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Poisson’s Ratio-Formula, Significance, Equation, Example

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

What is Poisson’s Ratio?

Poisson’s ratio of a material is a very important parameter in material science and engineering mechanics. When a force is applied to a bar it deforms (elongates or compresses) in the axial (longitudinal) direction. At the same time, a deformation is observed in the transverse (width) direction as well. Poisson’s ratio relates these changes in the transverse direction and axial direction. This effect is known as Poisson’s effect which is named after the French mathematician and physicist Simeon Poisson. The Poisson’s ratio is defined as the ratio of the transverse strain to that of the axial strain under the influence of the same force. It is a material property and remains constant.

What is Poisson's Ratio?
Fig. 1: Definition of Poisson’s Ratio

Poisson’s Ratio Formula

Let’s deduce the formula for Poisson’s ratio. From the above definition, Poisson’s ratio can be expressed mathematically as

Poisson’s Ratio=Transverse (Lateral) Strain/Axial (Longitudinal) Strain

Let’s understand this philosophy using the example in Fig. 2. In this image, A tensile force (F) is applied in a bar of diameter do and length lo. With the action of this force F, the bar elongates and the final length is l. Also, the diameter reduces and the final diameter is d.

Poisson's ratio explanation
Fig. 2: Poisson’s ratio explanation

So from the above, Axial Strain, Longitudinal Strain, or Linear Strain= (Change in Length/Original Length)=(l-lo)/lo. Similarly, Lateral Strain or Transverse Strain=(Change in Diameter/Original base Diameter)=(d-do)/do. So, as per the definition, the equation of Poisson’s Ratio or Poisson’s ratio formula can be written as follows

Poisson’s Ratio=Lateral Strain/Longitudinal Strain={(d-do)/do}/((l-lo)/lo}= lo(d-do)/do(l-lo)

Poisson’s Ratio Example

Similar to Young’s modulus, Poisson’s Ratio is the property of a material and is constant. However, the value of Poisson’s ratio changes with temperature. Young’s modulus, the shear modulus, and the bulk modulus are related to Poisson’s ratio. For these modules to have positive values, the Poisson’s ratio of a stable, isotropic, linear elastic material must be between −1.0 and +0.5. The value of Poisson’s ratio normally ranges between 0.0 and 0.5. The following table provides a few typical values (range) of Poisson’s ratio for common materials.

MaterialPoisson’s Ratio
Carbon Steel0.27–0.30
Cast iron0.21–0.26
Stainless steel0.30–0.31
Aluminium-alloy0.32
Copper0.33
Inconel0.27-0.38
Gold0.42–0.44
Silver0.37
Platinum0.39
Glass0.18–0.3
Foam0.10–0.50
Sand0.20–0.455
Molybdenum0.307
Concrete0.1–0.2
Clay0.30–0.45
Tin0.33
Titanium0.265–0.34
Magnesium alloy0.252–0.289
Rubber0.48-0.4999
Brass0.331
Bronze0.34
Ice0.33
Lead0.431
Monel0.315
Nickel0.31
Polystyrene0.34
Limestone0.2-0.3
Nickel Steel0.291
Tungsten0.28
Metallic Glass0.276–0.409
Boron0.08
Beryllium0.03
Cork0.0
Re-entrant foam-0.7
Table 1: Example of Poisson’s Ratio

Unit of Poisson’s Ratio

Poisson’s ratio is the ratio of two strains. Both longitudinal and lateral strains are dimensionless. So Poisson’s Ratio is dimensionless. There is no unit for Poisson’s Ratio.

Symbol of Poisson’s Ratio

Poisson’s ratio is normally denoted by the Greek letter ν (nu). However, this is not standardized. So users can use any symbol for Poisson’s ratio at their discretion.

What is Negative Poisson’s Ratio?

In general, for common materials, the cross-section becomes narrower when stretched. So, Poisson’s ratio is positive for most materials. However, certain materials (Origami-folded materials, certain solid woods, and certain crystals) show a negative Poisson ratio. This means when they are stretched in the longitudinal axis, their cross-sectional area increases. The main reason behind such type of behavior is due to their uniquely oriented, hinged molecular bonds. These materials are known as auxetic materials. Note that, more than three hundred crystalline materials have negative Poisson’s ratio in certain states. Some of the typical examples of auxetic materials are Li, Cu, Rb, Na, K, Ag, Fe, Ni, Co, BAsO4, Cs, Au, Be, Ca, Zn Sr, Sb, MoS2, Living bone tissue, Non-carbon nanotubes, Auxetic polyurethane foam, Chain organic molecules, etc.

Applications of Poisson’s Ratio

Poisson’s ratio is a very important parameter of materials. In engineering mechanics, the strength of materials, structural engineering, machine design, and fluid flow problems, Poisson’s ratio finds wide application. Some of the common applications of Poisson’s ratio are listed below:

In pressurized pipeline flow problems, Poisson’s effect has a significant influence. The internal pressure creates hoop stress in the pipe material. Due to Poisson’s effect, this hoop stress causes the pipe to increase in diameter and slightly decrease in length.

For studying the effect of stress, strain, and modulus of materials, the Poisson’s ratio plays an important role. It is an important parameter while converting from one modulus to the other.

The near-zero Poisson’s ratio for Cork material makes it ideal as bottle stoppers.

In structural engineering, Poisson’s ratio is essential for analyzing the deformation and stability of structures. It helps engineers predict how materials will respond to different load conditions.

Engineers use Poisson’s ratio in the design and manufacturing of components to predict and control deformations. This is crucial in ensuring that structures and products meet safety and performance requirements.

Poisson’s ratio is crucial in the design and analysis of composite materials, where different materials are combined to achieve specific mechanical properties. Understanding how these materials deform is essential for their effective use.

FAQs related to Poisson’s Ratio

In this section, we will try to answer some of the frequently asked questions related to Poisson’s Ratio to clarify the subject better.

What is Poisson’s Ratio?

Poisson’s ratio of a material is defined as the ratio of the lateral strain (change in the width per unit width of a material) to the axial strain (change in its length per unit length) due to the action of a Force.

What does a Poisson ratio of 0.5 Means?

Poisson’s ratio of 0.5 signifies that due to the application of a force the deformation change in the width direction is half the deformation change in the axial direction. Normally, for perfectly incompressible isotropic materials the value of Poisson’s ratio is 0.5. Rubber is a typical example.

What is the Poisson’s Ratio of Steel?

The Poisson’s ratio of steel is normally 0.27 to 0.30. When more authoritative data from tests are not available, normally 0.3 is used in design calculations as Poisson’s ratio of Steel material.

Can Poisson’s ratio be greater than 1?

For isotropic material, Poisson’s ratio can not exceed 0.5. However, for anisotropic materials, the value of Poisson’s ratio can be greater than 1 in certain directions. For example, polyurethane foam.

Why Poisson’s ratio is important?

Poisson’s ratio of a material is very important for studying the stress and deflection properties of engineering materials like pipes, beams, vessels, etc.

What if Poisson’s Ratio is Zero?

The Poisson’s ratio of Zero means it does not deform in the lateral direction during elongation or compression in the axial direction by the application of a force. The material Cork is believed to have a near-zero (~0) Poisson’s ratio. This is the reason Corks are ideally used as bottle stopper as it does not expand even when compressed.

Which material has the highest Poisson ratio?

Ignoring specifically designed anisotropic materials, Rubber has the highest value of Poisson’s ratio at 0.4999.

What is the Poisson’s Ratio of Aluminum?

The Poisson’s ratio of Aluminum normally varies between 0.3 to 0.35.

What is the Poisson’s Ratio of Concrete?

The Poisson’s ratio of Concrete normally varies between 0.1 to 0.25. For design calculation, in the absence of data, normally 0.2 is used as Poisson’s ratio of Concrete.

Few more related articles for you.

Introduction to Stress-Strain Curve (With PDF)
Stress or Strain: Which comes first?
Hooke’s Law: Statement, Equation, Graph, Applications, Limitations (With PDF)
Young’s modulus: Young’s modulus of Steels [With PDF]

What is Induction Bending? Hot Bending vs. Cold Bending

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

What is Induction Bending?

Induction Bending is a precisely controlled and efficient piping bending technique. Local heating using high-frequency induced electrical power is applied during the induction bending process. Pipes, tubes, and even structural shapes (channels, W & H sections) can be bent efficiently in an induction bending machine. Induction bending is also known as hot bending, incremental bending, or high-frequency bending. For bigger pipe diameters, when cold bending methods are limited, Induction bending of pipe is the most preferable option. Around the pipe to be bent, an induction coil is placed that heats the pipe circumference in the range of 850 – 1100 degrees Celsius.

Induction Bending (Hot Bending) Process

The following steps are performed for the induction bending of the pipe or pipeline system:

  • The pre-inspected pipe or pipeline to be bent is placed in the machine bed and clamped hydraulically.
  • Around the pipe, induction heating coils and cooling coils are mounted. To ensure uniform heating, the induction coil can be adjusted with a 3-plane movement.
  • By adjusting the radius arm and front clamp, the required bend radius can be fixed. There is one pointer to display the correct degree of turning.
  • Arc lengths are marked on the pipe. The pipe can be moved slowly whilst the bending force is applied by a fixed radius arm arrangement.
  • Once everything is set as required, hydraulic pressure, water level, and switches are inspected and then the induction bending operation is started.
  • Upon reaching the required temperature range, the pipe is pushed forward slowly at a speed of 10-40 mm/min, and the operation is stopped when the specified bend angle and pre-determined arc length are reached.
  • Just beyond the induction coil, the heated pipe material is quenched using a water spray on the outside surface of the pipe.
  • In the next step, the induction bend is removed and sent for inspection and measurement of tolerances.
  • The final step for the induction bends is the use of post-bend heat treatments for stress relieving, normalizing, etc.

Fig. 1 below shows a typical induction bending process.

Typical Induction Bending Process
Fig. 1: Typical Induction Bending Process

Induction bends are normally produced in standard bend angles (e.g. 45°, 90°, etc.). However, depending on the requirement they can be custom-made to specific bend angles. Compound out-of-plane bends in a single joint of pipe can also be produced. The bend radius for induction bending is specified as a function of the nominal pipe diameter (D) like 5D, 30D, 60D bends, etc. Fig. 2 below provides a schematic diagram of the induction bending mechanism.

Schematic Diagram of Induction Bending Mechanism
Fig. 2: Schematic Diagram of Induction Bending Mechanism

The important parameters that affect the induction bending process are:

  • Pipe Diameter
  • Surface Contamination
  • Process Parameters like Temperature, Speed, Cooling rate, etc
  • Bend Radius
  • Bend Angle
  • Process Interruptions
  • Hardenability of the Pipe Material, etc.

Induction Bending Standards

As the complex induction bending process involves various steps for producing bends, it must be controlled precisely to produce quality items. Different codes and standards govern this process. The most conventional and widely used standards for induction bends are the

  • ASME B16.49
  • ISO 15590-1(en)
  • Shell DEP 31.40.20.33

Advantages of Induction bending

The major advantages of induction bending are:

  • Lower risk of wall thinning and deformation of the cross-section
  • Thin-walled pipes can easily be bent.
  • Less costly and available faster than traditional components.
  • Uniform hardness and thickness.
  • Smooth flow due to large radii reducing friction, wear, and pump energy.
  • No pipe wrinkles.
  • Only a straight pipe is required for induction bending.
  • Precise bending radius and angle.
  • Diverse bendings: square pipe, flat bar, I-beam, H-beam, channel section, etc.

Applications of Induction bends

The majority of the Induction bends are found in the pipeline systems for liquid and gas transportation. Additionally, they are found in applications requiring large diameter bends with precision and reliability and where the laminar smooth flow is required. Typical applications of induction bends include the following industries:

  • Onshore and Offshore pipelines in the oil & gas sector
  • The refinery, chemical, and petrochemical sector
  • Powerplants
  • Industrial equipment
  • Infrastructure constructions and steel building constructions (a.o. bridges, construction, art objects, roller coasters)
  • Offshore energy (a.o. J-tubes, S-jubes)
  • Metallurgical industries
  • Shipbuilding, etc.

Induction Bending Materials

The following pipe materials are normally used for forming by induction bending:

Induction (Hot) Bending vs. Cold Bending

The main differences between Induction bending or Hot bending and Cold Bending are listed below in a tabular format:

Induction Bending / Hot BendingCold Bending
Heat Input is a must in induction or hot bendingCold Bend does not need any added heat.
Hot bending is a Slow ProcessCold bending is a Fast Process as no heating & cooling is involved
Better control is achieved in Hot bending.Cold bending does not provide precise control.
Highly efficient complex types of machinery are used for hot bending.The cold bending process uses Simple machines.
The hot bending Process is efficient for larger pipe diametersNot suitable for large pipe diameters. Cold bending is limited to smaller-diameter piping only.
Induction bending is a Costly processCold bending is not expensive.
In Hot bending usually no wrinkling on the pipe surface.The is a High probability of wrinkling on the pipe surface during cold bending.
The required force in hot bending is normally less.The physical Force requirement in cold bending is comparatively more
Hot Bending vs. Cold Bending

To get some more insight about hot bending and cold bending you can click here.

Pressure Transient Analysis for Liquid HC Pipelines | Water Hammer Calculation-Joukowsky Formula

Written by Ahmed Shafik in Mechanical,Pipeline,Piping Design Basics,Piping Interface,Process

What is Surge in Liquid HC P/L?

Its commonly called “Water Hammer”, and is defined as a sudden increase in pressure due to an instantaneous conversion of momentum to pressure when flowing liquid stops quickly.

Hydraulic surge is often caused by the transformation of kinetic energy to potential energy as a stream of fluid is suddenly stopped.

Once the pump tripped, you will observe that the pressure in the immediate discharge is decreasing because the flow still going forward with no current supply and a strong wave will rush back towards the pump discharge coming all the way from the close endpoint creating the pressure spike.

As noticed in the below graph, pressure spikes will continue hitting the pipe/pipeline trying to release the generated excessive energy and therefore your system will be at risk.

Water Hammer for Valve Operation
Pressure Surges

ASME B31.3 defined that the pressure rise due to surge and other normal operation variations shall not exceed the internal design pressure at any point in the piping system and equipment by more than 33%.

Here you have to ask yourself, Do I Have a Safe & Reliable System to Operate?!!!

Why Surge could happen?

All of the above will generate pressure waves that travel both upstream and downstream from point of origin.

Please note that some pipelines are in transient operations over 75% of the time.

Surge (pressure rise) increases as much as the pipeline segment length increases since the contained momentum will be higher (more volume).

A pressure surge can consist of multiple events, resulting in up to ten times the normal pipeline pressure. When a  surge relief valve opens, it vents the pressure to a safety system. Also, it is worth mentioning that Surge pressure is created during the last 20% of valve closure.

Other notes about the Water Hammer

  • The rapid closure of a valve can result in an initial reduced pressure downstream which may be sufficient to reduce the absolute pressure below the vapor pressure and generates a cavitation scenario.
  • The cavitation might lead to higher transient pressures and unbalanced forces.
  • Also, Fast pressurization of a closed system, can double the pressure rise at the far end of the system as the pressure wave is reflected from the closed end.
  • This can arise either from the fast opening of a  valve at the system inlet or due to pump startup with the pump discharge valve open.
  • The surge may result in the creation of huge unbalanced forces within the piping system which may damage the supports, collapse pipe bridges, or even line rupture and displacement from its original location.
  • Experiences indicate that the failure of pipework supports as a result of pressure surge is more likely than pipeline rupture due to overpressure.

Challenges of Water Hammer

  • Surge can significantly exceed the Maximum Allowable Operating Pressure (MAOP) plus any additional overpressure allowance, typically 33% above MAOP.
  • The sudden transition from momentum force (flow) to pressure force will lead to shaking/vibration of pipeline/piping and might lead to severe damage in pipeline/piping if the system design is not adequate.
  • Your system could be equipped with a surge relief valve, however, missing calibration and regular checks could lead to failure of the valve to act as required and accordingly lead to destructive failure of the system.
Surge Protection System Behaviour

Serious Industrial Incidents due to Lack of Proper Surge Protection

  • In 1999, a pressure relief valve failed on a 16-inch gasoline pipeline operated by the Olympic  Pipe Line Company in Bellingham, Wash., spilling 277,000 gallons of gasoline into the river. The gasoline exploded, killing three young boys. The incident resulted in five felony convictions for  Olympic employees and a $75 million wrongful death settlement.
  • In 2009, at the Sayano-Shushenskaya hydroelectric plant in Siberia, a severe water hammer ruptured a piping segment going to a turbine due to improper surge relief system design. A  transformer exploded, killing 69 people.
Impact of Water Hammer
Water Hammer Impacts

Calculation of Water Hammer

A- Manual calculation – Joukowski formula:

  • Role of Thumb used in the past to estimate the surge pressure, considering that the only  variable is the velocity, P is equal to

0.8 * Weight of liquid per cubic foot * Velocity Change

  • Another old way to estimate is to consider a 50 Psi change in pressure with the velocity change of  every 10 ft/sec

Can you still use these formulas?

Yes BUT ONLY while you are standing for a quick and rough estimation.

  • The Joukowsky equation is a simplified method for calculating the peak transient pressure  experienced when a valve is closed against a fluid in motion and may be represented as follows:

ΔP=ρ a Δv

  • ρ Liquid Density
  • a Pressure Wave Velocity
  • Δv Change in Liquid Velocity
  • The Joukowsky equation takes into consideration the elasticity of the pipe wall and the compressibility of the fluid itself through the calculation of the speed of sound (a), however, assumes instant closure of the valve.

Manual calculation – Joukowski formula

Joukowski formula

Required Inputs for Joukowsky Equation:

  1. Fluid Properties: Density, Viscosity, Vapor pressure, Bulk modulus & Temperature.
  2. Pipe Properties: Roughness, Young Modulus & Poisson ratio.

Explanation of main inputs:

  • Bulk modulus: is the property characterizing the compressibility of a fluid, i.e. how easily a unit volume of a fluid can be changed when changing the pressure working upon it.
  • The Bulk Modulus Elasticity can be expressed as:

Some fluids have ready-calculated Bulk Modulus Elasticity:

  • Relative roughness: Is the ratio between absolute roughness and pipe diameter  Relative roughness can be expressed as:

Some pipe material Roughness is available :

  • Young Modulus: is a measure of the stiffness of an elastic material.  It is used to describe the elastic properties of pipeline/piping.
  • Young’s modulus can be expressed as

Some pipe material’s Young Modulus are available :

  • Poisson ratio: the ratio of the relative contraction strain (transverse, lateral or radial strain) normal  to the applied load – to the relative extension strain (or axial strain) in the direction of the applied  load

Poisson’s Ratio can be expressed as

Some pipe material Poisson’s ratio is available :

Calculation sheet

Limitations – Joukowsky formula:

  • Although the Joukowsky formula is far better and more precious than the past rough estimation formulas, still it can be only applicable to a limited subset of fluid systems.
  • Its application should be limited to situations matching the following criteria: Simple ‘linear’ piping systems i.e. there are no branches by which pressure waves can be reflected back and cause constructive interference in the mainline. Valve closure time is significantly shorter than the pressure wave communication time. System frictional losses are similar to that of a water transport system.
  • Additionally, the Joukowsky equation does not consider column separation in its analysis of fluid hammer.  Column separation can often result in surge pressures exceeding those predicted by the Joukowsky equation and therefore the Joukowsky equation should not be applied when analyzing a system in which the pipeline pressure can rapidly drop below the fluid vapor pressure.
  • As a process engineer, you can use it to verify vendor documents or to identify the healthiness of your system,  however, for accurate and precise data you need to run PIPENET or similar software to estimate accurately the pressure rise. Then you will be translating this data into generated forces.
  • Once you have the generated forces, pick up the phone and call the piping engineer to run CAESAR software which will verify whether the piping/pipeline is granted well-designed supports and structure to make sure that it will not go anywhere else after the surge event occurs.

B- Pressure Transient Assessment using Modelling Software

There are currently various software packages that can be used for analysis such as

  • HyTran
  • Flowmaster
  • WANDA
  • Hammer
  • AFT Impulse
  • PIPENET
  • PTRAN
Sample of Pressure Transient Assessment using PIPENET
LNG Bunkering System Pressure Transient using PIPENET

Surge Protection Systems

Initially, we need to agree on the fact that the surge phenomenon is inevitable and therefore we have to identify an optimized option to protect our system with the least associated cost (CAPEX / OPEX). Please refer to our previous article on Optimization @ https://whatispiping.com/process-optimization

Design Consideration of Surge Protection systems:

  • The design of a complete surge relief system is dependent upon a complex range of factors, including the potential for pressure increases, the volumes which must be passed by the surge relief equipment in operation, and the capacity of the system to contain pressures.
  • Control or ESD valve closure times can also affect surge pressures in a pipeline. By extending valve closure time, a more gradual flow decay can be achieved.
  • Control narrative and system interlocks to ensure Staged pump shutdown sequence and linked ship/shore ESDs when your facility is linked to loading berths/jetties.
  • Carry out transient/surge analysis using detailed computer modeling to simulate the complex interactions of equipment, pipelines, and fluid to normal, fault, and emergency events.
  • Design piping to withstand maximum surge pressure – MSP.
  • Although many design approaches can help reduce surge pressures in pipelines, going for a higher pipe rating or massive support arrangements aren’t recommended for an associated significant cost, and a  surge relief valve is found to be the most feasible option to protect the system.
  • A correctly designed surge relief system will include components to dampen or slow the relief valve on closing, and this often requires sophisticated reverse flow plots.
  • In nitrogen-loaded Surge Relief valves, attention must be paid to the nitrogen gas system. The nitrogen system must supply a constant pressure (setpoint) to the modulating valve, even under conditions of varying ambient temperatures. Normally, the system is designed to use standard gas bottles and has its own control system to regulate the nitrogen supply pressure.

Surge Relief Solutions / Devices:

  • Ensure Proper design is applied considering the worst-case scenario with its respective control narrative for valve interlocking and proper mitigating means are in place.
  • MOVs / ESD Closing time are enough to absorb the wave velocity created by Surge. This can be assured by having a proper Equipment strategy in place which will ensure that Surge relief valves’ set points are verified and the valves are being calibrated on regular basis to ensure that they will be operated whenever required.
  • Ensure that operating procedures are in place and operations are well-trained and competent to operate.
  • Line design pressure/rating.
  • Piping Supports are well designed to withstand the shaking/vibration resulting from Surges.
  • Surge relief valve and associated relief Drum.

In general, Protection systems can be classified as either Active or Passive:

A- Active Protection

By using devices to actively protect the systems against the effects of pressure surge during  pipeline normal operation like:

B- Passive Equipment for Surge Protection

  • Surge Vessels.
  • Surge Shafts.
  • Air Valves.
  • Vacuum Breakers.
  • Pressure Relief Valves.
  • Surge Anticipation Valves.
  • Intermediate Check valves.

Please note that if there is a shortfall or limitation of this document then it is because of me, while any success or correctness would be solely from the great and generous Allah.

Resources

  • ASME B31.4 Pressure Pipeline Code prescribes requirements for the design, materials, construction, assembly, inspection, and testing of piping transporting liquids such as crude oil, condensate, natural gasoline, natural gas liquids, liquefied petroleum gas, liquid alcohol, liquid anhydrous ammonia, and liquid petroleum products between producers’ lease facilities, tank farms, natural-gas processing plants, refineries,  stations, ammonia plants, terminals, and other delivery and receiving points.
  • API RP 520, ‘Sizing, Selection, and Installation of Pressure-Relieving Devices in Refineries, Part 1 – Sizing and Selection’, Seventh Edition,  January 2000.
  • API RP 521, ‘Guide for Pressure-Relieving and Depressurizing Systems’ Fourth Edition, March 1997.
  • CRR 136/1998, Workbook for Chemical Reactor Relief Sizing, HSE.
  • DIERs Manual ” A perspective on Emergency relief system” by DIER Technical Committee. Guide to Pressure Relief (PSG 8), Part  C: Section 5, 1999.
  • Chemical Engineer’s Handbook – Perry, Seventh Edition
  • “Investigation Report: Refinery Explosion and Fire,” U.S. Chemical Safety and Hazard Investigation Board, March 2007.
  • “Olympic Pipe Line accident in Bellingham kills three youths on June 10, 1999,” History.org.
  • “Lessons from Russian Hydroelectric Plant Accident,” Engineering Ethics Blog.
  • “An Introduction to Liquid Pipeline Surge Relief,” Emerson Process Management, April 2007, page 2.

Want to know more!!! Kindly refer to the following:

Introduction to Pressure Surge Analysis (With PDF)
Understanding Centrifugal Compressor Surge and Control
Water Hammer Basics in Pumps for beginners
Pipe Stress Analysis from Water Hammer Loads

Flare System: Definition, Types, Components, and Design

Written by Ahmed Shafik in Mechanical,Piping Design Basics,Piping Interface,Process

What is a Flare System?

As per CAPP – Canadian Association of Petroleum Producers, a flare system is defined as the controlled burning of natural gas that cannot be processed for sale or use because of technical or economic reasons.
On the Other hand, API 537 defines a flare system as the system provided in a refinery or petrochemical plant to ensure the safe and efficient disposal of relieved gases or liquids.

The efficient flaring system exists at any facility accommodating Hydrocarbon pressurized systems such as:

  • Refineries.
  • Natural gas processing plants.
  • Petrochemical plants.
  • Wells / Rigs.
  • landfills.

Application of Flare System

Flares are primarily used for burning off flammable gas released by pressure relief valves during any over-pressure scenario of plant process unit/equipment, due to process upset or during startups & shutdowns, and for the planned combustion of gases over relatively short periods.

Flare systems are used for a variety of activities such as:

  • Normal Operation (as defined above).
  • Startup.
  • Maintenance.
  • Testing.
  • Safety and emergency purposes.

Features of Flare System

Fig. 1 shows a typical flare system in a process plant. The important features of a flare system are

  • When any equipment in the plant is over-pressured, the pressure relief valve is an essential safety device that automatically releases gases and sometimes liquids.
  • The height of the flame depends on the volume of released gas, while brightness and color depend upon composition.
  • The released gases and liquids are routed through large piping systems called flare headers to the flare. The released gases are burned as they exit the flare stacks.
  • Commonly, flares are equipped with a vapor-liquid separator (also known as a knockout drum – KOD) upstream of the flare to remove any large amounts of liquid that may accompany the relieved gases to avoid fireballs.
  • Steam is very often injected into the flame to reduce the formation of black smoke.
  • When too much steam is added, a condition known as “over-steaming” can occur resulting in reduced combustion efficiency and higher emissions.
  • To keep the flare system functional, a small amount of gas is continuously burned, like a pilot light, to assure that the flare system is always ready for its primary purpose as an over-pressure safety system.
Typical Flare System
Fig 1: Typical Flare System

When does a Flaring Incident Take Place?

The flaring system is normally activated during the following situations

  • Initial startup.
  • Poor reliable plant / old.
  • Planned maintenance / Projects / Shutdown activities.
  • Process upset led to overpressure scenarios.
  • Emergency situation.

Gas Flaring Composition

There is in fact no standard composition and it is, therefore, necessary to define some group of gas flaring according to the actual parameters of the gas.

  • For NGL & LNG plants, the flared gas composition is expected to be 80 – 90 % C1 & balance is C2+ & Inert gases such as N2 and CO2.
  • Gas flaring from refineries and Petrochemical plants will commonly contain a mixture of paraffinic & Olefinic HC, inert gases, and H2.
  • In landfill gas & biogas plants, the flared gas composition is a mixture of CH4 and CO2 along with small amounts of other inert gases.
  • Note: Changing gas composition will affect the heat transfer capabilities of the gas and affect the performance of the measurement by a flowmeter.

Flare system components

Fig. 2 below shows a typical flare system with elevated flare. The important flare system components are marked in the image.

Typical Flare System with Elevated Flare
Fig. 2: Typical Flare System with Elevated Flare

Types of Flares

  • Vertical
    • Self Supported.
    • Guyed (Cables).
    • Derrick supported (Steel).
  • Horizontal
    • The flared fluids are piped to a horizontal flare burner that discharges into a pit or excavation.
  • Enclosed Flame Flares
    • They are designed to conceal flares from direct view, reduce noise, and minimize radiation.

All the above flare types can be either single-point or Multi-burner staged flares. Also, Flares can be classified as either

  • smokeless (using air, steam, pressure energy, or any other means to create turbulence and entrain air within the flared gas stream ) or
  • Non-smokeless flares (used when smoke isn’t a concern or the flared fluid doesn’t generate smoke such as H2, NH3, H2S…etc).

Flare System Selection Considerations

The Flare system is normally selected based on the following considerations.

  • Safety requirements and environmental regulations must be satisfied.
  • CAPEX & OPEX.
  • Gas process conditions and properties.
  • Neighborhood relationships, availability, and cost of utilities.
  • Space availability.

Flaring Environmental impacts

  • The global warming potential of Methane is estimated at 34 times greater than that of CO2. Therefore, by converting the methane to CO2 before it is released into the atmosphere, the amount of global warming is reduced. However, flaring emissions contributed to 270 Mt CO2 in 2017, and reducing flaring emissions is key to avoiding dangerous global warming.
  • Improperly operated flares may emit methane and other volatile organic compounds as well as sulfur dioxide and other sulfur compounds, which are known to cause respiratory problems.
  • Emissions from improperly operated flares like aromatic hydrocarbons (benzene, toluene, xylenes) and benzo(a)pyrene, etc. are known to be carcinogenic.
  • It is now recognized as a major environmental problem, contributing an amount of about 150 billion m3 of natural gas that is flared around the world, contaminating the environment with about 400 Mt CO2 per year.

Gas Flaring Reducing and Recovery (R&R)

There are many types of FGRS (Flare Gas Recovery Systems) in the industry:

  1. Collection, compression, and injection/reinjection
  2. Generating electricity by generation and co-generation of steam and
    electricity

The gas collection and compression into pipelines for processing and sale is a well-established and proven approach to mitigating flaring and venting. According to environmental and economic considerations, FGRS has increased to reduce noise and thermal radiation, operating and maintenance costs, air pollution, and gas emission, and reduces fuel gas and steam consumption. Fig. 3 below shows a typical example of a flare gas recovery system.

Typical Flare Gas Recovery System
Fig. 3: Typical Flare Gas Recovery System

Flare System Design

API 537 is used for flare system design. This standard is applicable to Flares used in pressure-relieving and vapor-depressurizing systems used in General Refinery and Petrochemical Services. Although this standard is primarily intended for new flares and facilities, it may be used as a guideline in the evaluation of existing facilities together with appropriate cost and risk assessment considerations. API 537 must be referred to in consideration with

  • API RP521 (Guide for Pressure-Relieving and Depressurizing systems), and
  • API 560RP2A (Fired Heaters for General Refinery Service Recommended Practice and constructing fixed offshore platforms).

Factors Affecting Flare System Design:

Design factors that influence the flare system design are:

  • flow rate;
  • flare gas composition;
  • flare gas temperature;
  • gas pressure available;
  • utility costs and availability;
  • safety requirements;
  • environmental requirements;
  • social requirements.

The plant owner or the plant designer must provide these factors to define the flaring requirements.

A. Flare System Design Criteria

The prime objective of a flare system design is safe, effective disposal of gases without compromising appropriate design considerations like:

  • Reliable effective burning to reduce emissions to the permitted level.
  • System hydraulics shall be sufficient to deliver all of the waste gas and auxiliary fuel gas, steam, and air to the flare burner with sufficient exit velocities. System pressure cannot exceed the maximum allowable operating pressures at any active relief source, vent, or utility supply.
  • Liquid shall be removed sufficiently to prevent poor combustion, burning liquid droplets, and clogging the flare burner.
  • Air infiltration should be avoided using a proper seal system to avoid internal combustion within the riser and flashback in the flare header.
  • Flame radiation should be controlled within admitted limits to avoid nearby property damage or personnel injury.
  • A smoke suppression system, if required, should ensure Zero smoke operation.
  • Flare gas recovery system feasibility to be assessed to enhance plant efficiency and eliminate flaring incidents.

B. Flare Header Sizing

The take-off point for flare header sizing is to have a proper relief load calculation based on the worst credible scenario, where the pressure will increase until a predetermined relief pressure is reached, at which point the relief pressure valve will open, decreasing the pressure after the turnaround time. Refer to Fig. 4.

Flare Header Sizing Criteria
Fig. 4: Flare Header Sizing Criteria

ASME Boiler & Pressure Vessel Code VIII Guideline For overpressure protection Requirements:

The ASME Boiler and Pressure Vessel Code Sec VIII sets out requirements for standard pressure vessels (left) and the relief valves (right) protecting them as a percentage of the maximum allowable working pressure (MAWP) as shown in Fig. 5.

ASME Sec VIII Criteria for Flare Sizing
Fig. 5: ASME Sec VIII Criteria for Flare Sizing

Relief Valve Sizing Procedure

Refer to Fig. 6 below which shows a typical flowchart explaining the steps for the relief valve sizing procedure.

Relief Valve Sizing Procedure
Fig. 6: Relief Valve Sizing Procedure

Fig. 7 below shows a typical flare header system for a processing plant.

Typical Flare Header System
Fig. 7: Typical Flare Header System
  • Low-pressure pipe flares are not intended to handle liquids. Also, they do not efficiently perform when there is a liquid hydrocarbon release into the flare system.
  • Backpressure and Gas Velocity are the major criteria governing the sizing of the flare header.
  • The flare header size has to be large enough to prevent excessive back pressure on the plant safety valves and to limit gas velocity and noise to acceptable levels.
Flare Headers and Sub-headers
Fig. 8: Flare Headers and Sub-headers

Steps for finding ‘the maximum’ relief load for a specific process plant:

  • Prepare flare relief load summary including all Pressure Safety Valve with all of their relief cases.
  • Find out the maximum possible relief load for each of the cases, e.g. For cooling water failure, all Pressure Safety Valves (PSV) having this case will discharge simultaneously. So add up them.
    Note: The simultaneous occurrence of two or more contingencies (known as double jeopardy) is so unlikely that this situation is not usually considered as a basis for determining the maximum system loads.
  • Once you found the maximum case among all the scenarios, consider it as the ‘governing’ case for sizing your flare header.
  • You need to find what has superimposed back pressure at the plant battery limit. You need to calculate total back pressure based on superimposed backpressure and built-up backpressure. All these calculations need a thorough understanding of hydraulics and API guidelines.
  • Once you perform the above, you will have the size of a flare header

The sum of all pressure losses starting from the flare stack up to the safety valve yields the total backpressure. This backpressure must be lower than the maximum backpressure allowed in the system & corresponding to the lowest set pressure of the safety valves.

Hydraulic Design

The flare header is sized to limit the backpressure of each pressure relief device during various emergency events. The hydraulic design is a line sizing/rating problem:

  • Design minimizes the differential pressure to ensure each pressure relief device functions
  • Design is based on specific line length, size and the maximum expected relief load for each relief event.

Hydraulic Issues

Hydraulic issues specific to the flare header design:

  • The size of various sections is governed by the different relief events in the collection header.
  • A variety of material discharge to the flare system.
  • Potential pressure discontinuities where pipe flow stream meet.
  • Volume expansion throughout header piping.
  • High velocity and significant acceleration effects.

C. Flare Knock-Out Drum Sizing

The objectives of a knock-out drum are

  • Limit liquid droplet size entrained with gas to the flare to avoid liquid carryover to flare tip, smoke, flaming rain, and other hazardous conditions.
  • Provide adequate residence time for liquid.

Fig. 9 shows a typical known out drum (KOD). KOD is sized based on API 521.

  • Separation of liquid droplet size of 300-600 microns considering the design case for the flare.
  • 20-30 minutes of liquid hold-up time based on a relief case that results in maximum liquid.
  • No internals to facilitate separation.
  • Many orientations/options possible, horizontal KODs most preferred.
Typical Flare Knock Out Drum
Fig. 9: Typical Flare Knock-Out Drum
  • Flare Knock-Out Drum Elevation
    • KO drum elevation decides pipe rack elevation based on the 1:500 slope of the main flare header
    • KO drum elevation determined by pump NPSH requirement
  • To reduce pipe rack elevation options are
    • Reduce KOD elevation (option 1 in Fig. 10)
      • • Use a vertical can pump
      • • Locate the pump within a pit
      • • Locate the KO drum within a pit
    • Use intermediate KO drums (option 2 in Fig. 10)
Flare KO Drum Elevation Arrangement
Fig. 10: Flare KO Drum Elevation Arrangement

Flare System KOD Design Considerations

  • Flare KOD sizing depends on two aspects:
    • Liquid Hold up requirement during a major liquid or two-phase release.
    • A sufficient distance shall be available between the inlet & HHHLL. It is possible to have manually initiated depressurization even after HHHLLL. Any possible liquid shall be accommodated above HHHLL.
  • Knockout drum sizing is basically a trial-and-error process.
  • Distance between HLL and HHHLL shall be designed to accommodate the maximum liquid release scenario.
  • Determination of the drum size for liquid entrainment separation is The first step.
  • HHHLL is usually taken as the distance from the maximum liquid level.
  • The vertical velocity of the Vapour and gas should be low enough to prevent large slugs of liquid from entering the flare.
  • The thermal radiation fluxes and smoking potential are increased by the presence of small liquid droplets.

When do the Liquid particles separate?

  • Sufficient residence time.
  • When the gas velocity is sufficiently low to permit the liquid dropout to fall.

Long-term field experience has shown that the dropout velocity in the
drum may be based on the necessity to separate droplets from 300 μm to 600 μm in diameter.

D. Flare Stack Sizing

Flare Load, Radiation, and stack height:
Flare stack height depends on the flame radiation intensity, therefore you will need first to estimate the generated radiation in order to be able to identify the minimum acceptable stack height. Thermal radiation can be calculated by the following equation (Fig. 11):

Thermal Radiation from Flare Stack
Fig. 11: Thermal Radiation from Flare Stack

Flame length is a determining factor for the intensity of radiation and its angle in relation to the stack. It can be calculated using the following equation (Fig. 12):

Equation for Flame Length and Angle calculation
Fig. 12: Equation for Flame Length and Angle calculation

Using Flame length and flame angle, Radiation intensity can be determined and accordingly flare stack from charts.

E. Liquid Seal Drum

Liquid Seal Drum prevents the flashback from flare tip back to flare headers. It also helps to avoid air ingress into the flare system when the flare system is integrated with a flare recovery system or due to hot gas thermal contraction and/or condensation which can result in a substantial vacuum in the flare header. Fig. 13 shows a typical liquid seal drum.

Typical Liquid Seal Drum
Fig. 13: Typical Liquid Seal Drum

Note that the maximum vacuum protection achievable may be limited by piping and vessel elevations, In addition to maintaining the proper liquid level and restoring the level promptly after any hot relief and before the vacuum forms.

For extremely cold releases, the water as a liquid sealing fluid is not recommended. In such cases, water-glycol mixtures of sufficient concentration shall be used.

F. Flared Gas Measurement

As we get familiar with the impact of improper flaring on health and the environment, also it is highly required to measure the HC quantities sent to flare to decide on the plant performance, identify gaps and define the mitigating actions to eliminate or at least reduce flaring.

When trying to measure gas flaring, There are many challenges, including diameters of large pipes, high flow velocities over wide measuring ranges, gas composition changing, low pressure, dirt, wax, and condensate.

Important criteria to be considered to decide on the flow measurement instruments:

  • Operating range, the meter should accommodate the anticipated range of flows.
  • Accuracy will depend on the final use of the measurement data and applicable regulatory requirements.
  • Installation requirements, the flow meter should be installed to be able to measure the total final gas flow to the flare and be located downstream of any liquids knock-out drum.
  • Maintenance and calibration requirements.
  • Composition monitoring as most types of flow meters is composition dependent. There are two primary options for composition monitoring:
    • Sampling and subsequent laboratory analysis.
    • Online Analyzers.
  • Temperature and pressure corrections, the flow meter will need temperature and pressure compensation features to correct the measured flow to standard conditions (101.325 kPa and 15°C) or normal conditions (101.325 kPa and 0°C).
  • Multi-phase capabilities, if the gas stream contains high concentrations of condensable hydrocarbons, the gas flow meter should be installed as close as possible to the knockout drum, and consideration should be given to insulating and heat tracing the line.
  • Stainless Steel may be used for offshore platform’s corrosive saltwater on all exposed instrument materials, including sensors, process connections, and enclosures. Agency approvals for installation in hazardous locations, in environments with potential hazardous gases; enclosure-only ratings are inadequate (and risky).
  • Monitoring records should be kept for at least 5 years. These records should be included the flow measurement data, hours the monitor during operation, and all servicing and calibration records.
  • In flow verification, where a verifiable flaring rate is desired (provers), the systems should be designed or modified to accommodate secondary flow measurements to allow an independent check of the primary flow meter while in active service.
  • Flow test methods may be considered for making spot checks or determinations of flows in the flare header.
  • Stainless steel wetted parts and optional stainless steel process connections and enclosure housings.
  • Non-clogging, non-fouling, no moving parts design for lowest maintenance.
  • Must be in compliance with local environmental regulations. It should meet mandated performance and calibration procedures such as US EPA’s 10 CFR 40; 40 CFR 98; EU Directive 2007/589/EC; US MMR 30 CFR Part 250 and others

The main types of flow meter technologies for flare gas measurement in the industry are listed in Fig. 14 below:

Typical Flowmeters for Flare gas measurement
Fig. 14: Typical Flowmeters for Flare gas measurement

Few more related articles for you…

Pre-Commissioning and Commissioning Checklist for Flare Package
Routing Of Flare And Relief Valve Piping: An article
Elevated Flare systems used in Process Industries
Flare systems: Stress Analysis Points

What is Cladded Pipe? Difference Between Clad and Lined Pipe | Weld Overlay

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

A Cladded Pipe is a steel pipe having a metallurgically bonded Corrosion-Resistant Alloy (CRA) layer on its internal or external surface. The base material is carbon steel or low alloy steel. Clad pipes comply with the most stringent requirements of strength and corrosion resistance. The carbon steel outer pipe (backing steel or base metal) complies with the static requirements of strength and durability, whereas the highly alloyed inside pipe provides protection against corrosion. As more and more pipelines are operated under highly corrosive conditions, the use of CRA-cladded pipe is increasing in the pipeline industry, especially in offshore areas.

Applications of Cladded Pipe

An internal layer of corrosion-resistant alloy (CRA) material, known as a cladding material, is economically suitable as the thinner layer enhances the corrosion-resistant abilities with increasing cost. Because of this, cladded pipe is extensively used in subsea pipelines and natural gas industries for conveying sour oil and gas, saltwater pipelines, water reinjection systems, process pipes in the chemical industry, saltwater pipes, water injection pipelines, inter-field pipelines, riser pipelines, flow lines, power plants, and marine applications.

CRA Materials for Cladded Pipe

An extensive range of stainless steel and non-ferrous alloy materials to suit the temperature requirements can be used as cladded pipe material. In normal industrial applications the following materials are found suitable as cladding materials:

  • Stainless Steel SS 304, SS 316, SS 317, SS410,
  • Duplex Stainless Steel,
  • Alloy Steel 254 SMO 904,
  • Incoloy alloy 825, Inconel alloy 59, Inconel alloy 625,
  • Hastelloy C-276,
  • Hastelloy C-22,
  • Hastelloy B3,
  • UNS N0 8825, UNS N06625, UNS N04400,
  • Alloy 31,
  • AL6NX,
  • Alloy 20,
  • Monel alloy 400,
  • Zirconium,
  • Titanium, and
  • some copper alloys

The cladding material shall conform to ASTM A265, B898, B424, B443, B619, A240, A263, A264, B622, B675, B265, B551, etc. The thickness of the CRA layer is normally 0.25 mm to 6 mm.

Cladding material types and thicknesses can be selected to meet the specified environment.

API 5LD provides basic requirements for CRA cladded line steel pipe.

The main parameters that are considered while selecting a CRA material are:

  • Temperature
  • Chloride Concentration
  • Partial Pressure of CO2 and H2S
  • Environment pH
  • Presence or absence of Sulphur
Cladded Pipe
Fig. 1: Cladded Pipe

Manufacturing of CRA Cladded Steel Pipes

Two common types of pipe cladding processes are available for bonding the CRA cladding pipe layer to the steel pipe:

1. Metallurgical bonding of cladding pipe:

The metallurgical bonding of the cladding can be achieved by various methods like Weld Overlay, explosion bonding, hot rolling, coextrusion, powder metallurgy, etc. Clad plates are utilized as raw materials. However, The main problem with metallurgical bonding is the high costs due to a limited number of suppliers for such a complex and demanding manufacturing process of metallurgical bonding the plates.

Weld Overlay Process

Weld Overlay is the most widely used metallurgical bonding process for pipe cladding. A Weld Overlay is also known as cladding, weld cladding, hard facing, or weld overlay cladding. In this process, one or more metals are joined together via welding to the surface of a base metal (backing steel) as a layer. Surfaces prepared by the weld overlay method can even be highly customized by layering and alloying multiple different materials together.

The weld overlay process is suitable for smaller as well as very large diameter pipe spools, flanges, and fitting. The main benefits that weld overlay pipe cladding provides are:

  • The weld overlay process can be applied to complex requirements.
  • It provides long life and high-reliability corrosion resistance to harsh environment applications.
  • Weld overlay is an economical way to provide excellent corrosion resistance for steel without jeopardizing design thickness.

Other Metallurgical Bonding Processes

For manufacturing cladded pipe by explosion bonding, two dissimilar materials are bonded with the help of pressure and heat produced by the explosion. The clad material is kept on top of the base material and then the explosive material is spread on it. Upon ignition of the explosive, the resultant thrust bonds the clad plate on the base plate underneath. Depending on the job requirements, various combinations of the clad plate and base plate thickness can be bonded.

Roll bonded cladding technique is usually used for the mid-range of pipe sizes (16″ to 24″). Some of the advantages of Roll-bonded metallurgical bonding cladding methods are:

  • It provides a better surface as compared with overlay welding.
  • Roll-bonded clad plates are an economical alternative to expensive high-alloy solid plates. An optimum combination is arrived at by the mechanical properties of the base material and the corrosion resistance of the cladding material.
  • As compared with solid plates, it has thinner wall thicknesses and better workability.
  • More homogeneous bonding and a wider range of dimensions compared with explosion cladding.

2. Mechanical bonding of Cladding Pipe:

Mechanical bonding of the CRA pipe and the base steel pipe is performed by using spring back variation using Hydroforming or full-length pipe expander. Hydroforming is more expensive than a full-length pipe expander.

Inspection of CRA Cladded Pipes is done using Ultrasonic Testing Methods.

Typical CRA clad pipe
Fig. 2: Typical CRA-clad pipe

Difference between Clad and Lined Pipe

Some of the differences between a cladding pipe and a lined pipe are listed below:

Cladded PipeLined Pipe
Metallic material is used for cladding.For lining, non-metallic material is used.
Weld Overlay or explosion bonding process.Mechanical bonding process with adhesive
Suitable for high temperature and pressure applications.Normally used in low-pressure and temperature applications
Complicated fabricationEasy fabrication because of flanged joints.
Economically CostlyComparatively cheaper.
Cladded Pipe vs Lined Pipe

What is the Reynolds Number? The Equation for Reynolds Number and Its Significance

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

In the field of fluid mechanics, understanding the behavior of fluids in motion is of utmost importance. One crucial parameter that helps characterize the flow regime is the Reynolds number. Named after the pioneering scientist Osborne Reynolds, this dimensionless number provides insight into the transition between laminar and turbulent flow. In this article, we will delve into the concept of the Reynolds number, its equation, significance, and how it influences fluid flow.

What is Reynold’s Number? Definition of Reynold’s Number

Reynolds Number is a very important quantity for studying fluid flow patterns. It is a dimensionless parameter and is widely used in fluid mechanics. Reynolds Number of a flowing fluid is defined as the ratio of inertia force to the viscous force of that fluid and it quantifies the relative importance of these two types of forces for given flow conditions.

The concept of Reynold’s number was introduced by George Stokes in 1851. However, the name “Reynolds Number” was given with the name of the British physicist Osborne Reynolds, who popularized its use in 1883. The Reynolds number depends on the relative internal movement due to different fluid velocities. For fluid flow analysis, Reynold’s number is considered to be a prerequisite.

Importance of Reynolds Number

Reynolds Number (Re) is a convenient parameter that helps in predicting if a fluid flow condition will be laminar or turbulent. We know that Reynolds Number (Re)=inertia force/viscous force.

When viscous force dominates over the inertia force, the flow is smooth and at low velocities; the Reynolds Number value is comparatively less and the flow is known as laminar flow. On the other hand, when inertia force is dominant, the value of the Reynolds number is comparatively higher and the fluid flows faster at higher velocities and the flow is called turbulent flow. At low Reynolds Number Values (Re<2100) the viscous force is sufficient enough to keep fluid particles in line making the flow laminar which is characterized by smooth and constant fluid motion. While at large Reynold Number values (Re>4000), the flow tends to produce chaotic eddies, vortices, and other flow instabilities making the flow turbulent. With an increase in Reynolds Number the turbulence tendency of the flow increases.

Reynolds Number vs flow regimes
Fig. 1: Reynolds Number vs flow regimes

“2100<Reynolds Number (Re)<4000” indicates a flow transition from laminar to turbulent and the flow consists of a mixed behavior. However, note that the value of Reynolds number (Re) at which turbulent flow begins is dependent on the geometry of the fluid flow, which is different for pipe flow and external flow.

The Reynolds number associated with the laminar-turbulent transition is known as the Critical Reynolds Number. This laminar to turbulent transition is a highly complicated process, which is not yet fully understood.

The Equation for Reynolds Number

Mathematically, The Equation for the Reynolds number is represented as

Re=ρuD/μ

where 

  • ρ  is the fluid density Kg/m3)
  • D  is a length scale that characterizes the scale of the flow motions of interest (m)
  • u  is the fluid velocity (m/s)
  • μ  is the fluid dynamic viscosity (Pa.s or N.s/m2 or kg/m.s)
  • the term μ/ρ is known as kinematic viscosity, ν (m2/s)

Hence the formula for Reynold’s number can be written as Re=ρuD/μ=uD/ν

The Reynolds number (Re) of a flowing fluid can easily be calculated by multiplying the velocity of fluid flow by the pipe’s internal diameter and then dividing the result by the kinematic viscosity of the fluid.

Components of Reynolds Number Formula

Let’s understand the components of the Reynolds Number Formula:

Inertial Forces: Inertial forces arise from the tendency of a fluid to resist changes in its state of motion. They depend on the density of the fluid (ρ) and the velocity of the fluid (u). A higher density or higher velocity will result in greater inertial forces.

Viscous Forces: Viscous forces, on the other hand, are the internal frictional forces between adjacent fluid layers that resist the flow. These forces depend on the dynamic viscosity (μ) of the fluid. A higher viscosity implies stronger viscous forces.

Characteristic Length (D): The characteristic length (D) represents a characteristic dimension of the object or the flow domain. It could be the diameter of a pipe, the chord length of an airfoil, or any other relevant length scale. The choice of characteristic length is crucial and depends on the specific flow situation.

Unit of Reynold’s Number

Let’s find the dimension of Reynold’s number. The Primary dimension of ρ is (M/L3) and the velocity is (L/T)
Again the primary dimension of diameter/length is L and viscosity μ is (M/LT).
Substituting all these values in the above-mentioned formula of Reynold’s number we get [{M/L3 * L/T * L}/ (M/LT)]=M*L*L*L*T/L3*T*M=MTL3/MTL3=1 Which means Reynolds Number is dimensionless or unitless. The same concept can be put forth as follows:

As the Reynolds Number is the ratio of two forces, there is no unit of Reynolds Number. So, Reynold’s Number is dimensionless.

Factors Affecting Reynolds Number

The main factors that govern the value of the Reynolds Number are:

  • The fluid flow geometry
  • Flow velocity; with an increase in flow velocity the Reynolds number increases.
  • Characteristic Dimension; with an increase in characteristic dimension the Reynolds number increases.
  • Fluid Density; with a decrease in fluid density the Reynolds number value decreases.
  • Viscosity; with an increase in viscosity the value of the Reynolds number decreases.
Factors Affecting Reynolds Number
Fig. 2: Factors Affecting Reynolds Number

So, in one sentence we can conclude that Reynolds Number is directly proportional to Flow Velocity, Characteristic Dimension, and Fluid Density while inversely proportional to fluid viscosity.

Applications of Reynold’s Number

The Reynolds number plays a crucial role in fluid mechanics and has significant practical implications. Here are a few areas where the Reynolds number finds applications:

Flow Analysis and Design:

Understanding the Reynolds number is vital in the analysis and design of fluid flow systems. It helps engineers and scientists predict the behavior of fluids in pipes, channels, and around objects. By knowing the flow regime, appropriate design considerations can be made to optimize efficiency and minimize pressure losses.

Drag and Lift Forces:

The Reynolds number influences the drag and lift forces acting on objects moving through a fluid. In the case of aerodynamics, for instance, the Reynolds number determines the flow regime around an aircraft wing or an automobile, affecting factors such as lift, drag, and overall performance.

Heat Transfer:

The Reynolds number has implications for heat transfer processes. It helps in determining the convective heat transfer coefficient, which is crucial in applications such as cooling systems, heat exchangers, and thermal management.

Fluid Mixing:

The Reynolds number is a valuable parameter in understanding and controlling fluid mixing processes. It helps determine the efficiency and effectiveness of mixing operations in various industries, including chemical engineering, pharmaceuticals, and food processing.

Other Applications:

As Reynolds number is used for predicting laminar and turbulent flow, it is widely used as a design parameter for hydraulic and aerodynamic equipment. The Reynolds number for laminar flow is less than 2100. The value of the Reynolds number is a significant necessity for fluid flow analysis.

For the design of piping systems, aircraft wings, pumping systems, scaling of fluid dynamic problems, etc Reynolds number serves as an important design tool. To simulate the movement of any object in any fluid, the Reynolds Number is required.

Reynold’s number is used to calculate the value of the drag coefficient. In the calculation of pressure drop and frictional losses, the Reynolds number plays an important role. The following diagram (Fig. 3), known as the Moody chart provides a correlation between friction factor, Reynold’s Number, and Relative roughness and is widely used in solving fluid flow problems.

Reynolds number in Moody Chart
Fig. 3: Reynolds number in Moody Chart

Reynold’s number (Re) is also used to calculate the value of friction factor (f) using the Colebrook Equation as mentioned below:

Colebrook Equation for calculating friction factor using Reynold's number
Colebrook Equation for calculating friction factor using Reynold’s number

In the above equation, ε=Absolute Roughness.

Reynolds Number Values

The following table provides some typical Reynold Number values

Sr NoItemTypical Reynolds Number
1Laminar Flow<2100
2Turbulent Flow>4000
3Person Swimming4 × 106
4Blue Whale4 × 108
5Smallest fish1
6Atmospheric tropical cyclone1 x 1012
7Bacterium1 × 10−4
8Blood flow in the brain1 × 102
9Blood flow in the aorta1 × 103
10Fastest fish1 × 108
Typical Values of Reynolds Number (Reference: wikipedia.org)

Reynolds Number for Laminar Flow

Laminar flow is the smooth flow in layers. There is little or no mixing and the fluid velocity is typically lower. The motion of the fluid particles is ordered without any cross currents. This is typically found in fluids of high viscosity and at lower velocities. The value of Reynold’s Number for Laminar flow is less than 2100.

Reynolds Number for Turbulent Flow

In turbulent flow, there is turbulence and unpredictable mixing. The velocity is high and fluids do not move in layers similar to laminar flow. Waves in the sea or river, storms, etc are examples of typical turbulent flow. The Reynolds Number for Turbulent flow is usually considered greater than 4000.

Critical Reynolds Number

The transition from laminar to turbulent flow is not abrupt but gradual. There is a critical Reynolds number, known as the critical Reynolds number, below which the flow remains laminar and above which it becomes turbulent. The specific value of the critical Reynolds number depends on various factors such as the geometry of the object, surface roughness, and fluid properties.

Low and High Reynolds Number

At low values of Reynolds Number Re<<1, the inertial effect becomes negligible. The flow behavior is dependent on the viscosity and the flow is stable. Whereas when the Reynolds Number Re is very very high, the viscous effects are negligible. The fluid flow behavior depends on the momentum of the fluid and the flow is unsteady.

Conclusions

The Reynolds number provides valuable insight into the flow regime of fluids and the transition from laminar to turbulent flow. By considering the interplay between inertial and viscous forces, engineers and scientists can better predict and analyze fluid behavior in various systems. Understanding the Reynolds number is essential for optimizing design, predicting performance, and ensuring efficient and safe operation of fluid systems across numerous fields of application.