Moment of Inertia: Introduction, Definition, Formula, Units, Applications

Written by Anup Kumar Dey in Civil,Mechanical,Piping Stress Analysis,Piping Stress Basics

Moment of Inertia is a very useful term for mechanical engineering and piping stress analysis. It represents the rotational inertia of an object. The moment of inertia signifies how difficult is to rotate an object. In this article, we will explore more about the Moment of Inertia, Its definition, formulas, units, equations, and applications.

What is Moment of Inertia?

There are two types of moment of inertia; the mass moment of inertia and the area moment of inertia.

The moment of inertia of a Mass (I) is defined as the sum of the products of the mass (m) of each particle of the body and the square of its perpendicular distance (r) from the axis and is mathematically represented as

I = mr²

The mass distribution of a body of rotating particles from the axis of rotation is represented by the moment of inertia. The value of the moment of inertia is independent of the forces involved and depends only on the body geometry and position from the axis of rotation. The mass moment of inertia for rotation is analogous to mass in linear movement. So, the mass moment of inertia for rotation is treated the same way as the mass in linear motion with features like

The angular momentum of a body is given by I.ω. Newton’s Second Law of Motion, when applied to rotating bodies, states that the torque is directly proportional to the rate of change of angular momentum.
When a body with the mass moment of inertia (I) is rotated about any given axis, with an angular velocity ω, then it possesses some kinetic energy of rotation given by = 1/2 Iω²

The moment of Inertia of an Area (I) represents the distribution of points in a cross-sectional area with respect to an axis. It is also known as the second moment of area. For an elemental area dA in the XY plane, the area moment of inertia is mathematically defined as I_x and I_y as shown in Fig. 1 below.

**Fig. 1: Moment of Inertia with respect to X and Y axis**

The Formula for Moment of Inertia

In beam theory, the formula of the moment of inertia is very important. Depending on the cross-section of the object the equation of the moment of inertia varies. Note that, the moment of inertia is always positive. In this section, we will find out the moment of inertia formula for a few common geometrical cross sections.

Moment of Inertia Formula for Square Cross-Section:

The moment of inertia equation for a square is given by I_x=I_y= a⁴/12 where a=length of side.

The Equation for Moment of Inertia for Circular Cross Section:

The moment of inertia for a circular cross-section is given by I=πd⁴/64 where d=Diameter of the circle. In a similar way, the moment of area of a pipe is given by I=π(D⁴-d⁴)/64 Where D=Pipe OD and d=Pipe ID.

The following image provides the area moment of inertia formula for some more common shapes.

**Fig. 2: Moment of Inertia of Common Geometrical Shapes**

Units of Moment of Inertia

The unit of mass moment of inertia in the SI unit system is kg.m2 and in the FPS unit system is lbf·ft·s²

The unit of an area moment of inertia in the SI unit is m4 and in the FPS unit system is inches⁴.

Polar Moment of Inertia

The polar moment of inertia is defined with respect to an axis perpendicular to the area considered. It provides a beam’s ability to resist torsion or twisting. The polar moment of inertia (J) of a circular area is given by J=πd⁴/32.

Applications of Moment of Inertia

Mass moment of inertia provides a measure of an object’s resistance to change in the rotation direction.
Area moment of inertia is the property of a geometrical shape that helps in the calculation of stresses, bending, and deflection in beams.
A polar moment of inertia is required in the calculation of shear stresses subject to twisting or torque.
The moment of inertia “I” is a very important term in the calculation of Critical load in Euler’s buckling equation. The Critical Axial load, Pcr is given as P_cr=π²EI/L².
A moment of inertia is required to calculate the Section Modulus of any cross-section which is further required for calculating the bending stress of a beam. Bending stresses are inversely proportional to the Moment of Inertia. The larger the moment of inertia, the greater is the moment of resistance against bending.

Section Modulus

The section modulus of a section is defined as the ratio of the moment of inertia (I) to the distance (y) of extreme fiber from the neutral axis in that section. Section modulus is denoted by “Z” and mathematically expressed as

Z=I/y

In SI unit systems the unit of Section Modulus is m³ and in the US unit system inches³. The table provided in Fig. 3 provides the moment of inertia and section modulus formula for common geometrical shapes. (Here, Z_c and Z_t are the section moduli in compression and tension)

**Fig. 3: Moment of Inertia and Section Modulus Equations**

Deluge System: Definition, Working, Applications, and Advantages

Written by Anup Kumar Dey in Health & Safety,Mechanical,Piping Design Basics,Piping Interface,Process

What is a Deluge System?

A deluge system is a fixed fire protection system designed to protect against severe fuel hazards. A large number of sprinklers simultaneously act to bring any undesirable fire event under control. Consisting of unpressurized dry piping and open sprinkler heads, the deluge system is directly connected to a water supply and upon activation, a deluge valve releases the water to all the open sprinkler heads simultaneously. Deluge systems can also release other fire-suppressing materials like dry powder, foam, chemicals, or inert gases. Until the deluge valve is activated by an electric, pneumatic, hydraulic, or manual release system, the system piping remains empty and dry but when activated, the deluge system floods the area through pressurized water or other fire extinguishing material.

The main purposes behind using deluge systems are any one or combination of the following :

Extinguishment of fire
Control of burning
Exposure protection
Prevention of fire

Working of a Deluge System

As deluge systems are used in special hazard installations, they must work quickly to protect the entire area. Fig. 1 shows a typical deluge system. A deluge system comprises of three main components: deluge spray nozzles and lines, deluge valve set, and deluge system water supply. The working of a deluge system consists of the following four steps:

A fire detection (Smoke/Heat/Ultraviolet/Infrared/Optical flame Detector) system detects the fire and sends the signal to the fire alarm panel to activate the deluge valve.
Immediately the deluge valve opens which is connected to a water supply.
Water flows into the piping system and starts discharging from all nozzles and open sprinklers.
After use, the deluge valve can be easily reset to normal operating conditions by draining the water remaining inside the pipe and valve body.

Types of Deluge Systems

According to the method of release, Deluge systems are classified into three categories:

Pneumatic release deluge system
Hydraulic release deluge system
Electrical release deluge system

Applications of a Deluge System

Deluge systems are used in special hazard installations requiring a large quantity of water to control a fast-developing fire. They provide high-velocity suppression. Typical applications of deluge systems are found in:

Flammable liquid handling systems.
Flammable liquid storage, and chemical storage areas.
Hydrocarbon processing plants.
Refineries/ Fuel Processing Plants.
Oil extraction plants.
Separation, distillation plants.
Large aircraft hangars.
Transformers.
Crude tanks and vessels.
Power Plants.
Data Storage units.
Paint Shops.
Theatres.

Codes and Standards for a Deluge System

The governing codes and standards for a deluge system design and manufacturing are

NFPA 15: Standard for Water Spray Fixed Systems for Fire Protection
API RP 2030: Application of Fixed Water Spray Systems for Fire Protection in the Petroleum and Petrochemical Industries.
ISO 6182: Fire Protection-Automatic Sprinkler System
NFPA 13: Standard for the Installation of Sprinkler Systems
IP MODEL CODE P19, By Energy Institute – Fire Precautions at Petroleum Refineries and Bulk Storage Installations.

Piping Requirements for Deluge System Design

As per NFPA, Requirements for piping arrangements are
- Sch 40, Carbon Steel (Galvanized) Pipe for up to 8” sizes and
- Sch 30, Carbon Steel (Galvanized) Pipe for 8” & above
Requirements for Piping Installation:
- In the dry section of the pipe, a Suitable slope needs to be provided.
- A low-point drain at a suitable location is required.
Pipe Velocity criteria for deluge system: NFPA 15 allows up to 7.94 m/sec of water velocity for the deluge downstream side. However, based on the project piping design philosophy velocity may be limited to 5 m/sec downstream of the deluge valve and 3 m/sec upstream.
The deluge system should be designed in such a way that within 30 secs of activation, the water spray fully covers the equipment in that region.
As per NFPA 15, the minimum Pipe Size for Deluge Systems is 1”.

Advantages of Deluge System

The major advantages of using deluge fire protection systems over other kinds of systems are:

They can easily control rapidly spreading fire.
Very quick response as all sprinklers are open.
Their operation can be made fully automatic.
Deluge system being a dry system, no risk of frozen pipes
They can also be used in conjunction with foam concentrate for better controlling certain types of fire.
Water disperses over a large area for efficient fire extinguishing.

Duplex Stainless Steel (DSS): Definition, Grades, Composition, Properties, and Applications

Written by Anup Kumar Dey in Engineering Materials,Mechanical,Piping Design Basics

Duplex Stainless Steel is a specific group of engineering stainless steel materials consisting of the austenitic and ferritic phases in roughly equal proportions in the microstructure. They are widely popular because of their good corrosion resistance, high strength, and ease of fabrication. They are also popular by their acronym DSS. Compared to traditional austenitic stainless steel and ferritic stainless steel grades; Duplex Stainless Steels provide a range of benefits:

Improved Strength: Roughly two times stronger than normal stainless steel grades.
High Toughness and Ductility
High Corrosion Resistance
Cost-Effectiveness: High strength of DSS material required less pipe thickness reducing pipe weight. Also, lower levels of nickel reduce cost.

Applications of Duplex Stainless Steel

Excellent corrosion resistance with increased strength and affordable pricing makes duplex stainless steel (DSS) a popular choice for a variety of industries. Their wide uses are found in:

Chemical and liquid processing
Offshore (flowlines, risers) and other industrial operations
Naval parts and components
Pulp and paper production
Pollution control equipment
Water Treatment/Desalination plants
Construction, Infrastructure, Architecture
Hot water and brewing tanks
Food and Drink Storage
Boilers, Heat exchangers, pressure vessels
Marine Tanks
Renewable Energy
Nuclear Industry

Duplex Stainless Steel Grades

Duplex stainless steels have a higher chromium content, 20–28%; higher molybdenum, up to 5%; lower nickel, up to 9%, and 0.05–0.50% nitrogen as compared to austenitic stainless steels. For resistance against pitting corrosion, DSS material is an ideal selection. The resistance against pitting corrosion is characterized by the pitting resistance equivalence number, or PREN Number defined as follows:

PREN = %Cr + 3.3 %Mo + 16 %N

Depending on the PREN Number values, Duplex Stainless Steel is categorized into four grades.

Lean duplex grades (PREN range: 22–27): No deliberate Molybdenum addition. mainly used in the building and construction industry for bridges, pressure vessels, or tie bars. Example: S32001, S32101, S32304, S32202.
Standard duplex (PREN range: 28–38): The most widely used (More than 80%) duplex stainless steel material with mid-range properties. Example: S32003, S31803, S32205
Super duplex (PREN range: 38-45): Higher contents of Cr, Ni, Mo, N, and even W. Specifically designed for highly corrosive oil & gas and chemical industries. Example, S32750, S32760, S32950, S32808.
Hyper duplex (PREN >45): These are highly alloyed duplex stainless steel. Example S32707, S33207

Naming Convention for Duplex Stainless Steels

Various naming conventions are followed for duplex stainless steels such as:

Composition-based Names: For DSS 2205 or 2305; 22 or 23 denotes %Cr and 5 denotes %Ni in that specific DSS material.
UNS Designation: The Unified Numbering System or UNS designation of DSS materials is the most popular and listed on ASTM specifications.
AISI Designation: Only one DSS material type 329 has an AISI designation.

Duplex Stainless Steel Properties

As informed earlier the duplex name has arrived from the co-existence of both austenitic (FCC Structure) and ferritic (BCC Structure) in approximately equal proportions (Fig. 1). The major alloying elements are Chromium, Silicon, Molybdenum, Carbon, Nickel, Nitrogen, Manganese, Copper, Tungsten.

**Fig. 1: Duplex Stainless Steel Microstructure**

Typical duplex stainless steel exhibits a higher strength value as compared to stainless steel. But, the working temperature range of DSS is normally narrow as at around 300^oC undesirable intermetallic phases (α’ -alpha prime phase) start to precipitate which decreases the mechanical properties and corrosion resistance by embrittlement phenomenon. The following table provides some selected properties of common duplex stainless steel grades.

DSS Grades	ASTM A789 Grade S32520 Heat-Treated	ASTM A790 Grade S31803 Heat-Treated	ASTM A790 Grade S32304 Heat-Treated	ASTM A815 Grade S32550 Heat-Treated	ASTM A815 Grade S32205 Heat-Treated
Elastic Modulus	200 GPa	200 GPa	200 GPa	200 GPa	200 GPa
Elongation	25 %	25 %	25 %	15 %	20 %
Tensile Strength	770 MPa	620 MPa	600 MPa	800 MPa	655 MPa
Brinell hardness	310	290	290	302	290
Yield Strength	550 MPa	450 MPa	400 MPa	550 MPa	450 MPa
Thermal expansion coefficient	1E-5 1/K	1E-5 1/K	1E-5 1/K	1E-5 1/K	1E-5 1/K
Specific Heat capacity	440 – 502 J/(kg·K)	440 – 502 J/(kg·K)	440 – 502 J/(kg·K)	440 – 502 J/(kg·K)	440 – 502 J/(kg·K)
Thermal Conductivity	13 – 30 W/(m·K)	13 – 30 W/(m·K)	13 – 30 W/(m·K)	13 – 30 W/(m·K)	13 – 30 W/(m·K)

Table-1: Properties of Duplex Stainless Steel

The stress-strain curve of austenitic, ferritic, and duplex stainless steels are plotted in the following curve for reference:

Stress Strain curve comparison for SS and DSS.png — **Fig. 2: Stress-Strain curve comparison for SS and DSS**

Composition of Duplex Stainless Steel

The following table in Fig. 3 and Fig. 4 provides the chemical compositions in %wt for common DSS and SDSS materials.

Composition of Lean & Standard Duplex Stainless Steel Materials — **Fig. 3: Typical Chemical Composition of Duplex Stainless Steel**

Composition of Super & Hyper Duplex Stainless Steel Materials — **Fig. 4: Typical Chemical Composition of Super and Hyper Duplex Stainless Steel**

Corrosion Resistance of Duplex Stainless Steel

Due to the presence of a relatively high % of chromium, molybdenum, and nitrogen, Duplex Stainless Steels exhibit a high level of corrosion resistance capability in a variety of environments. DSS materials are specifically selected for oxidizing, acidic, and hot alkaline environments. To fight against pitting corrosion, DSS is the ideal material choice. The PREN Number defined above describes the resistance of DSS against localized pitting corrosion. An increase in PREN Number increases the resistance against pitting corrosion that is quantified using Critical Pitting Temperature. Materials with higher CPT are more resistant to pitting corrosion.
Duplex stainless steels possess better Stress Corrosion Cracking resistance than austenitic stainless steel.

Fabrication of Duplex Stainless Steel

Duplex Stainless steel is supplied in a pipe, plate, sheet, tube, fittings, or bar form. Depending on the requirement they must be fabricated. Special tools are required for the fabrication of duplex stainless steel materials. They have very good weldability and hot-forming capability. However, DSS materials are normally difficult for machining purposes.

Difference Between SS, DSS, and SDSS

Some of the important differences between SS, DSS, and SDSS are provided here: What is SS, DSS, and SDSS in Piping for Oil and Gas Applications

Differences between DSS and SDSS?

Duplex Stainless Steel (DSS) and Super Duplex Stainless Steel (SDSS) are both types of stainless steel that combine the properties of austenitic and ferritic stainless steel. However, the key differences between them are:

Composition: SDSS has higher chromium (25-27%), molybdenum (3-5%), and nitrogen content compared to DSS, which typically has 22-25% chromium, 3-4% molybdenum, and lower nitrogen content.
Strength: SDSS offers higher yield strength than DSS, making it suitable for more demanding applications.
Corrosion Resistance: SDSS has superior resistance to pitting, crevice corrosion, and stress corrosion cracking, particularly in aggressive environments like seawater, sour gas, and chloride-rich conditions.
Applications: SDSS is often used in more extreme environments, such as subsea equipment and high-pressure pipelines, where the material’s superior performance is critical.

Fig. 5 below provides a nice image showing some of the applications of DSS and SDSS material in Onshore Oil & Gas:

**Fig. 5: Applications of DSS & SDSS in Onshore Oil & Gas**

Relationship between SDSS and DSS

SDSS (Super Duplex Stainless Steel) is an enhanced version of DSS (Duplex Stainless Steel). While both materials share a similar duplex microstructure (a roughly equal mix of austenite and ferrite phases), SDSS is designed for even higher performance. The relationship is that SDSS builds on the foundation of DSS by offering increased strength and better corrosion resistance, making it suitable for more demanding environments. Essentially, SDSS is a more advanced form of DSS with higher alloy content and improved properties.

Differences between SS and DSS

Stainless Steel (SS) and Duplex Stainless Steel (DSS) differ primarily in their microstructure, composition, and performance:

Microstructure: SS can be austenitic, ferritic, or martensitic, while DSS has a mixed microstructure of approximately 50% austenite and 50% ferrite.
Corrosion Resistance: DSS generally offers better resistance to pitting, crevice corrosion, and stress corrosion cracking, particularly in chloride-containing environments, compared to SS.
Strength: DSS has nearly twice the yield strength of austenitic SS, allowing for thinner sections and potential cost savings in certain applications.
Applications: SS is widely used in a variety of applications, while DSS is favored in more demanding environments, such as offshore platforms, subsea pipelines, and chemical processing plants.

DSS Pipe Material Specification

The DSS Pipe Material Specification defines the chemical composition, mechanical properties, and acceptable testing methods for Duplex Stainless Steel piping. A common specification is ASTM A790/A790M, which covers seamless and welded duplex stainless steel pipes for high-temperature and general corrosive service. The specification outlines requirements such as:

Chemical Composition: Specific ranges for elements like chromium, nickel, molybdenum, and nitrogen.
Mechanical Properties: Minimum yield strength, tensile strength, and elongation requirements.
Testing Methods: Includes hydrostatic testing, nondestructive testing (NDT), and intergranular corrosion testing.

Frequently Asked Questions of DSS with Answers

What is meant by duplex stainless steel?
- The word duplex in stainless steel refers to the two-phase microstructure of DSS material. Duplex stainless steel is a family of stainless steel having ferritic and austenitic phase microstructure in approximately equal proportions.
Is 304 stainless steel a Duplex?
- No, 304 stainless steel is austenitic stainless steel. It is not a duplex.
Is 316 stainless steel a Duplex?
- Stainless steel 316 is not a duplex SS. 316 SS is austenitic in nature.
What is the purpose of duplex stainless steel?
- Duplex stainless steels have roughly twice the strength of austenitic stainless steels and higher resistance to pitting corrosion, crevice corrosion, and stress corrosion cracking.
Does duplex stainless steel rust?
- Duplex Stainless steel has a very high chromium content that prevents the DSS material from rusting. So, in general, duplex stainless steel does not rust. However, under a suitable corrosive environment, DSS may corrode or rust.
Is 2205 duplex stainless steel magnetic?
- As duplex stainless steels are ferritic as well as austenitic, it does have magnetic properties. 2205 super duplex is also magnetic. All DSS materials are magnetic.
Does duplex 2205 rust?
- 2205 stainless steel being a DSS usually does not rust. But when exposed to severe conditions, it may corrode.
What is the difference between a duplex and a super duplex stainless steel?
- Super duplex stainless steel is an improved duplex stainless steel. It possesses additional characteristics as compared to DSS. DSS has 25% chromium, 7% nickel, and 4% molybdenum content which makes the material have higher corrosion resistance and . strength than duplex stainless steel.
How strong is duplex stainless steel?
- Duplex stainless has more strength as compared to other groups of stainless steel. Roughly, duplex stainless steel is around twice as strong as either ferritic or austenitic stainless steel.
Who invented the super Duplex?
- Super Duplex stainless steel was developed by Langley Alloys in the mid-1960s and was launched in 1969.
What grade is a super duplex?
- DSS grades UNS S32760, S32750, F55, 1.4501, etc are super duplex.
What is the DSS Material Code?
- The material code for Duplex Stainless Steel (DSS) typically refers to a standardized designation used in engineering and procurement to specify the type of material. One common code system is the Unified Numbering System (UNS), where DSS is often designated by codes such as:
  - UNS S31803: Standard grade of DSS, also known as 2205.
  - UNS S32205: An improved version of S31803 with slightly higher nitrogen content, offering enhanced corrosion resistance.
Which is cheaper: DSS or SDSS?
- Duplex Stainless Steel (DSS) is generally cheaper than Super Duplex Stainless Steel (SDSS). The lower cost of DSS is primarily due to its lower alloy content, particularly the reduced levels of chromium, molybdenum, and nickel compared to SDSS. While SDSS offers superior strength and corrosion resistance, its higher material cost reflects these enhanced properties. However, the choice between DSS and SDSS should be based on the specific application requirements, as SDSS may provide cost savings in the long term by reducing maintenance and extending service life in harsh environments.

Click here to learn cathodic protection design for DSS pipes

Guided Cantilever Method

Written by Anu Sharma in Piping Design Basics,Piping Stress Analysis,Piping Stress Basics

The guided Cantilever method is one of the approximate methods for piping flexibility checking. This method is widely used by piping designers to check the approximate flexibility of simple piping configurations. A Guided cantilever is a beam whose one end is fixed and the other end is held parallel to its original position. The image shown in Fig. 1 represents a Regular and Guided Cantilever beam.

**Fig. 1: Guided Cantilever Beam Example**

Application of Guided Cantilever Method

The guided cantilever beam shown in Fig. 1 is basically half of the fixed beam subject to a concentrated load. To calculate approximate forces and moments in a given length of the pipe due to thermal expansion, these beam models are often used. However, the major application of the guided cantilever method is to calculate the leg length (absorbing leg) required for a given thermal displacement. The distance of the first guide after a long straight turn or the expansion loop length in between two fixed anchors can be approximately calculated using the guided cantilever method. Refer to Fig. 2 below.

**Fig. 2: Absorbing Leg Length using Guided Cantilever Method**

Using the guided cantilever method, the absorbing leg L, perpendicular to Dimension A (Fig. 2) can be calculated using the following Formula:

Here,

E=Elasticity Modulus
D=Pipe OD
S=Allowable Stress.
∆=Thermal Expansion

For Carbon steel, the above equation can be approximated as L=66 (D∆)^1/2

Assumptions in Guided Cantilever Method

The assumptions behind the guided cantilever method can be listed as follows:

The piping system has only two terminal points which are composed of a straight leg of a pipe with uniform thickness and size and the square corner intersection,
The thermal expansion is absorbed only by a leg in the perpendicular direction
All piping legs are parallel to coordinate axes.
The amount of thermal expansion a given length can absorb is inversely proportional to its stiffness.
The legs act as guided cantilevers subjected to bending under end displacements and the rotation of the end is not permitted.

Limitations of the Guided Cantilever Method

The guided cantilever method is limited to simple geometries only; For complex configurations, it can not be applied.

Differences between a Centrifugal Pump and a Positive Displacement Pump

Written by Anup Kumar Dey in Mechanical

Centrifugal and Positive displacement pumps are the two main categories of pumps used widely. The main purpose of both groups of pumps is to pump fluid from one point to another. But they have some distinct differences. The working principle of both these pump groups is different. A Centrifugal Pump transfers the kinetic energy of the motor to the liquid through the rotating impeller. This increases the velocity and pressure at the discharge. The discharge velocity remains constant when the motor rpm is constant. On the other hand, Positive displacement pumps trap a fixed volume of fluid in their cavity and force it to discharge into the pump outlet. So, it is a constant volume device. Positive displacement comes in rotary, reciprocating, or diaphragm style. Centrifugal pumps are high-capacity and relatively low-head pumps whereas positive displacement pumps are low-capacity high-head pumps. In the next paragraphs, we will discuss, other major differences between Centrifugal and Positive Displacement Pumps.

Centrifugal vs Positive Displacement Pump: Fluid Handling

With an increase in the fluid viscosity, the efficiency of the centrifugal pump decreases due to frictional losses. That’s why centrifugal pumps are not suitable for highly viscous fluids. Whereas, with an increase in viscosity, the efficiency of the positive displacement pump increases.

Also, positive displacement pumps can handle liquids with suspended solids and liquids with abrasive particles.

Centrifugal vs Positive Displacement Pump: Pump Speed & Shearing of Liquid

Centrifugal Pumps are high-speed pumps. It causes shearing of liquids. Hence, not suitable for sensitive mediums. On the other hand, positive displacement pumps operate at lower velocities which causes very little shear.

Centrifugal vs Positive Displacement Pump: Pump Performance

In centrifugal pumps, the flow varies with change in pressure whereas in positive displacement pumps flow remains constant with changing pressure. For both pumps, flow can be regulated by changing the speed. Fig. 1 below shows how a centrifugal pump and a positive displacement pump behave with changes in different factors.

**Fig. 1: Centrifugal Pump vs Positive Displacement Pump Performance**

The above curves show that “with an increase in Viscosity, Flow Rate and Efficiency of the centrifugal pump drops to a huge extent. Also, with changes in pressure head centrifugal pump flow rate and efficiency changes”

In a centrifugal pump the Net Positive Suction Head required (NPSHr) varies as a function of flow determined by pressure. But in a Positive Displacement pump, the NPSHr varies as a function of flow determined by speed. The lower the speed of a Positive Displacement pump, the lower the NPSHr.

Centrifugal vs Positive Displacement Pump: Efficiency

Centrifugal pumps perform better in the center of the curve known as BEP (best efficiency point). At lower or higher pressure levels, the centrifugal pump efficiency reduces. It is therefore suggested to operate centrifugal pumps within a window of 80-110% of its BEP for optimum pump performance. When moving far enough to the right or left from the curve center, pump life is reduced due to shaft deflection or increased cavitation.

Positive displacement pumps can operate at any point of the curve. The efficiency increases with an increase in pressure.

Centrifugal vs Positive Displacement Pump: Priming Requirement

Standard centrifugal pumps require priming before starting the pump. Whereas positive displacement pumps create a vacuum on the suction side; So fluid can automatically enter the pump. Positive displacement pumps are called self-primed pumps.

Centrifugal vs Positive Displacement Pump: Cavitation

Due to the presence of entrapped gases, centrifugal pumps are more susceptible to cavitation as compared to positive displacement pumps. Also, during low-flow operation, centrifugal pumps are more prone to overheating.

Centrifugal vs Positive Displacement Pump: Series and parallel operation

In parallel operation of two or more pumps to increase the flow. Normally, positive displacement (PD) pumps in parallel will provide larger flows as compared to centrifugal pumps as PD pumps will inherently compensate for the higher system pressure, and in the case of centrifugal pumps due to frictional losses the combined flow is not doubled.

For series operations in centrifugal pumps, the head created by each pump is added. But for PD pumps in series operation, no advantage is obtained and hence, PD pumps are not run in series.

Centrifugal vs Positive Displacement Pump: Which one to Select?

A Positive Displacement pump will be a preferred selection in the following situations:

For high viscous applications.
For variable pressure conditions.
When the pump will be operating away from the BEP.
For changing viscosity conditions.
For very high-pressure applications.
For shear-sensitive liquids.

However, these are only a few criteria. Actual pump selection is more detailed and an experimental study is required for selecting the right pump.

Centrifugal vs Positive Displacement Pump: Cost

The operational and maintenance cost of a positive displacement pump is normally lower than the a centrifugal pump. The initial cost can be more or equivalent to a centrifugal pump depending on the positive displacement pump type.

Due to Low-speed operation, Positive displacement pump seals work longer as compared to centrifugal pump seals.

Centrifugal vs Positive Displacement Pump: Applications

Centrifugal pumps are best suited for thin liquids possessing low viscosity levels like water, thin oils and fuels, and chemicals. It is, therefore, the most commonly used for high-volume applications with high flow rates at low pressures. Some of the popular applications of centrifugal pumps include

Irrigation
Municipal water and water supply systems
Chemical, Petrochemical, and light fuel transfer stations
Air conditioners and water circulators
Boiler feeds
Firefighting
Cooling towers

On the contrary, positive displacement pumps are used for high pressure and low flow conditions to move highly viscous fluids. Some of the popular applications include

Manufacturing facilities to move thick paste and jelly.
Municipal Sewage systems.
Thick Oil Processing
Food Processing plants

The main differences between Centrifugal Pump and Positive Displacement Pumps are tabulated below

Centrifugal Pump	Positive Displacement Pump
The efficiency of centrifugal pumps decreases with increasing viscosity	The efficiency of the positive displacement pump increases with increasing viscosity
The flow of the centrifugal pump varies with changing pressure	The flow for positive displacement pumps is insensitive to changing pressure
The Pump Efficiency decreases at both higher and lower pressures for centrifugal pumps.	The efficiency of positive displacement pumps increases with increasing pressure
For centrifugal pumps, Priming is Required	Pump Priming is not required for positive displacement pumps.
Centrifugal pumps provide a Constant Flow	Positive displacement pumps provide a Pulsating Flow
Centrifugal pumps are High-Velocity Pumps	Positive displacement pumps have Low internal velocity
Centrifugal pumps are High Capacity and Low Head	Low Capacity and High Head is the characteristic of positive displacement pumps.
Centrifugal pumps work based on Centrifugal Action	Positive displacement pumps work based on rotary, reciprocating, or diaphragm principle

Centrifugal Pump vs Positive Displacement Pump

Flange Bolt Torque Calculation and Pipe Flange Bolt Torque Chart

Written by Anup Kumar Dey in Mechanical,Piping Design Basics,Piping Interface

Proper bolt loading is essential for ensuring proper sealing of the flanged joint to avoid flange leakage problems. This bolt load for gasket sealing and flange seating is provided by Flange Bolt Torque. So Flange Bolt Torque calculation should be done with utmost care for the proper functioning of the flanged joints. However, there is no direct method of measuring this load on the gasket, but the applied torque on the flanged bolts can be measured and controlled. In this article, we will learn the basics of flange bolt torque calculation and some of the typical torque values in a chart format.

What is Flange Bolt Torque?

Torque is a measure of rotational force applied to a bolt or screw, and it plays a vital role in achieving the correct clamping force on flanged connections. Proper torque ensures that the flange bolts are neither too tight nor too loose, which is essential for preventing issues such as leaks, flange separation, and joint failure.

When a flange is bolted together, the torque applied to the bolts compresses the gasket or sealing material between the flanges, creating a tight seal. This clamping force must be carefully controlled to maintain the integrity of the seal and ensure the system functions correctly under operating conditions.

Flange Bolt Torque Calculation Formula

Bolt Torque is the twisting or turning force applied to tighten the nut on a bolt. Using a calibrated torque wrench (Manual or Hydraulic Torque Wrench), flange bolt torque can be measured during flange assembly. This torque creates an axial force in the bolt. More torque is applied the nut stretches the bolt more and the load on the gasket increases. Bolt torque is calculated for a flanged assembly using the following equation.

Applied Torque, T= (k∙f∙d)/12 in FPS Unit

Where:

T=Torque in ft-lb
k=Dimensionless nut factor or tightening factor
f=axial force in pounds
d=Nominal bolt diameter in inches

In the Metric System,

Torque Applied, T = (k.d.f)/1000

where

T = Torque in N-m
f = Bolt load in N
d = Bolt diameter in mm
k=Dimensionless nut factor or tightening factor

Nut Factor on Flange Bolt Torque Calculation

The nut factor or tightening factor (k) is a “modified” friction factor. It is an empirically derived correlation factor that includes the impact of friction. The nut factor depends on various factors including the following:

Geometric factor – shape or type of threads
The friction of the nut against the bearing surface of the flange
Friction between threads of nuts and bolts
Bolt diameter
Bolt material
Assembly temperature, etc.

Because of so many factors, the applied torque between the two fasteners always varies between 20-30%. A small change in the nut factor/tightening factor results in large changes in the gasket load. For same torque values with a 0.1 nut factor would produce twice the axial force as a 0.2 nut factor. That’s why well-lubricated bolts, nuts, and washers are always preferred.

Factors Affecting the Applied Torque

The required torque in a flanged joint is dependent on various factors:

Nut and bolt size, class, and material
Burr of the nuts
Lubrication
Dust, chips, and dirt on bolts and nuts
Notches
State of the flange surface on which to rotate
Gasket material and thickness

Pipe Flange Bolt Torque Chart

Even though flange blot toque calculation is possible, they are normally selected from the pipe flange bolt torque chart. The entire bolt pattern shall be tightened at least three times around the flange at 30%, 70%, and 100% of the torque value. For bolt diameters greater than 1.25”, Hydraulic Tensioning is recommended to achieve more uniform gasket stress. The following images provide some typical Pipe flange bolt torque charts.

**Fig. 2: Typical pipe flange bolt torque chart for Spiral Wound Gaskets**

**Fig. 3: Typical pipe flange bolt torque chart for Spiral Wound Gaskets with Inner and Outer Rings**

**Fig. 4: Typical Torque values for Line Seal gaskets**

Typical toque values for API 6A Wellhead Connection Flanges — **Fig. 5: Typical torque values for API 6A Wellhead Connection Flanges**

**Fig. 6: Typical Torque Values for Metallic Lined Pipes**

**Fig. 7: Typical Torque Values for HDPE Flange Adapters**

Flange Bolt Torque Sequence

The first step in flange bolt torquing is to examine the flange alignment and inspect the nut, gasket, stud, or bolts. Here’s a simplified version of the bolt-torquing sequence:

Finish All Pre-Checks: Before you start tightening, make sure everything is checked.
Tighten Bolts in a Criss-Cross Pattern: Follow the criss-cross pattern for tightening and make sure to use three passes with the final torque value.
Pass 1: Tighten bolts to 30% of the final torque. Check that the gasket is compressing evenly.
Pass 2: Tighten bolts to 60% of the final torque.
Pass 3: Tighten bolts to the full final torque (100%).
Final Check: After the three passes, go over the bolts again using the final torque in a criss-cross pattern until the nuts don’t turn anymore.

The following images (Fig. 8 to Fig. 10) show the torquing sequence with respect to the number of bolts:

**Fig. 8: Bolt Torquing Sequence for 4-Bolt and 8-Bolt Flanges**

**Fig. 9: Bolt Torquing Sequence for 12-Bolt and 16-Bolt Flanges**

Bolt Torquing Sequence for 20-Bolt and 24-Bolt Flanges — **Fig. 10: Bolt Torque Sequence for 20-Bolt and 24-Bolt Flanges**

The following table provides the required flange bolt torque sequence

Flange Bolt Torque Sequence Table (4-bolt to 32-bolt)
Number of Bolt / Stud (Refer to ASME B16.5 with Respective Pressure Class)	Required Bolt Tightening Sequence
4-bolt Flange	1,3,2,4
8-bolt Flange	1,5,3,7,2,6,4,8
12-bolt Flange	1,7,4,10,2,8,5,11,3,9,6,12
16-bolt Flange	1,9,5,13,3,11,7,15,2,10,6,14,4,12,8,16
20-bolt Flange	1,11,6,16,3,13,8,18,5,15,10,20,2,12,7,17,4,14,9,19
24-bolt Flange	1,13,7,19,4,16,10,22,2,14,8,20,5,17,11,23,6,18,12,24,3,15,9,21
28-bolt Flange	1,15,8,22,4,18,11,25,6,20,13,27,2,16,9,23,5,19,12,26,3,17,10,24,7,21,14,28
32-bolt Flange	1,17,9,25,5,21,13,29,3,19,11,27,7,23,15,31,2,18,10,26,6,22,14,30,8,24,16,32,4,20,12,28

Table 1: Flange Bolt Torque sequence for flanges with 4 to 32 bolts

Hot Torquing

When the tightening of all bolts of a flanged joint is performed at the operating temperature, the process is known as Hot Torquing. For flanges that are known to leak at elevated temperatures due to gasket relaxation, the Hot Torqueing method is applied. It is normally performed when the temperature of the flange or the bolts is between 150°C and 230°C, or within 24 hours of a unit start-up if the joint temperature remains below 150°C.

Flange Bolt Torquing Guidelines

The following guidelines should be followed

Flanges and Gaskets must be inspected prior to torque application.
All working surfaces must be cleaned and lubricated properly.
Gaskets must be new, Re-use is normally not permitted.
Flange Bolt torquing must be done following the appropriate flange bolt tightening sequence. To know more about the flange bolt tightening sequence, Read: Flange Bolt tightening Procedure/Bolt Tightening Steps

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