigerant	Liquid	1.8
	Gas	30
Organic liquids and oils		1.8 to 2
Natural gas		25 to 35
Chlorine	Liquid	1.5
	Gas	10 to 25
Hydrochloric acid	Liquid (aqueous)	1.5
	Gas	10
Inorganic liquids		1.2 to 1.8
Gas and vapours		15 to 30

Table 1: Suggested Fluid Velocities in Pipe

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Pressure Drop-in Pipe

Fanning or Darcy equation gives the relation between pressure drop and pipe diameter. It is derived for steady flow in uniform circular pipes running full of liquid under isothermal conditions.

$\frac{\Delta p}{L}=\frac{2fv^2\rho}{D_i}=\frac{32fG^2}{\pi^2 \rho D_i^5}$

where, Δp = Pressure drop, Pa

L = Length of pipe, m

ṁ = Mass flow rate of fluid, kg/s

ρ = Density of fluid, kg/m³

Di = Pipe inside diameter, m

v = Velocity of fluid, m/s

f = Fanning friction factor

The friction factor is a function of the Reynolds number (Re) and the roughness of the inside surface (ε).

Table 2 – Values of Surface roughness (ε) for various materials

Material	Surface Roughness (ε), mm
Commercial steel or Wrought iron	0.045 72
Galvanized iron	0.152
Cast iron	0.259
Concrete	0.305 – 3.05
Riveted steel	0.914 – 9.14
Brass, Lead, Glass, Cement, and Bituminous Linings	0.001 524

Table 2: Values of Surface roughness (ε) for Various Materials

A plot of Fanning friction factor as a function of Reynolds number (Re) and relative roughness, ε/D, is given as

A more accurate relationship between f and Re for turbulent flow is given by

$\frac{\Delta p}{L}=4.07×10^{10} G^{1.84} \mu^{0.16} D_i^{-4.84} \rho^{-1}$

where, Δp = Pressure drop, kPa

L = Length of pipe, m

Di = Pipe inside diameter, mm

Pressure Drop in Fittings and Valves

In addition to pipes, the piping system contains fittings and valves. These fittings and valves offer additional frictional loss or additional pressure drop. This additional frictional loss of a fitting or of a valve is expressed either as an equivalent straight pipe length (Le) or as a number of velocity heads (K), lost in a pipe of the same size and of the same material.

Equivalent Length of Pipe (Le) for Fittings and Valves

The equivalent length of a valve or of a fitting is the length of a straight pipe of the same size creating the same friction loss as the fitting or the valve in consideration.

Often, Le is expressed in terms of the inside diameter of the pipe. Then Le = (Le/Di) Di,

where,

Di = Inside diameter of the pipe.

Table 3 – Values of Le/Di for valves and fittings

Valve or fitting	L_e/D_i
Gate valve (fully open)	7 to 10
Gate valve (3/4 closed)	800 to 1100
Gate valve (1/2 closed)	190 to 290
Globe valve (fully open)	330 to 480
Angle valve (fully open)	165 to 220
Plug valve (fully open)	18
90° elbows (standard radius)	30
45° elbows (long radius)	5.8
45° elbows (short radius)	8.0
Return bend (medium radius)	39 to 56
Coupling or union	Negligible
Tee, straight through	22

Table 3: Values of Le/Di for valves and fittings

Another way of calculating pressure drop through the fittings and valves is the use of factor K.

“Number of velocity heads (K) lost in pipe” for fittings or valves is defined by the equation

$\frac{\Delta F}{V^2/2}=\frac{\Delta p/\rho}{v^2/2}=K$

$\Delta p=K\rho v^2/2$

where, ΔF = Additional frictional loss, J/kg or N · m/kg

Δp = Additional pressure drop, N/m²

v = Average fluid velocity through the pipe of the same size as valve or fitting, m/s

Table 4 – Values of K for normally used fittings and valves are given in below

Type of fitting or valve	Equivalent number of velocity heads (K) (applicable only for turbulent flow)
Gate valve (open)	0.17
75% Open	0.90
50% Open	4.50
25% Open	24.00
Globe valve,
Bevel seat, Full Open	06.00
50% Open	09.50
Composition seat, Full Open	06.00
50% Open	08.50
Plug disk, Full Open	09.00
75% Open	13.00
50% Open	36.00
25% Open	112.00
Plug valve (open)	0.4
(α = 5°)	0.05
(α = 10°)	0.29
(α = 20°)	01.56
(α = 40°)	17.30
(α = 60°)	206.00
Diaphragm valve, Full Open	02.30
75% Open	02.60
50% Open	04.30
25% Open	21.00
Check valve
Swing Check	02.00
Disk Check	10.00
Ball Check	70.00
Angle valve (open)	02.00
Foot valve	15.00
Coupling, Union	0.04
90^o elbows (standard)	0.75
90° elbows (long radius)	0.45
90° elbows (Square or miter)	01.30
45^o elbows standard	0.35
45^o elbows (long radius)	0.20
90° bend	0.75
180° bend (closed return)	01.50
Tee straight through (Standard)	0.40
Tee Used as elbow, entering run, entering branch, Branching flow	01.00
Butterfly valve
(α = 5°)	0.24
(α = 10°)	0.52
(α = 20°)	01.54
(α = 40°)	10.80
(α = 60°)	118.00
Check valve (swing type)	02.00
Y or blow off valve, full open	03.00
Water meter,
Disk	07.00
Piston	15.00
Rotary (star-shaped disk)	10.00
Turbine-wheel	06.00

Table 4: Values of K for normally used fittings and valves

References

Sinnott, R. K. (2005). Coulson & Richardson’s CHEMICAL ENGINEERING VOLUME 6 FOURTH EDITION Chemical Engineering Design. Elsevier.

Thakore, S. B. and B. B. I. (2015). Introduction to process engineering and design. McGraw-Hill Education.

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