The term sizing of a piping system refers to the completion of two independent design functions: the ﬂuid ﬂow design and the pressure-integrity design. The purpose of the ﬂuid ﬂow design is to determine the minimum acceptable inside diameter of the various segments of the piping system. The purpose of the pressure-integrity design is to determine the minimum acceptable pipe wall thickness and the pressure ratings of the in-line components.

**System Fluid Flow Design**

The objective of the ﬂuid ﬂow design is to determine the minimum acceptable inside diameter of each segment of the piping system that will accommodate the design ﬂow rate while maintaining the pressure drop and ﬂow velocity within reasonable limits.

Most piping systems use pumps to develop the pressure or head required to maintain the system design ﬂow rates. Piping system pressure drops must be maintained within reasonable values to limit the installed size of the system pumps and their prime movers. Pump and prime-mover size limitations are necessary to control initial system construction costs and continuing system operating costs. The optimum pipe size is based on an economic trade off between the installed capital cost of the piping system and the sum of the capital plus lifetime operating costs of the pumping system.

System ﬂow velocities are limited by design to avoid a number of potential operating problems. These problems have already been discussed in previous sections of this chapter. In the absence of any other formal or more limiting criteria,

the ﬂow velocities given for water in Table B2.7 and for steam in Table B2.8 are considered reasonable for normal industrial applications.

The detailed ﬂuid ﬂow design of a piping system requires the consideration of a number of ﬂuid parameters including ﬂow rate, viscosity, density, and pipe wall frictional drag.

**Pressure-Integrity Design**

The pressure-integrity design of a piping system normally requires the consideration of at least two issues. The ﬁrst is the determination of the minimum or nominal pipe wall thickness, and the second is the determination of the pressure rating of the in-line components, such as ﬁttings and valves.

**Determination of Pipe Wall Thickness**

After the ﬂuid design is complete and the minimum inside diameters of the various segments of the piping system are determined, the piping pressure-integrity design may proceed. The major steps in the process are as follows:

Using the minimum inside diameter determined from the ﬂuid ﬂow evaluation, select the next-larger standard nominal or outside diameter (OD) size pipe from the listings provided in ASME B36.10M for standard wrought steel pipe or B36.19M for stainless-steel pipe.

Based upon the ﬂuid and service, select a suitable piping material, and if necessary, determine the required corrosion, erosion, joining, or mechanical strength allowances.

Using equations provided in the design code, calculate the required minimum wall thickness to provide for pressure integrity and allowances.

Refer to ASME B36.10M or B36.19M to select an appropriate nominal wall thickness or schedule. Refer to App. E2 and E2M.

Conﬁrm that the standard manufacturing tolerance will not reduce the nominal wall thickness selected in step 4 below the minimum required, as calculated instep 3.

Conﬁrm that the inside diameter of the pipe selected, based upon the nominal wall thickness selection of step 4, is compatible with the minimum inside-diameter requirements obtained from the ﬂuid ﬂow evaluation.

The process described above is demonstrated in the following example:

**Example B2.3.** A carbon-steel pipe having a required minimum inside diameter of 11.2 in (284 mm) is to transport water at 700 psig (4830 kPa gage) and 90 deg F (32 deg C). The design code is ASME B31.1, and the design life is 8 years. The water has a nominal oxygen content of 1 ppm. Butt-welded construction is used.

**Evaluation.**

An economical grade of seam-welded carbon-steel pipe (ASTM A53 Grade A) is selected. From ASME B31.1, Appendix A, Table A-1, the allowable working stress at 90 deg F (32 deg C) is 10,200 psi (70.4 MPa). From Fig. B2.3, the corrosion rate is estimated at 0.02 in (0.5 mm) per year. The pressure-integrity design will be based upon ASME B31.1, Paragraph 104.1.2, equation (3):

From ASME B36.10M, NPS 12 (DN 300) [12.75-in (324-mm) OD] is tentatively selected.

Using the stated 8-year design life and 0.02 in/yr corrosion rate, the total corrosion allowance of 8 X 0.02 = 0.16 in (4 mm) is calculated. Butt-welded construction is speciﬁed; therefore, no additional wall thickness allowance for joining (threading,grooving, etc.) is required.

From ASME B31.1, Table 104.1.2(A), y = 0.4 is selected for ferritic steels at temperatures at or below 900 deg F (482 deg C). Equation (B2.5) may now be used to calculate the required minimum wall thickness:

From ASME B36.10M, under the listings for NPS 12 (DN 300), Schedule 80 pipe with a nominal wall thickness of 0.688 in (17.5 mm) is tentatively selected. The wall thickness tolerance for ASTM A53 pipe, which is +0, -12¹⁄₂ percent, is checked next:

Finally, the nominal inside diameter is checked against the minimum ﬂow diameter:

The problem requirements are satisﬁed; NPS 12 (DN 300) seam welded Schedule 80 pipe meeting ASTM Speciﬁcation A53 Grade A is acceptable.

The previous example did not consider the effects of bending on the pipe wall. In most instances the pressure design will dominate in the determination of pipe wall thickness. However, if the pipe span between supports is unusually long or if the pipe has a very heavy in-line component, such as a valve, then the longitudinal bending stress may dominate the design.

To complete this chapter, ﬁve more example problems are presented. They demonstrate the concepts developed and bring them together to show how the design of a simple piping system might proceed.

**Determining the Pressure Class for In-Line Components**

The ﬁrst two examples provided here demonstrate the process used to determine the pressure classiﬁcation for in-line components. The ﬁrst demonstrates the selection process for a standard ﬂange; the second demonstrates the selection process for a special-class valve.

**Example B2.4.**

An NPS 16 (DN 400) carbon-steel pipeline operates at 840 psig (5800 kPa gage) and 740 deg F (393 deg C). Select a standard weld-neck ﬂange for the service.

**Evaluation.**

Table B2.1 lists various materials of construction for standard pipe ﬂanges. Under Material Group 1.1, ASTM Speciﬁcation A105, Forgings, Carbon Steel, for Piping Components, is listed. Next refer to Table B2.3, which lists ASME pressure-temperature ratings for Material Group 1.1 ﬂanges. Noted that a Class 600 ﬂange has a pressure-temperature rating of 1010 psig (6970 kPa gage) at 750 deg F (399 deg C). Since this rating exceeds the requirements of 840 psig (5800 kPa gage) at 740 deg F (393 deg C), this ﬂange is acceptable.

**Example B2.5.**
An NPS 12 (DN 300) butt-welding end gate valve is required to operate at 2350 psig (16,220 kPa gage) and 1015 deg F (546 deg C). The valve material is ASTM A217 Grade WC9. Determine the appropriate ASME pressure classiﬁcation.
**Evaluation.**
Tables B2.9a and B2.9b list the pressure-temperature ratings for standard and special class valves of ASTM A217 Grade WC9.
There are two correct answers to this problem. The ﬁrst and simplest answer is to select a standard Class 4500 valve from Table B2.9a. This valve has a pressure-temperature rating of 2625 psig (18,040 kPa gage) at 1050 deg F (566 deg C) and obviously meets the stated requirements. However, this valve may prove to be a very expensive alternative since Class 4500 valves are massively constructed, and valve prices vary according to the weight of the material used in their construction.
The second alternative is to consider the Special Class 2500 valves whose ratings are provided in Table B2.9b. Special-class valves undergo mandatory nondestructive examinations and, if necessary, defect repairs to allow them to qualify for higher pressure-temperature ratings. For a more detailed discussion of special-class valves,the reader is referred to Section 8 of ASME B16.34.26 To determine whether a Special Class 2500 valve will meet the requirements of Example B2.3, a linear interpolation of the ratings in Table B2.9b is required. The process is illustrated below:

Since the interpolated pressure rating of 2462 psig (16,990 kPa gage) is greater than the speciﬁed requirement of 2350 psig (16,220 kPa gage), a Special Class 2500 valve will satisfy the requirements of Example B2.5.

**Determining the Design Conditions and Pressure Class of a Piping System**

To minimize procurement complications and storage and handling problems during the construction phase, piping systems are frequently designed for the maximum

conditions permitted for each pressure class. This allows conservatism, which can accommodate changes in design conditions as a result of design development and minimizes the need to specify and buy different piping for each individual application. In addition, this approach provides an added allowance in the event of unexpected deterioration of the pipe wall thickness in service. The following examples provide an illustration of determining the design pressure and design temperature for a piping system. They also provide insight into the method of establishing the pressure-temperature rating or pressure class of an entire piping system.

**Example B2.6**
Fluid: Water
Normal conditions: 350 psig (2415 kPa gage) @ 350 deg F (177 deg C)
Maximum conditions: (1) 375 psig (2588 kPa gage) @ 390 deg F (199 deg C)
(2) 435 psig (3002 kPa gage) @ 375 deg F (191 deg C)

Condition 1 has a maximum duration of 3 h. Condition 2 has a maximum duration of 10 min in any 24-h operating period. Pipe sizes: NPS 6 (DN 150), NPS 10 (DN 250), NPS 14 (DN 350)

**Evaluation.** The piping system being considered is designed in accordance
with ASME B31.1; however, the approach discussed below can be used to design a piping system in accordance with other codes.
The ﬂuid and the temperature dictate the use of carbon-steel piping. Assume the following materials:

Pipe: ASTM A106 GR B Valve body: ASTM A216, WCB Flanges: ASTM A105

Determine the pressure-temperature ratings for all conditions. The ratings are determined from the pressure-temperature tables of ASME B16.5 and ASME B16.34. The ﬂange and valve materials are in material group 1.1; refer to ASME B16.5, Table 2-1.1, and ASME, B16.34, Table 2-1.1.

350 psig (2415 kPa gage) @ 350 deg F (177 deg C)—Class 300 375 psig (2588 kPa gage) @ 390 deg F (199 deg C)—Class 300 435 psig (3002 kPa gage) @ 375 deg F (191 deg C)—Class 300

Since Class 300 is required for each condition, the design conditions should be selected so as not to exceed the pressure-temperature ratings of Class 300. Other-wise, the design conditions will be overly conservative.

Determine design conditions from normal and maximum conditions.

The design conditions are selected to ensure that the minimum wall thickness requirements of ASME B31.1 are met. This requires consideration of two factors: pressure and temperature. Pressure. The greater the pressure, the greater the required wall thickness of the pipe. The design pressure must be selected so that each of the following requirements is satisﬁed:

The design pressure shall be not less than the maximum sustained operating pressure (MSOP) within the piping system including the effects of static head (ASME B31.1, Paragraph 101.2.2).

The design pressure shall be of sufﬁcient magnitude that the stress resulting from a variation in pressure and/or temperature in the piping system does not exceed the allowable stress by more than 15 percent during 10 percent of any 24-h operating period, or by more than 20 percent during 1 percent of any 24-h operating period (see ASME B31.1, Paragraph 102.2.4).

Maximum condition 1 will cause a stress in the pipe wall which is less than 15 percent over the stress caused by the normal condition pressure

Therefore, maximum condition 2 can be treated as an occasional condition. The minimum acceptable design conditions are

**Example B2.7**
Fluid: Steam
Normal conditions: 400 psig (2760 kPa gage) @ 600 deg F (316 deg C)
Maximum conditions: 575 psig (3970 kPa gage) @ 600 deg F (316 deg C)

This condition occurs in less than 1 percent of any 24-h operating period. Pipe sizes: NPS 12 (DN 300), NPS 18 (DN 450)

**Evaluation.**

The ﬂuid and the temperatures allow the use of carbon steel. Assume the following materials:

Pipe: ASTM A106, Gr. B Valve body: ASTM A216 WCB Flanges: ASTM A105

Determine the pressure-temperature ratings. With the help of ASME B16.5, Table 2-1.1, and ASME B16.34, Table 2-1.1, the suitable classes for the normal and maximum conditions are established as follows:

400 psig (2760 kPa gage) @ 600 deg F (316 deg C)—Class 300 575 psig (3970 kPa gage) @ 600 deg F (316 deg C)—Class 400

The normal condition requires Class 300 ﬂanges and valves while the maximum condition requires Class 400 ﬂanges and valves. The maximum permissible (sustained) pressure for Class 300 at 600 deg F (316 deg C) is 550 psig (3,800 kPa gage). This pressure may be exceeded in the same manner as discussed in Example B2.4 (15 percent for 10 percent of the time; 20 percent for 1 percent of the time). Thus, the peak pressure that the ﬂanges and valves may be exposed to is greater than the system maximum of 575 psig (3,970 kPa gage). Therefore, Class 300 can be used.

Determine the design conditions such that 575 psig exceeds the design pressure by not more than 20 percent.

The minimum design conditions are

This piping can also be designed for the maximum design condition permitted for Class 300 ﬂanges made from material group 1.1 per ASME B16.5. The maximum design conditions, per B16.5, Table 2-1.1, are

The piping may also be designed for the minimum design conditions shown above (479 psig at 600 deg F). Sometimes this can result in substantial savings in material, fabrication, and installation costs. This is particularly true for high-pressure and high-temperature applications that require the use of low- and high-alloy steels.

**Design of Piping for Internal and External Pressure**

**Example B2.8.**

An NPS 24 (DN 600) seamless steel pipeline carries puriﬁed water from an onshore water treatment plant to an offshore island-sited nuclear power plant. The line runs vertically down in an open shaft to a depth of 120 ft (36.6 m) below grade. It then runs horizontally 100 ft (30.5 m) below the surface of a seawater strait that separates the two facilities. The discharge pressure of the pumping system that transfers the water is 350 psig (2415 kPa gage) at ambient temperature. The material is ASTM A106, Grade B, and the internal corrosion allowance is 0.065 in (1.7 mm). The line is coated to prevent external corrosion. At times, the line is shut down and drained for maintenance. Under these conditions it must withstand the external pressure exerted by the seawater, without collapse.

Determine the required wall thickness to safely contain the water at the internal design pressure, and verify that this thickness is adequate to withstand the external pressure. The design code is ASME B31.1.

**Solution.**

The pipeline design will be developed initially for the internal pres-sure condition. It will then be checked for the external pressure.

The internal design pressure has two components: the pump discharge pressure and the static head due to the vertical run to 120 ft below grade. The head pressure is

The internal design pressure is therefore 350 + 52 = 402 psig. The minimum wall thickness based upon this pressure is determined by using Eq. (B2.5):

The values of the variables are

Substituting these values yields

The commercial wall thickness tolerance on ASTM A106 pipe is + 0, - 12¹⁄₂ percent; therefore the nominal wall thickness is determined by dividing the minimum wall thickness by 0.875.

The next-larger standard pipe wall thickness for ASTM A106, per ASME B36.10M, is 0.500 in (12.7 mm). This nominal thickness is accepted preliminarily, and will be investigated for its adequacy to withstand the external pressure condition. ASME B31.1, Paragraph 104.1.3, invokes the ASME Boiler and Pressure Code, Section VIII, Division 1, Pressure Vessels, Subsections UG-28 through UG-30, for the external pressure design of straight pipe. This subsection provides a series of empirical procedures for the external pressure design of shells and tubes. They may be stiffened or unstiffened. The procedures rely on equations presented in UG-28 to UG-30, and a series of external pressure design charts given in ASME Section II, Part D, Subpart 3.

This example problem is a basic case involving an unstiffened straight tube under external pressure, and simplifying assumptions have been made. The reader is encouraged to study Subsections UG-28 through UG-30 in their entirety, prior to attempting the solution of this class of design problems.

The nomenclature is

**Detailed Procedure.**

The following procedure applies to cylindrical shells or tubes whose diameter-to-thickness ratio Do /t is greater than 10.

For this example the minimum required wall thickness t is taken as the commercial minimum wall thickness, less the corrosion allowance.

For the assumed thickness t, determine the ratios L/Do and Do/t. If L/Do is greater than 50, assume L/Do = 50.

Using the values for L/Do and Do/t, proceed to Fig. B2.4 and determine the value of A. From Fig. B2.4, at L/Do = 50 and Do/t = 64.4, A equals 0.00025.

Using the value of A found above, proceed to the material chart shown in Fig. B2.5 to determine the value of B. From Fig. B2.5, at the value of A = 0.00025; B equals 3600.

Use the following formula to calculate the maximum allowable external working pressure which may act on the pipe:

This maximum allowable external working pressure must be compared with the actual external pressure due to the submergence in seawater, to determine whether the design is adequate.

The submergence depth is given as 100 ft, and the density of seawater is taken as 64.0 lb/cubic ft. The seawater pressure Psw acting on the outside of the pipe is

Since the maximum allowable external working pressure for the pipe Pa exceeds the seawater pressure acting on the pipe Psw, the design is acceptable.