Recent Posts

Design of Centrifugal Compressor Piping and Appurtenances excluding Anti-Surge Systems

Written by Ankur Srivastava in Mechanical,Pipeline,Piping Design Basics,Piping Interface,Process

Centrifugal compressors are widely used in process plants to compress gases. Centrifugal Compressors, being rotary equipment, are highly sensitive and prone to vibration. So, the connected piping system must be designed with care to get optimum performance. In this article, we will explore the design of centrifugal compressor piping and appurtenances.

Refer to Fig. 1 below which shows a typical process flow diagram of a single-stage centrifugal compressor.

Process Flow Diagram of a Single-Stage Centrifugal Compressor
Fig. 1: Process Flow Diagram of a Single-Stage Centrifugal Compressor

The surge control or anti-surge system shown in the above PFD is a very basic representation of the system. There are many variations to the basic representation shown in the PFD including the measurement of temperature at suction and discharge providing feedback to the anti-surge system.

The design considerations for the centrifugal piping are divided into two parts.

  • Suction Piping Design Considerations and
  • Discharge Piping Design Considerations

Centrifugal Compressor Suction Piping Design

Process Considerations for Suction Piping Design

The rule of thumb is to size the suction piping of the compressor’s first stage such that the pressure drop should not exceed 3.4 kPa or 1% of operating pressure (whichever is smaller), and a maximum actual velocity of 9.1 m/sec.  To determine the velocity, use the formula provided in Eqn. 1, and to determine the pipe’s internal diameter based on the maximum velocity rule of thumb use the formula provided in Eqn. 2 of Fig. 2 below.

Formula for Centrifugal Compressor Suction Pipe Diameter Calculation
Fig. 2: Formula for Centrifugal Compressor Suction Pipe Diameter Calculation

Where

  • Vgact = actual gas velocity, m/s
  • T = gas temperature at suction, K
  • d = Pipe ID, mm
  • P = Pressure, kPa (abs)
  • Qg = gas flow rate, Sm3/h (Note: Sm3/h flow rate is at 15⁰C and 101.325 kPa(abs))
  • Z = gas compressibility factor at T, P

Piping Considerations for Suction Piping Design

1.  Straight Length Requirement

The following figures (Fig. 3 & Fig. 4) establish the practice for straight length ahead of the inlet or suction nozzle of the compressor. The sketch is applicable for multistage compressors including the inlet or suction piping of the subsequent stage after the first stage. The sketch is for the base case for the suction piping provided with one long radius elbow (plane parallel to the rotor). For cases other than the base case various multipliers are used to define the straight length of pipe required ahead of the suction nozzle. All the other cases are also discussed as a subset of the base case using the multipliers:

Compressor Inlet Correction Factors for various Piping Arrangements
Fig. 3: Compressor Inlet Correction Factors for various Piping Arrangements
Various Piping Configurations for Compressor Suction
Fig. 4: Various Piping Configurations for Compressor Suction

When suction piping straight length for axial or single-stage compressors needs to be found, the straight length obtained based on the above figures for the various piping arrangement cases shall be multiplied by an additional factor of 1.25.

2.  Slope of Compressor Suction Piping

Piping shall slope continuously downward from the suction scrubber to the compressor suction connection.  A desirable configuration for the slope of the suction piping would be to provide a slope from the upstream flange of the suction line isolation valve towards the suction scrubber and a slope towards the compressor suction nozzle from the downstream of the suction line valve. Valves shall be located only in horizontal piping.

3.  Suction Strainer

The provision of suction strainers is mandated in most applications to trap any solid particles that can cause damage to the compressor internals. Screens and Filters used shall have high mechanical integrity and strength to prevent their failure and entry into the compressor casing.  All strainers shall be installed as close to the compressor as feasible.

When temporary suction strainers are used, pressure gauge taps shall be provided upstream and downstream for the commissioning of the compressor.  When the temporary strainers are removed, the tapped connections shall be plugged, and seal welded.

4.  Low Point Drain

Compressors having a suction nozzle orientation such that the suction line connects from the bottom forming a low point in the suction line shall be provided with a small boot or sump with a local gauge glass and a local drain connection to drain any condensed liquid. The boot or sump shall be provided as close as feasible to the compressor suction nozzle and at the lowest point in the suction piping.

5.  Lube & Seal Oil System

Hose connections shall not be used in lube and seal oil systems of compressors.

Centrifugal Compressor Discharge Piping Design

Process Considerations for Discharge Piping Design

The interstage and discharge piping thumb rule for sizing is a pressure drop not to exceed 2 percent of operating pressure or 34 kPa (whichever is higher) and a maximum actual velocity (adjusted for temperature and compressibility) of 15.2 m/sec.

Equations 1 & 2 (Fig. 2 above) can be used for evaluating the velocity for a given diameter and the discharge pipe diameter based on the aforementioned maximum velocity.

Maximum velocity considerations are also based on noise criteria observed in gas lines.

Many operators of natural gas transmission pipelines have concluded that velocities up to 20 m/s are acceptable with due consideration of noise. Companies like Shell recommend velocities of 5-10 m/s for continuous operation in long-distance natural gas pipelines and a maximum of 20 m/s for intermittent operation.

Fig. 5 below shows a typical centrifugal compressor piping system.

Typical Centrifugal Compressor Suction and Discharge Line
Fig. 5: Typical Centrifugal Compressor Suction and Discharge Line

Other Important Design Considerations for Centrifugal Compressor Piping System

Minimum Line Sizes & End Connections

Normally line sizes below 2” are avoided. Threaded connections are not used due to pressure and temperature considerations. For hydrocarbon and other flammable/toxic gases, threaded connections are strictly prohibited. Most designers prefer to use Schedule 80 pipes in high-pressure gas compression applications.

Suction Isolation Valve

For isolating the compressor suction a suction isolation valve is provided in the suction piping which is manually operated. The valve location shall be evaluated on a case-to-case basis. For large-size valves, the manual valve is provided with a gear operator for ease of operation.

Discharge Isolation Valve

For isolating the compressor discharge a discharge isolation valve is provided in the discharge piping which is manually operated. The valve location shall be evaluated on a case-to-case basis, with the general objective of locating it as close as possible to the discharge connection. For large-size valves, the manual valve is provided with a gear operator for ease of operation.

Discharge Check Valve

The check valve prevents reverse flow and reverses the rotation of the compressor unit which can cause serious damage to the seals and bearings. Install the check valve as close as possible to the discharge nozzle considering all aspects of accessibility and maintainability.

Blowdown Valve

The function of the blowdown valve is to relieve the high-pressure gas trapped in the compressor system during a breakdown or a planned shutdown. Most operators use automatic blowdown valves to reduce the hazards of trapped gas. If the blowdown valve has been tied into a closed vent system to route gas to a safe area for flare or vent, a second separate blowdown valve may be required. This valve should vent directly to the atmosphere, with nothing else tied into its line. This practice prevents backflow from the closed vent system while the compressor is down for maintenance and permits small leaks of gas from the compressor to vent safely. The Process Flow Diagram flowsheet shows a manual valve to accomplish this. Occasionally, a three-way valve is used for this purpose.

Flare Valve

As suction pressure increases, the head requirement will decrease, and the gas flow rate will increase. The increased flow rate beyond the design maximum may force the compressor to operate in the stonewall region, which would result in damage to the machine, or it may create too high a power demand for the driver. To avoid these possibilities, a flare valve tied to the vent header is installed at the suction side of the compressor. The valve is operated by a pressure controller, which is attached to the suction line upstream of the suction scrubber. The flare valve will also open if the compressor shuts down, allowing the operator time to react before the process must be shut in.

Suction Throttle Valve

Flaring or venting may be reduced by installing a control valve in the suction line (not shown in the PFD illustrated). This valve regulates either flow or pressure to avoid operating the compressor in the stonewall region or overloading the driver. As this valve begins to throttle flow into the compressor, pressure will begin to increase in the upstream equipment. If the high flow condition persists, the flare valve will eventually open. However, if the upstream equipment is rated for a high enough pressure and there is a large enough difference between the throttle valve and flare valve set pressures, it is possible that surges of gas can be processed without flaring.

Emergency Shutdown Valves (ESDV)

An ESDV is an actuated valve with generally a full close action designed to stop the flow of a hazardous fluid in the enclosed system or prevent loss of containment to the external environment, upon the detection of a dangerous event. The ESDV thus acts to mitigate any catastrophic damage to equipment and the environment. In many cases, an ESDV by its action can prevent injury or loss of life due to a catastrophic event or accident.

Quarter-turn valves are the most common ESD valves for actuation. They can be hydraulically, pneumatically, or electrically operated.

Centrifugal compressors in all sizes shall have a remote-operated emergency shutdown valve in the suction piping.  The compressor suction isolation valve, if remotely operated, can also be the emergency shutdown valve. For field operation of the ESDV, a pushbutton station with a position indicator shall be located in the area of the compressor, at least 15m away, and in a location that is easily accessible. Location consideration shall also take into account that the pushbutton station is not exposed to fire.  The remotely operated ESDV shall also be operable from the central control room.

Fireproofing of remote-control emergency shutdown valve assemblies is required.  All resilient seated emergency shutdown valves shall be of a fire-safe design.

Silencers (as required)

Silencers are required to suppress the intake noise from compressors which is generated by the high-speed rotation of the impeller(s). They may be installed as per the application on a case-to-case basis. Silencers shall be located as close as possible to the suction and discharge nozzles as feasible. On the discharge side, the silencer is required to be located downstream of the check valve. To optimize the layout, the silencers may be arranged with side or end connections.  Silencer shells and flanges shall conform to the piping class and specifications of the respective piping they are connected with.

Few more related articles for you.

Basics of Centrifugal Compressors: A presentation
A Brief Overview of Centrifugal Compressor System Process Design
Compressor Piping Layout: Compressor Piping Design
Stress Analysis of Centrifugal Compressor Connected Piping Systems using Caesar II
Difference between Centrifugal and Reciprocating Compressor

What is Time History Analysis? Steps with example

Written by Rajesh Ramadas in Caesar II,Piping Stress Analysis,Piping Stress Basics

Time history analysis is quite popular in pipe stress analysis as it provides the most realistic specification of dynamic loads in CAESAR II. The program’s modal time history analysis can simulate system response to several force-versus-time events. Time history is best suited to impulse loadings (slug, water hammer, PSV reaction, etc.) or other transient loadings where the profile is known.  Only one dynamic load can be defined as a time history analysis. This dynamic load case can be used in as many static/dynamic combination load cases as necessary. The single load case may consist of multiple force profiles that can be applied to the system simultaneously or sequentially. Each force versus time profile is entered as a spectrum with an ordinate of Force (in current units) and a range of Time (in milliseconds). The profiles are defined by entering the time and force coordinates of the corner points defining the profile. In this article, we will explore the methods followed for dynamic time history analysis using Caesar II considering an example of a slug flow system.

Reason for Dynamic Time History Analysis

While the adoption of a pseudo-static approach, the application of a static load corrected using an appropriate dynamic load factor, can also provide a conservative result. In some short pipe routing it is required to check how the pipe routing responds to loads with very short durations. This is why time history analysis is often considered a better approach and can be performed with commercial software such as CAESAR II.

Time history analysis provides a method of assessing displacements, stress, and reactions developed in a piping system over time. In order to carry out such an analysis there is a need to be able to define the loading, be it the forces associated with a fluid slug traveling through a piping system.

Time History Analysis Example using Caesar II

In the following paragraphs, we will discuss the time history analysis for the design of a Flowline of a typical Wellhead piping system. The pipeline system shown in Fig. 1 is used for dynamic time history analysis.

3D model of the system under Time History Analysis
Fig. 1: 3D model of the system under Time History Analysis

Time History Analysis Input

Time history analysis input can be divided into three steps listed below:

  1. Modification in the Static Model
  2. Dynamic Load Definition and
  3. The setting of Dynamic Control Parameters

1. Modification in the Static Model

Element length needs to be kept at a minimum for getting proper mass distribution, mode shapes, and natural frequency of the system. The following thumb rule for maximum element length can be followed:

  • Minimum of 10 times of nominal diameter i.e 10D and 6000 mm.
  • 5 times of nominal diameter near anchor or line stop supports.
  • at least 1 node in between two supports.
  • At least 1 node between two bends.

Support stiffness values can be considered to get more accurate results.

2. Defining Dynamic Loads for Time history analysis

The main inputs required to enter the spreadsheet for dynamic time-history analysis are listed below:

  • Slug Force can be calculated by collecting fluid density and velocity from the Process department.
  • The time duration for traveling from one elbow to another can be calculated by dividing the pipe length between two elbows by flow velocity. Two-time durations need to be calculated. Those are slug duration and slug periodicity. Both of these time durations will be required to create a time history spectrum for analysis. So, before opening the caesar ii dynamic input module, Calculate slug force, slug duration, and periodicity for each elbow node where the slug is expected to hit.

Let’s move on to the actual caesar ii time history analysis module. Before starting the dynamic module the static analysis need to be performed and the system must be safe in all static stress analysis aspects.

Step 1-Starting the Time history module: Open the Caesar II time history module as shown in Fig. 2

Fig. 2: Starting time history module in Caesar II

Step 2- Force Time profile definition: Refer to Fig. 3 below to understand the node numbers of the system.

Time history analysis model with node numbers
Fig. 3: Time history analysis model with node numbers

Slug force needs to be applied in each elbow node (50, 60, 120, 130, 140, etc) as shown in the above system. For each elbow node, force-time profile is to be created for time history analysis. As shown in Fig. 4 enter values corresponding to each elbow node.

Fig. 4: Force-Time Inputs for profile generation

Input Range type as time, Ordinate Type as Force, Range Interpol, and Ordinate Interpol as Linear. Now click on the highlighted button (Fig. 5) for generating a time-history profile for each node entered in Fig. 4.

Fig. 5: Time history spectrum generation

Now select each node one by one and enter the earlier calculated time and force values to generate a spectrum for each node as shown in Fig. 6 below:

Creating Time History Spectrum
Fig. 6: Creating Time History Spectrum

Further steps of creating Force Sets, Time history load cases, and static-dynamic load combinations are the same as explained in the earlier article “Slug Flow Analysis Using Dynamic Spectrum Method in Caesar II“. Kindly click on the link provided to learn the same.

3. Setting up the Dynamic Control Parameters

The control parameters can be set as provided in Fig. 7

Control Parameters for Time History Analysis
Fig. 7: Control Parameters for Time History Analysis

The Advanced control parameters can be set as provided in Fig. 8

Fig. 8: Advanced Control Parameters for Time History Analysis

Once the input parameters are entered and the control parameter is set up as explained above, run the analysis to get output results. The output results to be checked are similar to the earlier article titled “Slug Flow Analysis Using Dynamic Spectrum Method in Caesar II“

Response Spectrum vs Time History Analysis

The response spectrum method is a linear dynamic analysis method but Time history analysis is normally a non-linear analysis. Time history is a more detailed analysis involving the time instant.

In time history analyses the structural response is computed at a number of subsequent time instants. In other words, time histories of the structural response to a given input are obtained as a result. In response spectrum analyses the time evolution of response cannot be computed. Only the maximum response is estimated. No information is available also about the time when the maximum response occurs. 

Factor of Safety: Definition, Equation, Examples, Calculator

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

The factor of safety or safety factor is a very important term in engineering design. While designing any Engineering product or component, safety is of utmost importance. To ensure the safety of those items, each component is designed to bear more loads than its actual operating loads. So, there will always be some margin or cushion as compared to its operating capabilities. This is ensured during the design stage by considering a suitable factor of safety. In this article, we will discuss the following:

  • What is the Factor of Safety?
  • Importance of Factor of Safety in Engineering Design
  • Factors Affecting the Factor of Safety
  • Equation of Factor of Safety
  • Examples of Factors of Safety, and
  • Many More…

What is the Factor of Safety?

The factor of safety is defined as the ratio of the ultimate stress of the component material to the working stress. It denotes the additional strength of the component than the required strength. Factor of Safety is also popular by its abbreviated form FoS or FS. It is a numerical value that quantifies the safety level and reliability in engineering design. So, the factor of safety provides a buffer zone for engineers to ensure that their design will not fail under certain extreme conditions.

Importance of Factor of Safety

A factor of safety is related to the safety of people. It reduces the risk of failure of a component by adding some cushion in the design. Also, there always will be some hidden circumstances or unknown parameters that can not be considered accurate in design. At the same time, the reliability of the material is not 100% and the load used in design calculation is not the maximum load. So the factor of safety or safety factor provides protection against those unknown events to some extent.

Although all components are designed with a factor of safety, it’s always suggested to use those components within their design limit.

Factors Affecting Determination of Factor of safety

Component design codes & standards normally provide a minimum factor of safety for that component. However, choosing the exact safety factor is dependent on various parameters like

  • Material type Ductile vs. Brittle
  • Loading type Static vs. dynamic
  • Whether cyclical loads
  • The intensity of stress concentration
  • Unforeseen Misuse of the component
  • Accuracy and stress complexity during a calculation, Reliability of Data used in the factor of safety calculation.
  • Environment and design temperature and pressure.
  • Impact of failure
  • Cost of component or material
  • Corrosion rate
  • Maintenance frequency
  • Application of the component
  • Industry Standards and Regulations
  • Historical Data and Experience
  • Design Optimization
  • Client or Stakeholder Requirements

Factor of Safety Equation | Formula for Factor of Safety

As defined in the first paragraph, the factor of safety is a ratio of two loads or two stresses. Mathematically factor of safety can be expressed as

Factor of safety=Ultimate Load (Strength)/Allowable Load (Stress)

As understood from the above equation the allowable stress is always less than the ultimate failure stress. Hence, the factor of safety is always greater than 1. The ultimate stress for brittle material is considered as ultimate tensile strength and for ductile material is considered as yield strength.

Also, as the equation for the factor of safety is the ratio of two stress or load values, it is dimensionless. The difference between the Factor of Safety and 1 is known as the Margin of Safety. So,

The margin of safety = (Factor of safety-1).

Examples of Factors of Safety

Typical examples of the factor of safety for some materials depending on application and loading types are listed below in Table 1. However, please note that the table only provides a typical range or typical values to provide an example. Actual values for the factor of safety must be taken from the design standard of the relevant component. For example, the factor of safety for pressure vessel design must be taken from the ASME Sec VIII code.

Sr NoMemberTypical Factors of safety range
1Structural Members in building services2
2Pressure Vessel3.5 to 4
3Automobiles3
4Aircraft and Spacecraft1.2 to 3.0
5Aircraft components1.5 to 2.5
6Boilers3.5 to 6
7Bolts8.5
8Cast-iron wheels20
9Engine components6.0 to 8.0
10Heavy duty shafting10.0 to 12.0
11Lifting equipment – hooks8.0 to 9.0
12Pressure vessels3.5 – 6
13Turbine components – static6.0 to 8.0
14Turbine components – rotating2.0 to 3.0
15Spring, large heavy-duty4.5
16Structural steelwork in buildings4.0 to 6.0
17Structural steelwork in bridges5.0 to 7.0
18Wire ropes8.0 to 9.0
19Highly reliable materials where loading and environmental conditions are not severe1.3 to 1.5
20Moderately reliable materials where loading and environmental conditions are not severe1.5 to 2
21Ordinary materials where loading and environmental conditions are not severe2 to 2.5
22For use with less tried and for brittle materials where loading and average environmental2.5 to 3
23For use with materials where properties are not reliable and where loading and environmental conditions are not severe, or where reliable materials are used under difficult and environmental conditions3.0 to 4.0
24Impact Forces3.0 to 6.0
25Brittle Material1.0 to 6.0
Table 1: Typical Factor of Safety Range

Factor of Safety Calculator

Various factor of safety calculators are available online to calculate the values of the factor of safety with known ultimate strength and allowable stress values. Let’s take an example to calculate the factor of safety for the following situation:

The yield strength of a ductile material is 240 MPa. If the material is subjected to a loading condition that generates the maximum allowable stress of 140 MPa. Then the factor of safety of that material is 240/140=1.7. However, note that both stress values are in the consistent unit before calculating the factor of safety.

Note that with an increase in the factor of safety, the safety level increases. But, the design cost also increases at the same time. So, engineering judgment must be made following industry codes and guidelines to consider a proper factor of safety.

Free Body Diagram: Definition, Purpose, Examples, Steps

Written by Anu Sharma in Civil,Mechanical,Piping Interface,Piping Stress Analysis,Piping Stress Basics

The concept of a free-body diagram is widely used in engineering and physics. A free-body diagram is a force diagram (a graphic, dematerialized, symbolic representation) that shows the relative magnitude and direction of all forces that act on an object in a specified situation. All forces and moments acting on the object are represented using two-dimensional or three-dimensional representation using the free body diagram or FBD concept. As the forces are vector quantities, FBD is also known as a vector diagram. In this article, we will explore more details about the free body diagram.

Purpose of the Free Body Diagram

The purpose of the free-body diagram is to deconstruct a given problem by using only the necessary information. Students can use this diagram as a reference for setting up the calculations to find unknown variables, for example, force directions, moments, or force magnitudes. Free-Body Diagram allows students to clearly visualize a particular problem in its entirety or closely analyze a particular portion of a more complex problem. So basically, FBD is a very useful aid to visualize and solve engineering problems. Note that, for solving a complex problem, a series of free-body diagrams may be required.

Drawing a Free-Body Diagram

 In a Free-Body Diagram, the object is represented by its expression, usually a line, box, or dot. The force vectors that act upon the object are represented by a straight arrow while moments are represented by a curved arrow around their respective axis as shown in the image below where a force is acting at B and a moment acts around A. The force vector indicates the magnitude and direction of each force that is acting upon the object. The direction is normally indicated by degrees from the vertical or the horizontal axis while the magnitude is indicated by the units of force. In the case of an unknown direction of a force or magnitude, the unknown value must be labeled.

In addition, it is common to indicate the various types of forces with letters and distinguish between common ones by using subscripts. In the example problem shown in Fig. 1, weight and tension are represented by W and T, and the normal force and force of friction are represented by Ffrict and Fnorm. There are no hard rules about how forces are labeled as long as their meaning is clear. Free-Body Diagrams should have a labeled coordinate system and must include all the given dimensions, such as length and angles. Generally, a xy-coordinate system is used; however, when dealing with a problem, that is, in three-dimensional space, an xyz-co-ordinate system is required. Coordinate systems can be placed according to the student’s discretion in order to simplify the solving process, so long as the students are following the right-hand rule. 

Types of Forces for Free Body Diagram

In order to identify and label forces of a Free-Body Diagram, one must recognize the various types of forces that they will encounter and must know how these forces will interact with each other in order to calculate them. 

Weight: 

Any object with a mass is known as weight. It can be shown in pounds or Newton’s (N). If the weight is not given, it can be calculated in Newton (N) by multiplying the mass in kilograms (kg) with the Earth’s gravitational constant (9.8 m/s2). 

Normal Force: 

According to Newton’s Third Law, every action has an equal and opposite reaction. Due to this law, an object that rests on a surface, that is, an object that is not in free fall has a normal force acting in a perpendicular direction to the surface of the object on which it is resting. In the absence of any additional forces, the magnitude of the vertical component of the normal force is equal to the weight of the object. 

Friction Force: 

Friction force resists movement and always acts in the opposite direction of the movement or potential movement. It also acts parallel to the surface and is perpendicular to the normal force. The friction force is equal in magnitude to the force that provides the movement until and unless the opposing force exceeds the maximum friction force. The maximum friction force can be calculated by multiplying normal force by the surface coefficient of static friction. 

Tension: 

This force is the pulling force that is exerted on an object by a rope, chain, or cable. Tension force is continuous from one end to another. Because tension force is always continuous and a rope is flexible, pulleys can be utilized to redirect the rope and by extension, the tension force. 

Applied Force: 

The applied force is a force that is applied by a person or by some other object. 

Free Body Diagram Examples

Now we will explain the FBD concept, using the following free body diagram example problem as shown in Fig. 1.

A 50 kg stationary box must be pulled up a 30-degree inclined by a pulley system. The coefficient of static friction between the box and that incline is 0.25. Assuming there is no friction in the pulley system, what force in Newton’s (N) must be applied to the rope in order to move the box up the incline? 

Example of Free Body Diagram
Fig. 1: Example of Free Body Diagram

How to draw free body diagram

Step 1: Draw the object with no extra features.

Step 2: Identify the forces acting on the box. The box has mass, so it should also have weight, and a force acting downward. Because the stationary box is on a surface, there is a normal force that acts perpendicular to the surface. Further, attached to the box, there is a rope with tension applied. This tension force will act in the direction of the rope. Since the rope is directly attached to the box and in order to move it up the incline, there will be frictional force impeding movement. This force will then act in the opposite direction, down the incline. 

Step 3: Add the forces to the image of the object and label the directions of forces in degrees from the vertical or horizontal axis as understood by the geometry in the example. Refer to Fig. 2 which shows the above 3 steps.

Drawing a Free Body Diagram
Fig. 2: Drawing a Free Body Diagram

Step 4: Label all the known values. At this point, weight is known, that is mass (50 kg) multiplied by gravitational constant (9.8 m/s2). The FBD now contains all the given, important information. 

Step 5: As a general rule, the Free-Body Diagram has to be oriented, so that the direction of movement is along with one of the principal axes. In this example, the entire diagram could be reoriented by rotating it to 30° counter-clockwise. This step results in the direction of movement that occurs along the x-axis, and this results in three of the four forces that also get oriented along the x or y-axis. Fig. 3 shows Steps 4 & Step 5.

Steps for Drawing a Free Body Diagram
Fig. 3: Steps for Drawing a Free Body Diagram

Solving the Free-Body Diagram 

To solve the problem, the force on the rope required to move the box up the incline should be found. This is called the tension force. Finding this force requires a system of equations. As there is currently one known variable, the weight, there are three unknown variables also; therefore, three equations are required. These equations establish a relationship between all of the forces and are required in order to solve for each force.

In this system of equations, the first one creates a relationship between normal force and frictional force. Since the box will not move until the tension force overcomes the frictional force, the maximum frictional force is needed. The maximum frictional force is equal to the normal force multiplied by the surface coefficient of static friction, that is 0.25, so the first equation will be: Fnorm * 0.25 = Ffrict 

As the question refers to the minimum force required to begin moving the object, the system will be in static equilibrium before the time of movement. When a system that is in static equilibrium is concerned, there are two equations that are formed: ∑Fx=0 and ∑Fy=0, or, the sum of all the forces in the y and x-direction should be equal to zero. 

When all forces in each direction are summed up, it is noted that any force that acts along either the x or y-axis (in this case tension, frictional and normal force) will only be present in that axis equation. However, weight does not act along one axis, and therefore, should be broken down into its component parts. This we get by using trigonometric functions. In this case, since the weight acts at a 60-degree angle, the vertical component will be Sin 60 degrees * W, and the horizontal component will be Cos 60 degrees * W. 

To achieve the final two equations, the components of the various forces will be added together that act on each axis. Because of the direction of the positive x and y-axis chosen in the previous step, forces on the x-axis which is acting to the left will be negative, whereas forces that are acting to the right will be positive. Likewise, forces on the y-axis which is acting downwards will be negative, and forces that are acting upwards will be positive. Looking at the FBD, three forces will act in the x-direction: the tension force, the horizontal component of the weight, and the frictional force, and two forces will act in the y-direction: the vertical component of the weight and the normal force. This leads to the final equations as follows:

 ∑Fx= Ffrict+cos(60°)*W–T = 0 or Ffrict + cos(60°)*W=T 

∑Fy= Fnorm– sin(60°)*W = 0 or Fnorm= sin(60°)*W

Now that the system of equations has been found, the unknown variables can be found by using known information, such that the weight is 490 Newton. Then Equations are combined in order to solve the tension. Fnorm=sin (60°)*490 N = 424.4 N 

424.4 N*0.25 =Ffrict = 106.1 N 

106.1 N+cos(60°)*490=T = 351.1 N 

With tension force found, the answer to the problem is 351.1 N, that is, this amount of force should be applied to the rope in order to move the box up the incline. 

In a similar way, most physics or engineering problems can be simplified, visualized, and solved by drawing a free-body diagram of the problem. If there is more than one object then a free-body diagram of each object can be generated.

Flexible Metal Hoses: An essential guide

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

A flexible hose is a type of piping used to connect two distant points to transport or transfer fluid. In Oil & Gas applications, hoses are used when there is a considerable relative movement. A variety of fluids and fluidized solids can easily be transferred through flexible hoses to other locations. These are most commonly known as hosepipes. Along with loading and unloading services in processing plants, these are widely used by homeowners as garden hoses. Normal Flexible hoses are made of non-metals like soft plastic material or synthetic rubber. However, flexible hoses of chemical industries that are designed to absorb pipe movements are made of metallic materials.

Non-metallic Flexible Hoses

Flexible hoses are made by extrusion or vulcanization process. To add strength to the non-metallic flexible hoses, they are reinforced using a crisscrossed grid of fibers combined together through braiding, spiraling, or knitting. These reinforced hoses can be long enough. Basically, flexible hoses have four parts; inner tube, reinforcement, End fittings, and protective outer cover.

Flexible Metal Hoses

Metallic flexible hoses consist of corrugated tubing, braid, braid collars, and end-fittings as shown below:

Typical Flexible hoses
Fig. 1: Typical Flexible hoses

Metallic flexible hoses are available in various end connections like welded pipe ends, flanged ends, threaded ends, tube ends, coupling ends, etc to meet a broad range of application requirements.

Flexible Hose End Connections
Fig. 2: Flexible Hose End Connections

Types of Metallic Flexible Hoses

Two types of metallic flexible hoses are widely used in industries.

  • Corrugated hoses and
  • Interlocked hoses

Fig. 3 below shows the basic construction of corrugated and interlocked flexible hoses.

Corrugated vs Interlocked flexible hoses
Fig. 3: Corrugated vs Interlocked flexible hoses

Corrugated Hose:

A corrugated hose is constructed with a bellow of very long length. Fundamentally, the behavior of a corrugated flexible hose is the same as the bellow expansion joint. The flexible hose has to resist the hoop pressure stress, but cannot sustain the longitudinal pressure stress. Also, it has a tendency to squirm under internal pressure. To resist the longitudinal pressure stress and prevent squirm, corrugated hoses are often constructed with braids wrapping around the outside surface as shown in Fig. 4. The braided cover also protects the corrugation from scratch and wear. The braided hose, similar to a tied expansion joint, cannot accommodate any axial movement. On the other hand, the un-braided hose can sustain very small internal pressure.

Due to the lack of a limiting mechanism, a corrugated flexible hose is prone to abuse. It should not be bent beyond its acceptable range. For braided hoses, the situation is even more critical.

As the corrugations are not visible from the outside, a braided hose does not show immediately when damaged. Therefore, for manual handling in such situations as loading/unloading and switching operations corrugated hose is not suitable. The corrugated flexible hose has a continuous metal wall thus making it pressure-tight. It is suitable for handling any type of gas and liquid as long as it is compatible with the hose material.

Unbraided and braided flexible hose
Fig. 4: Unbraided and braided flexible hose

Interlocked Hose:

An interlocked hose is constructed with links that are kept tight with packing material. There are clearances provided between the links that afford the capability of accommodating some axial movement. As the hose is being bent, the clearances gradually close. The hose becomes stiff and cannot bend any further at a certain point when the clearances are completely closed. This sudden stiffening effect serves as a warning to the handler, preventing the interlocked hose from being over-bent. This automatic warning feature makes the interlocked hose especially suitable for manual handling.

The packing mechanism at the interlocked links does not offer a perfect seal. Therefore, the interlocked hose is satisfactory for carrying low-pressure air, steam, and water, but is generally not suitable for conveying gases and “searching” liquids such as kerosene and alcohol. The outside of the interlocked hose is relatively smooth, making it easy to handle without any covering.

Stress Analysis Consideration for Flexible Hoses

The flexible hose assembly is normally not analyzed. In most situations, the end displacements from piping or equipment connections are calculated from pipe stress analysis software and those values are transferred to the vendor for their consideration. Accordingly, the hose length and installation space are determined.

Pipe Supporting for optimum flexible hose working

A piping system that utilizes a flexible metal hose to absorb pipe movement must be properly anchored and guided to assure correct functioning and maximum service life of the metal hose assembly. The following basic principles should be observed:

  • The direction of pipe motion must be perpendicular to the centerline (axis) of the hose.
  • To prevent torsional stress, the pipe shall be anchored at each change of direction where a flexible metal hose is employed. Typical examples of correct and incorrect guiding are shown below in Fig. 5.
Pipe Supporting Examples
Fig. 5: Pipe Supporting Examples

Installation considerations for Flexible Hoses

Flexible Hoses are used to accommodate piping and equipment displacements. Hoses are extremely flexible, installations are very easy. However, a few general precautions should be exercised during installation to avoid hose failures.

  • The hose should not be subjected to twisting; Also, the installation should be such that flexing takes place only in the plane of bending.
  • The length of the hose should be sufficient to accommodate the offset and movement
  • The installation space should be adequate to accommodate the length.
  • Sharp bends should be avoided while installing flexible hoses. The Technical Data Section of the vendor catalog should be followed to maintain the minimum centerline bend radius for intermittent flexing.

While installing flexible hoses, the allowable minimum bend radius is the most fundamental limitation. For interlocked hoses, the limiting radius depends largely on the clearances between links. It has less to do with stress and fatigue, so it generally has only one limiting radius for all applications. For corrugated hoses, on the other hand, the limiting radius depends on the stress at the corrugations.

For pressure hoses with braided reinforcement, the corrugation stress comes mainly from the bending of the hose. Therefore, the corrugation stresses can be controlled by setting a limitation on the bending. In other words, the installation is acceptable if the hose is not bent beyond the limiting radius. Similar to the situation discussed in the bellow expansion joint, the mode of failure of the hose corrugation is due to fatigue. Therefore, the bend radius limitation depends also on the number of operating cycles expected. Most manufacturers provide two limiting radii, one for static applications involving a one-time fit-up installation, and the other for operational movement involving many cycles of intermittent flexing. The whole design and installation process actually ensures that this minimum radius is maintained during the initial layout and throughout the operation.

Factors for Metallic Flexible Hose Selection

The main factors that should be considered while selecting a flexible hose are:

  • Design and maximum working pressure.
  • Maximum service temperature of the material.
  • Fluid flow velocity
  • Axial, Angular, Offset, Radial, and unpredictable displacements if any.
  • Vibration tendency if any.
  • Required cycle/service life.

Materials for Metallic Flexible Hoses

The most common materials used for metallic flexible hoses are:

  • Carbon Steel
  • Stainless Steel
  • Bronze
  • Monel
  • Inconel
  • Copper
  • Brass
  • Aluminum
  • Aluminized Fiberglass
  • Silicone coated fiberglass

Depending on the operating service temperature range, these materials are decided.

Codes and Standards for Flexible hoses

The codes and standards used for design guidance are listed below:

  • The Society of Automotive Engineers (SAE) SAEJ513: Requirements for Hydraulic hoses.
  • ISO 10807: Corrugated flexible metallic hose assemblies for the protection of electrical cables in explosive atmospheres
  • Interlocked hoses are manufactured from a helically (spiral) wound and overlapping profiled strip in accordance with BS EN ISO 15465.
  • Pressure equipment directive (PED 97/23/EG)
  • DIN EN 14585-1: Pipework-Corrugated metal hose assemblies for pressure applications
  • EN 12434: Cryogenic vessels – cryogenic flexible hoses
  • DIN EN ISO 10380: Pipework-Corrugated metal hoses and metal hose assemblies
  • ISO 10806: Pipework – Fittings for corrugated metal hoses
  • ISO 21969: High-pressure flexible connections for use with medical gas systems
  • EN 2827: Hose assemblies of stainless steels for chemical products
  • DIN 3384: Stainless steel flexible hose assemblies for gas applications-safety requirements, testing, marking
  • EN 14800: Corrugated safety metal hose assemblies for the connection of domestic appliances using gaseous fuels

Applications of Flexible Hoses

Specific applications of flexible hoses include the following:

  • to water plants or to convey water to a sprinkler (Garden hose).
  • to water crops in agriculture (tough hose) for drip irrigation.
  • to convey water to the site of the fire for firefighting service (fire hose).
  • to carry air from a surface compressor (Air hose) or from air tanks.
  • In chemistry and medicine, flexible hoses are used to move liquid chemicals or gases around.
  • A fuel hose carries fuel.
  • to move liquids under high pressures in the oil industry.
  • For Heat Tracing
  • For Auto heater tubing, Ventilating ducting, Moderate suction lines, Automotive exhaust, Dust collecting Ducting,  Air Blower ducting, Wiring conduit, Refrigeration tubing armor, Carburetor air intake, hot ash granulate, etc

Data required for ordering a flexible hose

The following data must be supplied while ordering a flexible hose:

  • Size of hose and connected fittings
  • Design & Operating temperature
  • Design and Operating Pressure
  • Displacements
  • Service and Application
  • End-fitting attachment type
  • Developed Assembly length

All flexible hoses are subject to aging and their performance deteriorates after a number of years. So flexible hoses must be inspected following a company-approved inspection plan or as per manufacturer recommendation.

What are Slip Joints in Piping?

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

What is a Slip Joint?

Slip Joints are mechanical joints that allow the contact surfaces of the pipes joined together to slip away from each other. When there is a large thermal movement of pipe and an expansion loop can not be provided due to other constraints, slip joints can be used to solve expansion stress problems. The slip joint has a rugged construction that makes it suitable for hostile environments, such as inside a ditch, underwater, or underground. However, as the sliding surfaces do not create perfect sealing, leakage may develop along the surface. This concern limits the use of slip joints in hazardous materials. To ensure the slip joint tightness, a considerable force needs to be maintained on the gasket or packing. This results in a fairly large internal friction force resisting the slipping movement. In some cases, this internal friction force is so huge that the joint simply losses its flexing capability. Slip joints are sometimes also known as slip-type expansion joints.

Types of Slip Joints

Depending on the modes of the sliding motion, slip joints are divided into two main types:

  • Axial slip joint and
  • Rotational slip joint.

Axial Slip Joint:

An axial slip joint allows the pipe to slide into it axially and at the same time allows the pipe to also rotate axially. Axial slip joints come in different styles. For low-pressure and temperature lines, the compression sleeve as shown in Fig. 1 (b) is used. When some moderate thermal expansion needs to be absorbed similar types of clamp-on couplings are commonly used. The compression sleeve, also known as Dresser Coupling, is very popular in water distribution systems where the temperature change is mainly due to climate change. For large movements at higher temperatures and pressures, an internally guided construction with a secure packing gland as shown in Fig. 1 (c) is used. All axial slip joints need main anchors to resist the pressure thrust force similar to bellow expansion joints.

Schematic of Slip Joints
Fig. 1: Schematic of Slip Joints

To ensure column stability, properly located guides are needed. However, joints with internal guides are not required.

The internal friction force of an axial slip joint is very significant and should be taken into consideration in the design and analysis of piping and supports. Because an axial joint is normally installed to accommodate the expansion of a straight piping run, the anchor design load can be accurately estimated by the simple addition of the pressure thrust force plus the joint internal friction force plus the support external friction forces.

A computerized analysis normally requires for piping systems that are not entirely straight. The internal friction force can be simulated as the spring force of the axial flexible joint. Because the internal friction force is the product of movement and spring constant, it varies with the actual movement. The analysis may require a couple of iterations to match the spring force with the internal friction force provided by the manufacturer of the joint.

Axial Slip Joints
Fig. 2: Axial Slip Joints

The axial slip joint can also accommodate the axial rotation of the pipe. Occasionally, a joint is specially constructed to accommodate only the axial rotation of the pipe. Because no axial movement is allowed, internal lugs can be installed to resist the pressure thrust force. Therefore, for this type of axial rotation joint, no anchor is needed. By strategically locating a couple of these types of rotational joints, the resulting piping system, much like a multi-hinged system, can accommodate very large movements.

Rotational Slip Joint:

A rotational slip joint is also known as a ball joint or a ball-and-socket joint. As shown in Fig. 1(a), the common type of ball joint is constructed with three main pieces. It has an inner ball-shaped adapter enclosed by a two-piece, dome-shaped housing. At the junction of the two housing pieces, the gasket is placed. As permitted by the opening of the outer housing, the joint can rock at a specific range. It is also capable of rotating 360 degrees axially. It is considered capable of rotating in any direction in a practical sense.

The rotational slip joint or ball joint is a very rugged component that is suitable for hostile environments, such as offshore and loading dock applications. It can sustain considerable abuse by piping and equipment operators. Again, to maintain the tightness of the joint, sufficient force has to be applied and maintained at the gasket or packing. This results in a considerable friction force creating a fairly large resisting moment against the rotation of the joint. The moment required to rotate the joint is called the break-off moment, whose magnitude is available from the manufacturer of the joint. This break-off moment can have a very significant effect on the flexibility of the piping and has to be taken into consideration in the design and analysis of the piping system.

Applications of Slip Joints

Slip joints are widely used in the wastewater plumbing industry. Also, they are popular in the piping industry for non-hazardous piping systems. Other applications of slip joints are:

  • Slip joints are used in large structures for allowing independent motion of large components while enabling them to be joined. Bridges and overpasses frequently have slip joints that allow a deck to move relative to piers or abutments. The joints are constructed with elastomeric pads to permit motion or can use rollers on flat surfaces to allow the ends to move smoothly.
  • Slip joints are used to adjust the length of the propeller shaft when demanded by the rear axle movements in the Automobile industry.