Thursday, 30 January 2020

Rotodynamic pumps Hydraulic performance acceptance te st s Grades 1 and2 BS EN IS0 9906:2000

Rotodynamic pumps
Hydraulic performance
acceptance te st s
Grades 1 and2
BS EN IS0
9906:2000

This International Standard specifies hydraulic performance tests for acceptance of rotodynamic pumps (centrifugal, mixed flow and axial pumps, hereinafter simply designated as “pumps”). It is applicable to pumps of any size and to any pumped liquids behaving as clean cold water (such as defined in 5.4.5.2). It is neither concerned with the structural details of the pump nor with the mechanical properties of their components.
This International Standard contains two grades of accuracy of measurement: grade 1 for higher accuracy, and grade 2 for lower accuracy. These grades include different values for tolerance factors, for allowable fluctuations and uncertainties of measurement.
For pumps produced in series with selection made from typical performance curves and for pumps a with power input of less than 10 kW, see annex A for higher tolerance factors.
This International Standard is applicable both to a pump itself without any fittings and to a combination of a pump associated with all or part of its upstream and/or downstream fittings.



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Pump Handbook EDITED BY Igor J. Karassik Joseph P. Messina Paul Cooper Charles C. Heald

Pump Handbook
EDITED BY
Igor J. Karassik
Joseph P. Messina
Paul Cooper
Charles C. Heald

It is difficult to follow in the footsteps of Igor J. Karassik, whose vision and leadership
played a major role in the concept of a handbook on pumps that is broad enough to encompass
all aspects of the subject—from the theory of operation through design and application
to the multitude of tasks for which pumps of all types and sizes are employed. That
vision was realized in the first edition of the Pump Handbook, which appeared a quartercentury
ago, with the capable and dedicated co-authorship of William C. Krutzsch,Warren
H. Fraser, and Joseph P. Messina. Acceptance of this work globally soon led these distinguished
pump engineers to assemble a second edition that not only contained updated
material but also presented all numerical quantities in terms of the SI system of units in
addition to the commonly used United States customary system of units.
Worldwide developments in pump theory, design and applications have continued to
emerge, and these have begun to affect the outlook of pump engineers and users to such
an extent that a third edition has become overdue. Pumps have continued to grow in size,
speed, and energy level, revealing new problems that are being addressed by innovative
materials and mechanical and hydraulic design approaches. Environmental pressures
have increased, and these can and are being responded to by the creative attention of
pump engineers and users. After all, the engineer is trained to solve problems, employing
techniques that reflect knowledge of physical phenomena in the world around us. All of
this has led the current authors to respond by adding new sections and by revising most
of the others as would be appropriate in addressing these developments. Specifically the
following changes should be noted.
Centrifugal pump theory, in the rewritten Section 2.1, proceeds from the basic governing
fluid mechanics to the rationale that underlies the fundamental geometry and performance
of these machines—while maintaining the concrete illustrations of design
examples. A new subsection on high-energy pumps is included.


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Friday, 24 January 2020

Pump Sizing And Hydraulic Losses Case Material

Pump Sizing And Hydraulic Losses Case Material

Introduction
Pump sizing involves matching the flow and pressure rating of a pump with the flowrate and pressure required for the process. The mass flowrate of the system is established on the process flow diagram by the mass balance. Achieving this mass flowrate requires a pump that can generate a
pressure high enough to overcome the hydraulic resistance of the system of pipes, valves, and so on that the liquid must travel through. This hydraulic resistance is known as the system head.
the system head is the amount of pressure required to achieve a given flowrate in the system downstream of the pump.
Pump sizing,  is the specification of the required outlet pressure of a rotodynamic pump (whose output flow varies nonlinearly with pressure) with a given system head (which varies nonlinearly with flow).

Understanding system head
The system head depends on properties of the system the pump is connected to — these include the static head and the dynamic head of the system.
The static head is created by any vertical columns of liquid attached to the pump and any pressurized systems attached to the pump outlet. The static head exists under static conditions, with the pump switched off, and does not change based on flow. The height of fluid above the pump’s centerline can be determined from the plant layout drawing.
FIG 1

The dynamic head varies dynamically with flowrate (and also with the degree of opening of valves). The dynamic head represents the inefficiency of the system — losses of energy as a result of friction within pipes and fittings and changes of direction. This ineffiency increases with the square of the average velocity of the fluid.
FIG 2
Dynamic head can be further split into two parts. The frictional loss as the liquid moves along lengths of straight pipe is called the straight-run headloss, and the loss as a result of fluid passing through pipe fittings such as bends, valves, and so on is called the fittings headloss.

Main principles of pumps selection
Selection of the pumping equipment is a crucial point that determines both process parameters
and in-use performance of the unit under development. During selection of the type of pump
three groups of criteria can be distinguished:
         1) Process and design requirements
         2) Nature of pumped medium
         3) Key design parameters

1- Process and design requirements:
In some cases the pump selection is determined by some stringent requirements for a number of
design or process parameters. The pump process and design requirements are seldom definitive, and ranges of suitable types of pumps for various specific cases of application are known as a matter of experience accumulated by humanity, and there is no need to enumerate them in detail.
2- Nature of pumped medium:
Characteristics of the pumped medium often become a decisive factor in pumping equipment
selection. Different types of pumps are suitable for pumping of various media differing in viscosity,
toxicity, abrasiveness and many other parameters.
3- Key design parameters:
Operational requirements specified by different industries can be satisfied by several types of
pumps.

What is friction in a pump system
Friction is always present, even in fluids, it is the force that resists the movement of objects.
FIG 3
When you move a solid on a hard surface, there is friction between the object and the surface. If you put wheels on it, there will be less friction. In the case of moving fluids such as water, there is even less friction but it can become significant for long pipes.
Friction can be also be high for short pipes which have a high flow rate and small  diameter as in the syringe example.
In fluids, friction occurs between fluid layers that are traveling at different velocities within the pipe (Figure 4). There is a natural tendency for the fluid velocity to be higher in
the center of the pipe than near the wall of the pipe. Friction will also be high for viscous
fluids and fluids with suspended particles.
FIG 4
Another cause of friction is the interaction of the fluid with the pipe wall, the rougher the pipe, the higher the friction.
Friction depends on:
     - average velocity of the fluid within the pipe
     - viscosity
     - pipe surface roughness

Determining frictional losses through fittings (minnor loss)
Dynamic, or friction, head is equal to the sum of the straight-run headloss and the fittings headloss.
The fittings headloss is calculated by what is known as the k-value method. Each type of valve, bend, and tee has a characteristic resistance coefficient, or k value
FIG 5

We should count the number of valves on the piping and instrumentation diagram (P&ID), and the fittings, bends, and tees on the plant layout drawing for the relevant suction or delivery line. Multiply the number of each type of fitting by the corresponding k value, and add the k values for the various types of fittings to get the total k value. Use the total k value to calculate the headloss due to fittings:

hm = k × (ρ v²)/2
where :
hm  = is the fittings headloss (Pa (N/m²), psf (lb/ft²))
k   = is the minor loss coefficient k value, 
v   = is the superficial velocity (m/sec,), 
ρ   is the density of the fluid,kg/m³,slugs/ft³

Summarized Minor Losses

Minor head loss can be expressed as:

hm = k v²/ 2 g 
where
k = minor loss coefficient
hm  = is the fittings headloss (m, ft)


Calculating straight-run headloss

Pressure loss in steady pipe  flow is calulated using the Darcy-Weisbach equation.
This equation includes the Darcy friction factor. The exact solution of the Darcy friction factor in turbulent flow is got by looking at the Moody diagram or by solving it from the Colebrook equation.
The Darcy-Weisbach equation, for calculating the friction loss in a pipe, uses a dimensionless value known as the friction factor (also known as the Darcy-Weisbach friction factor or the Moody friction factor) and it is four times larger than the Fanning friction factor.
FIG 6


Reynolds Numbers
Fluid flow in a pipe encounters frictional resistance due to the internal roughness (e) of the pipe wall, which can create local eddy currents within the fluid. Calculation of the Reynolds Number helps to determine if the flow in the pipe is Laminar Flow or Turbulent Flow.
Pipes that have a smooth wall such as glass, copper, brass and polyethylene cause less fritional resistance and hence they produce a smaller frictional loss than those pipes with a greater internal roughness, such as concrete, cast iron and steel.
The velocity profile of fluid flow in a pipe shows that the fluid at the centre of the stream moves more quickly than the fluid flow towards the edge of the stream. Therefore friction occurs between layers within the fluid.
Fluids with a high viscosity flow more slowly and generally not produce eddy currents, thus the internal roughness of the pipe has little or no effect on the frictional resistance to flow in the pipe. This condition is known as laminar flow.

Kinematic viscosity = dynamic viscosity/fluid density
Reynolds number = (Fluid velocity x Internal pipe diameter) / Kinematic viscosity
where :
ρ   is the density of the fluid,kg/m³,lbm/ft³
D  is the pipe internal diameter (hydraulic diameter), m,mm
μ  is the fluid dynamic viscosity. Ns/m², lbm/s ft)
𝜈 = μ/ρ is the kinematic viscosity. (cSt ,m²/s, ft²/s)
V  is the average velocity. m/sec ft/sec,   
𝖰  is volumetric flow rate (m³/sec.ft³/sec)
𝘮 is mass flow  rate (kg/sec,lb/sec)

If the flow is transient - 2300 < Re < 4000 - the flow varies between laminar and turbulent flow and the friction coefiicient is not possible to determine. The friction factor can usually be interpolated between the laminar value at Re = 2300 and the turbulent value at Re = 4000.


Pipe Roughness  

Absolute Roughness
The roughness of a pipe is normally specified in either mm or inches and common values range from 0.0015 mm for PVC pipes through to 3.0 mm for rough concrete pipes.
Relative Roughness
The relative roughness of a pipe is its roughness divided by its internal diameter or ε/D, and this value is used in the calculation of the pipe friction factor, which is then used in the Darcy-Weisbach equation to calculate the friction loss in a pipe for a flowing fluid.
e = ε/D

where :
ε is Absolute Roughness . (mm,m) the absolute roughness of the pipe inner wall.
D is the pipe internal diameter (hydraulic diameter), (mm,m)

For turbulent flow the friction coefficient depends on the Reynolds Number and the roughness of the duct or pipe wall. Roughness for different materials can be determined by experiments.
Absolute roughness - ε - for some common materials :

Friction Factor Calculations
The Darcy-Weisbach equation, for calculating the friction loss in a pipe, uses a dimensionless value known as the friction factor (also known as the Darcy-Weisbach friction factor or the Moody friction factor) and it is four times larger than the Fanning friction factor.

Friction Factor for Laminar Flow
The friction factor for laminar flow is calculated by dividing 64 by the Reynold's number.
Friction factor (for laminar flow) 
fD = 64 / Re
Friction Factor for Turbulent Flow
The Colebrook-White approximation can be used to estimate the Darcy friction factor (fD) from Reynolds numbers greater than 4,000:

where
fD     is Darcy-Weisbach friction coefficient
D    is the hydraulic diameter of the pipe,(m,ft)
ε    is the surface roughness of the pipe, (m,ft)
Re  is the Reynolds number
FIG 7
Blasius
The Blasius equation is the most simple equation for solving the Darcy friction factor. Because the Blasius equation has no term for pipe roughness, it is valid only to smooth pipes. However, the Blasius equation is sometimes used in rough pipes because of its simplicity. The Blasius equation is valid up to the Reynolds number 10⁵ . The Blasius equation is
Swamee-Jain
Swamee and Jain  have devoloped the following equation to the Darcy friction factor
Haaland
Haaland  has deduced the equation
In the Haaland equation there is no need to iterate the Darcy friction factor. The accuracy of the Darcy friction factor solved from this equation is claimed to be within about 2 %, if the Reynolds number is greater than 3000
Major Head Loss
Darcy Weisbach Formula
The Darcy formula or the Darcy-Weisbach equation as it tends to be referred to, is now accepted as the most accurate pipe friction loss formula, and although more difficult to calculate and use than other friction loss formula, with the introduction of computers, it has now become the standard equation for hydraulic engineers.
Weisbach first proposed the relationship that we now know as the Darcy-Weisbach equation or the Darcy-Weisbach formula, for calculating friction loss in a pipe.

where
hf  is  pressure loss (Pa (N/m²), psf (lb/ft²))
fD   is the Darcy friction factor
L  is length of pipe or pipe part (m,ft)
D is inner diameter of the pipe
ρ   is the density of the fluid,kg/m³,slugs/ft³)
V  flow velocity (m/sec,ft/sec)

Summarized Major Losses

The major head loss for a single pipe or duct can be expressed as:
hf = fD (L/ D) (v² / 2 g) 

where

hf = head loss (m, ft)
fD= Darcy-Weisbach friction coefficient
L = length of duct or pipe (m)
D= hydraulic diameter (m)
v = flow velocity (m/s, ft/s)
g = acceleration of gravity (m/s2, ft/s2)

Hazen-Williams Formula
Before the advent of personal computers the Hazen-Williams formula was extremely popular with piping engineers because of its relatively simple calculation properties.

However the Hazen-Williams results rely upon the value of the friction factor, C hw, which is used in the formula, and the C value can vary significantly, from around 80 up to 130 and higher, depending on the pipe material, pipe size and the fluid velocity.

Also the Hazen-Williams equation only really gives good results when the fluid is Water and can produce large inaccuracies when this is not the case.

The imperial form of the Hazen-Williams formula is:

hf = 0.002083 x L x (100/C)¹′⁸⁵ x (gpm¹′⁸⁵/ D⁴′⁸⁶⁵⁵)

where:
hf = head loss in feet of water
L = length of pipe in feet
C = friction coefficient
gpm = gallons per minute (USA gallons not imperial gallons)
D = inside diameter of the pipe in inches

The empirical nature of the friction factor C hw means that the Hazen-Williams formula is not suitable for accurate prediction of head loss. The friction loss results are only valid for fluids with a kinematic viscosity of 1.13 centistokes, where the velocity of flow is less than 10 feet per sec, and where the pipe diameter has a size greater than 2 inches.

Notes: Water at 60° F (15.5° C) has a kinematic viscosity of 1.13 centistokes.

Static head.head loss and total head 
The head loss of a pipe, tube or duct system, is the same as that produced in a straight pipe or duct whose length is equal to the pipes of the original systems plus the sum of the equivalent lengths of all the components in the system. This can be expressed as
hloss = Σ hmajor_losses + Σ hminor_losses
hloss  = Σhf +Σhm
where :
hloss   is total head loss 
hf      is head loss of each straigth pipe
hm     is head loss of each compenent (fitting )
FIG 8
Total dynamic head 
As in figure 8
H = (hd -hs) + hloss
where :
H is total head
hd is discharge static head 
hs is suction static head

And as in figure 9
FIG 9
H = (hd +hs) + hloss
Hydraulic power, pump shaft power 
The hydraulic power which is also known as absorbed power, represents the energy imparted on the fluid being pumped to increase its velocity and pressure. The hydraulic power may be calculated using one of the formulae below, depending on the available data
FIG 10

Hydraulic power
Ph = (Q ×H × ρ ×g)/1000 
Where:
Ph = input power of the centrifugal pump (Kw)
ρ = density of water (Kg/m³)
g = acceleration due to gravity (m/sec²)
H =  total head (m)
Q = capacity (m³/s)

or 

SHAFT POWER
The shaft power is the power supplied by the motor to the pump shaft. Shaft power is the sum of the hydraulic power (discussed above) and power loss due to inefficiencies in power transmission from the shaft to the fluid. Shaft power is typically calculated as the hydraulic power of the pump divided by the pump efficiency as follows:

P= Ph/η 

Where :
η = pump efficiency

MOTOR POWER
The motor power is the power consumed by the pump motor to turn the pump shaft. The motor power is the sum of the shaft power and power loss due to inefficiencies in converting electric energy into kinetic energy. Motor power may be calculated as the shaft power divided by the motor efficiency
Pump curves
A pump curve is a plot of outlet pressure as a function of flow and is characteristic of a certain pump. The most frequent use of pump curves is in the selection of centrifugal pumps, as the flowrate of these pumps varies dramatically with system pressure. Pump curves are used far less frequently
for positive-displacement pumps. A basic pump curve plots the relationship between head and flow for a pump (Figure 11 ).
On a typical pump curve, flowrate (Q) is on the horizontal axis and head (H) is on the vertical axis. The pump curve shows the measured relationship between these variables, soit is sometimes called a Q/H curve. The intersection of this curve with the vertical axis corresponds to the closed valve head of the pump. These curves are generated by the pump manufacturer under shop test conditions and ideally represent average values for a representative sample of pumps
FIG 11
More-advanced curves usually incorporate efficiency curves, and these curves define a region of highest efficiency. At the center of this region is the best efficiency point (BEP).
We can often generate acceptable pump curves using the curves you have and the following approximate pump affinity relationships:
CALCULATION OF PUMP SPECIFIC SPEED
Pump specific speed is calculated using the relationship below

Ns  = specific speed (rpm)
n    = rotational speed rpm)
Q   = Capacity (m³/sec)
H   =head (m)
for multi-stage pumps the specific speed is calculated for the first stage only. For pumps with a double-suction inlet the flow rate Q, should be half the total flow rate for the pump.


Dimensionless Form

The traditional pump specific speed is not a dimensionless number, thus it is critically important that the units used are reported along with the pump specific speed value. A dimensionless form can be created by multiplying the pump head by the gravitation constant and measuring the shaft rotation in radians.
The resulting Nd . N​d​​ will be dimensionless provided consistent units are used. Rotational speed nrad ​​ should be measured in radians per second. The metric units m³/s, m/s² and m for Q, g and h respectively are consistent. The imperial units ft³/s, ft/s² and ft as the units of Q, g and h respectively also result in a dimensionless number.
The typical ranges of pump specific speed and the corresponding impeller diameter to eye diameter ratios for several impeller types are shown
FIG 12
Piston pumps (positive displacement pumps)
For single-acting piston pump the flow rate formula will look like the following:

Q – flow rate (m /s)
F – piston cross-sectional area, m
S –piston stroke length, m
n – shaft rotation speed, s
ηv – volumetric efficiency

Gear pumps (positive displacement pumps)
Gear pump performance capacity can be calculated in the following way:

Q – gear pump performance capacity, m /s
f – cross-sectional area of space between adjacent gear teeth, m
z – number of gear teeth
b – gear tooth length, m
n – teeth rotation speed, s⁻¹
ηv – volumetric efficiency

Screw pumps (positive displacement pumps)
Single-screw pump performance capacity can be calculated in the following way:

Q – screw pump performance capacity, m /s
e – eccentricity, m
D – diameter of rotor screw, m
Т – pitch of stator screw surface, m
n – rotor rotation speed, s⁻¹
ηv– volumetric efficiency

Pump Selection Considerations 

Pumps transfer liquids from one point to another by converting mechanical energy from a rotating impeller into pressure energy (head). The pressure applied to the liquid forces the fluid to flow at the required rate and to overcome friction (or head) losses in piping, valves, fittings, and process equipment. The pumping system designer must consider fluid properties, determine end use requirements, and understand environmental conditions. Pumping applications include constant or variable flow rate requirements, serving single or networked loads, and consisting of open loops (nonreturn or liquid delivery) or closed loops (return systems). 

Fluid Properties 
The properties of the fluids being pumped can significantly affect the choice of pump. Key considerations include: 
     • Acidity/alkalinity (pH) and chemical composition. Corrosive and acidic fluids can degrade                 pumps, and should be considered when selecting pump materials. 
     • Operating temperature. Pump materials and expansion, mechanical seal components, and                     packing materials need to be considered with pumped fluids that are hotter than 200°F.             
     • Solids concentrations/particle sizes. When pumping abrasive liquids such as industrial                       slurries,  selecting a pump that will not clog or fail prematurely depends on particle size,                      hardness, and  the  volumetric percentage of solids. 
     • Specific gravity. The fluid specific gravity is the ratio of the fluid density to that of water under           specified conditions. Specific gravity affects the energy required to lift and move the fluid, and            must be considered when determining pump power requirements. 
      • Vapor pressure. A fluid’s vapor pressure is the force per unit area that a fluid exerts in an                  effort  to change phase from a liquid to a vapor, and depends on the fluid’s chemical and                      physical properties. Proper consideration of the fluid’s vapor pressure will help to minimize the           risk of cavitation. 
     • Viscosity. The viscosity of a fluid is a measure of its resistance to motion. Since kinematic                   viscosity normally varies directly with temperature, the pumping system designer must know the         viscosity of the fluid at the lowest anticipated pumping temperature. High viscosity fluids result         in reduced centrifugal pump performance and increased power requirements. It is particularly             important to consider pump suction-side line losses when pumping viscous fluids.

System Flow Rate and Head
The design pump capacity, or desired pump discharge in gallons per minute (gpm)or  m3/sec is needed to accurately size the piping system, determine friction head losses, construct a system curve, and select a pump and drive motor. Process requirements may be met by providing a constant flow rate (with on/off control and storage used to satisfy variable flow rate requirements), or by using a throttling valve or variable speed drive to supply continuously variable flow rates. The total system head has three components: static head, elevation (potential energy), and velocity (or dynamic) head. Static head is the pressure of the fluid in the system, and is the quantity measured by conventional pressure gauges. 
The height of the fluid level can have a substantial impact on system head. The dynamic head is the pressure required by the system to overcome head losses caused by flow rate resistance in pipes, valves, fittings, and mechanical equipment. Dynamic head losses are approximately proportional to the square of the fluid flow velocity, or flow rate. If the flow rate doubles, dynamic losses increase fourfold. 

Environmental Considerations 
Important environmental considerations include ambient temperature and humidity, elevation above sea level, and whether the pump is to be installed indoors or outdoors.

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Sunday, 19 January 2020

Hydrocarbon Seals Importance for Exploration and Production

Hydrocarbon Seals
Importance for Exploration and Production


  • Chapter headings and selected papers: Preface. Fault Seals. Fault seal analysis: successful methodologies, application and future directions (R.J. Knipe et al. ). The emplacement of clay smears in synsedimentary normal faults: inferences from field observations near Frechen, Germany (F.K. Lehner, W.F. Pilaar). Fault seal processes: systematic analysis of fault seals over geological and production time scales (J.R. Fulljames et al. ). Complexity in fault zone structure and implications for fault seal prediction (C. Childs et al. ). Late Jurassic-early Cretaceous caprocks of the southwestern Barents Sea: fracture systems and rock mechanical properties (R.H. Gabrielsen, O.S. Klovjan). Fault properties and the development of cemented fault zones in sedimentary basins: field examples and predictive models (E. Sverdrup, K. Bjorlykke). Quantitative fault seal prediction: a case study from Oseberg Syd (T. Fristad et al. ). Fault seal analysis in hydrocarbon exploration and appraisal: examples from offshore mid-Norway (A.I. Welbon et al. ). Fracture flow and fracture cross flow experiments (A. Makurat et al. ). Fault seal analysis: reducing our dependence on empiricism (T.R. Harper, E.R. Lundin). Migration and Top Seal Integrity. Sealing processes and top seal assessment (G.M. Ingram et al. ). The dynamics of gas flow through rock salt in the scope of time (D. Kettel). Pressure prediction from seismic data: implications for seal distribution and hydrocarbon exploration and exploitation in the deepwater Gulf of Mexico (N.C. Dutta). Pore water flow and petroleum migration in the Smorbukk field area, offshore mid-Norway (R. Olstad et al. ). The Njord field: a dynamic hydrocarbon trap (T. Lilleng, R. Gundeso). Pre-cretaceous top-seal integrity in the greater Ekofisk area (D.M. Hall et al .). References index. Subject index.

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The Seal Man's O-Ring Handbook



The Seal Man's O-Ring Handbook



13 O-Ring Materials
Over 4,000 Sizes Listed
Complete Design Information
Every Metric & Inch Size O-Ring
2,073 Fluid Comparability Listings

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SKF Seal Handbook

SKF Seal andbHook

This Seal handbook contains complete product data for the selection of SKF shaft seals, Speedi-Sleeves®, Wear Sleeves, Hydraulic/Pneumatic products, Defender Bearing Isolator, V-Rings and Heavy Duty DF® (HDDF) seals. Size listings for each style and type of seal or sleeve, material and compound selection guide, compound compatibility chart, and recommended operating conditions charts complement the product data. Installation instructions and troubleshooting

guidelines are also provided.
Simply organized, the illustrative charts and detailed product data make the Seal handbook a valuable tool for industrial distributors, designers, engineers and anyone involved in the selection or specification of these products. SKF’s team of engineers and product managers have thoroughly reviewed and updated all these listings.
Reference tables and complete size listings enable fast selection of the correct shaft seal. Concise descriptions and expanded technical data enable the user to find the correct product for their specific
application.



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Tuesday, 14 January 2020

Basic Components Of Rotary Shaft Seal

Basic Components Of Rotary Shaft Seal



Labels:

Hydraulic fluid power — Sealing devices — Standard test methods to assess the performance of seals used in oil hydraulic reciprocating applications

Hydraulic fluid power — Sealing devices — Standard test methods to assess the performance of seals used in oil hydraulic reciprocating applications
ISO 7986

It  is  widely  recognized  that  the  results  from  reciprocating  seal  testing  can be  unpredictable.  The  background  research  carried  out  in  support  of  the preparation  of  this  International  Standard  has  demonstrated  that  this unpredictability  is  primarily  a  function  of  lack  of  control  of  critical  variables affecting  seal  installation  and  operation.  In  order  to  carry  out  direct comparisons  of  seal  performance,  it  is  necessary  to  control  these  variables to  closer  limits  than  may  be  normal  in  industrial  practice.  The  major variables  that  can  affect  seal  performance,  often  even  within  normal manufacturing tolerance ranges, 


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Hydraulic fluid power — Housings for elastomer-energized, plastic-faced seals — Dimensions and tolerances — Part 2 : Rod seal housings ISO 7425-2

Hydraulic fluid power — Housings for elastomer-energized, plastic-faced seals — Dimensions and tolerances — 
Part 2 : 
Rod seal housings
ISO 7425-2

In hydraulic fluid power systems, power is transmitted and controlled through a liquid under pressure within an enclosed circuit. Sealing devices are used to contain the pres­ surized  fluid  within  components  having  elements with  linear  motion,  i.e.  hydraulic cylinders. These sealing devices are used with both cylinder rod and piston seal housings. 
This part of ISO 7425 is one of a series of standards covering dimensions and toler­ ances, and relates to housings for a specific type of rod seal. Alternative choices of housing size may be found in ISO 5597 : 1987, Hydraulic fluid power — Cylinders — Housings for piston and rod seals in reciprocating applications — Dimensions and tol­ erances.



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Monday, 13 January 2020

Rotary shaft lip-type seals incorporating thermoplastic sealing elements Part 1: Nominal dimensions and tolerances BS ISO 16589-1:2011

Rotary shaft lip-type seals
incorporating thermoplastic
sealing elements
Part 1: Nominal dimensions and tolerances
BS ISO 16589-1:2011

Rotary shaft lip-type seals are used to retain fluid in equipment where the differential pressure is relatively low. Typically, the shaft rotates and the housing is stationary, although in some applications the shaft is stationary and the housing rotates.
Dynamic sealing is normally the result of a designed interference fit between the shaft and a flexible element incorporated in the seal. Similarly, a designed interference fit between the outside diameter of the seal and the diameter of the housing
bore retains the seal and prevents static leakage.
Careful storage and handling and proper installation of all seals are necessary to avoid hazards, both prior to and during installation, which would adversely affect service life.




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Seals and Sealing Handbook, Fifth Edition by Robert K. Flitney

Seals and Sealing Handbook, Fifth Edition
by Robert K. Flitney


Wherever machinery operates there will be seals of some kind ensuring that the machine remains lubricated, the fluid being pumped does not leak, or the gas does not enter the atmosphere. Seals are ubiquitous, in industry, the home, transport and many other places. This 5th edition of a long-established title covers all types of seal by application: static, rotary, reciprocating etc. The book bears little resemblance to its predecessors, and Robert Flitney has re-planned and re-written every aspect of the subject. No engineer, designer or manufacturer of seals can afford to be without this unique resource.

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Pump, centrifugal pumps, PD pumps, seals & mechanical seals data


Pump, centrifugal pumps, PD pumps, seals & mechanical seals data

In addition to the technical papers shown in the above index, I have published information on over 6oo pump and seal subjects on the web. This information is avilable to you by either looking up the subject in any search engine, or by purchasing my CD , where the subjects are indexed and linked.
Seal and Pump Cheat Sheet Index
Introduction to the Tutorials
Is this a seal application?
Learning about pumps
Choosing the seal
Selecting an impeller
Selecting a pump
Installing the pump
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Monday, 6 January 2020

An Introduction To Seals types ,Selection And Applications

An Introduction To Seals  types ,Selection And Applications 


Introduction
Seal is a device or substance that is used to join two things together so as to prevent them from coming apart or to prevent anything from passing between them.Seals are an important part of machine design in situations where the following conditions apply:
     1. Contaminants must be excluded from critical areas of a machine.
      2. Lubricants must be contained within a .space.
      3. Pressurized fluids must be contained within a component such as a valve or a hydraulic                       cylinder.
Excessive leakage in a hydraulic circuit reduces efficiency and results in power loss or creates a housekeeping problem or both.Hydraulic seals prevent leakage by closing off oil passageways; they seal the gaps to prevent fluid loss.

Seals Classification
The purpose of seals is to contain the working fluid within the hydraulic or pneumatic unit and to keep external contamination out. They may be classified as one of the following.
1- Static seals,
2- Dynamic seals
      • Sliding seals
      • Rotary seals.




1-Static Seals 
A static seal is one that is compressed between two rigidly connected parts to seal the fluid passage and has a compression of approximately 25 per cent.
Stationary seals are used between the flanged joints of pipes, on the cylinder heads of engines pumps and compressors, between crank cases and oil sumps and under inspection and access covers.
Sometimes a liquid sealant is used and there are many proprietary brands that are resistant to oil and water. Some of them solidify after assembly whilst others are intended to remain tacky.
Separation of the surfaces for maintenance can sometimes be a problem after which they have to be carefully cleaned before re-assembly.

1-1 GASKETS

Gaskets are cut out of thin sheets of material and placed between mating surfaces which are then squeezed together by screws or bolts. The materials used are paper, copper, brass, rubber and so on. Typical applications are between flanges on pipes and flanges on the fluid port of a pump or motor.

FIG 1

Types of Gaskets

1. Non- Metallic
2. Semi- Metallic
3. Metallic
FIG 2
1-2 RINGS
Rings are placed in grooves between the mating surfaces and stand proud of the groove so that they are squeezed when the surfaces are pulled together. The rings are usually circular in section and are then called O rings but they may have rectangular sections also.
FIG 3

static axial seal 
A static axial seal acts similar to a gasket in that it is squeezed on both the top and bottom of the O-ring’s cross section. (figure 4)This type of seal is typically employed in the face (flange) type applications
Static Axial Seal Gland

FIG 4
Static Radial Seals

Static Radial Seals are squeezed between the inner and outer surfaces of the O-ring. They are typically employed in cap and plug type applications,Static Radial Seal
FIG 5

STATIC CRUSH SEALS

In crush seal applications, the O-ring is completely confined and pressure deformed (crushed) within a triangular gland made by machining a 45° angle on the male cover. Squeezed at an angle to the O-ring’s axis, crush seals are used in such simple applications 
STATIC CRUSH SEALS
FIG 6
STATIC SEALS WITH DOVETAIL GLANDS

O-rings are sometimes employed in static or slow moving dynamic situations calling for specially machined “dovetail” glands. Because of the angles involved, controlling the tolerances in these glands may be difficult.
The purpose of these glands is to securely hold the O-ring in place during machine operation and/or maintenance disassembly.
A typical valve seat application In this application, O-ring squeeze is primarily axial in direction (valve operation exerts force on top and bottom seal surfaces).
To avoid tearing or nicking, the use of O-ring lubrication is recommended while installing the O-ring into the dovetail gland. Because of the difficulty in creating the groove and tight tolerances required, this type of seal application should only be used when necessary.
 STATIC SEALS WITH DOVETAIL GLANDS
FIG 7
Back-up rings

Back-up rings are plastic or rubber rings used to prevent the O-ring from entering the clearance gap. When high pressures are exerted on the O-ring, its soft rubber material can be forced into the clearance gap causing the O-ring to extrude 
FIG 8
METAL O RING SEAL

Metal O Rings are a superior sealing method, these seals are created to improve the capability in intense operations. Used in many cases where elastomers don’t provide sufficient reliability for certain applications. They have the capability to withstand wide scope of temperatures, corrosive chemicals, high pressures, and radiation. Metal O Rings are commonly made from tubing. A classic tubing is made out of stainless steel and high-temperature alloys. this divided to :
- metal O ring seal
- metal C ring seal
- metal E ring seal
FIG 9
1-3WASHERS

Sealing washers are placed under the head of screwed fittings with parallel threads to prevent fluid leaking up the thread and escaping under the head. Plastic washers are sufficient for pneumatic applications and copper washers are also often used.
FIG 10
DOWTY (Bonded) WASHERS

These are used for containing high pressure fluids. They are usually aluminium rings with a rubber seal glued to the inner surface. The shape of the seal is such that fluid leaking up the thread presses the rubber firmly against the sealing surfaces.
FIG 11

2-  Dynamic seals
 A dynamic seal is one that is installed between two parts that move relative to one another, for example on a rotating shaft or a sliding piston. The sealing principle requires the seal to be compressed slightly (approximately 10 per cent) during installation. The seal is allowed to flex in the sealing chamber and a mechanical or fluid pressure forces the seal to distort and block the passageway.
These seals require lubrication during movement or sealing
This classification of seals is used in situations involving reciprocating (sliding), rotating or oscillating motion.
Dynamic seal performance may be substantially affected by a number of operating environmental factors.
2-1 Sliding seals

Sliding seals are mainly used with cylinders to prevent fluid escaping around a piston rod or from passing from one side of a piston to the other. All sliding seals are rings but many different types exist. These may be solid rings such as O rings or rings with rectangular sections. For more demanding applications, more sophisticated designs are used with lips or cups to make the seal fan out and fill the gap between the sliding parts.

Reciprocating seals

As depicted in figure 12 , are used in situations involving a moving piston and a rod. These seals constitute the predominant dynamic application for O-rings.
For optimum performance of reciprocating seals, careful consideration of the following factors is
required
FIG 12
Common types are U ring, Cup, Flange, Chevron, O ring and T ring
The figure 13 shows a U ring seal on a piston to prevent fluid passing from the top to the bottom of the piston. Two seals placed back to back would be used for a double acting cylinder. U ring seals may be used for piston rods also and there is a large variety of shapes for shapes for different applications.
FIG 13
Cup seal 
which is suitable for simple single acting cylinders with low pressure. The fluid pressure forces the cup out against the cylinder walls.
Flange seal
which is used on the piston rod. The flange is tightened down and squeezes the seal into the gap between the rod and the cylinder end.
FUG 14
chevrons Seals

The seal is made up of chevrons embedded in a softer material. They are forced into the gap by the screwed ring and the chevrons spread out and form a seal.

The wiper ring 
The wiper ring is not strictly a seal. Its purpose is to remove oily dirt from the rod as it is drawn into the cylinder. The action is similar to that of a car wind screen wiper.
FIG 15

Piston ring 

Piston rings are metallic piston rings used to seal cylinders. They have a higher working temperature than elastomeric, fabric, or polymer materials. Piston rings are available in a variety of configurations, including compression rings, split rings, and cord rings.
FIG 16
Exclusion seals 

Exclusion seals (figure 17) are dynamic seals such as wipers and scrapers that support sliding or reciprocating motion. They clean the surface by scraping abrasive particles such as dirt, mud, and ice. Exclusion seals are very important because they protect the seal and extend its service life. The wipers should be checked frequently to ensure they are in good working condition. Often the wipers fail causing the seal to fail.
FIG 17

Packing's and Braided Rope Seals

Rope packing's used to seal stuffing boxes and valves and prevent excessive leakage can be
traced back to the early days of the Industrial Revolution.

Compression packing seals or gland seals are used to seal a variety of fluids under a range of conditions (figure 18). They are used to help contain water, acids, solvents, gases, oil, and other chemicals that are subjected to various temperatures and pressures.

Compression packing is a common sealing process where a gland along the top ring is tightened, and the packing compressed onto the surface to be sealed.
FIG 18

The packed gland seal for pump applicataions is, due to it's high maintenance requirements, is now rarely fitted to new pumps then mostly in conjunction with long coupled bed plate mounted pumps. Specific operating conditions require distinctly different types packed gland seals.
They require regular checks and maintenance adjustments.. Proper lubrication of the gland packing requires a certain leakage rate.
Special manufacturers recommendation's are to be observed individually. Service life expectancy is between 1 and 2 years, this can sometimes extend to several years on favourable conditions. Extremely bad fluid conditions (sediments, additives, overheating) can however drastically cut short their service life.
Packed glands should preferably be used in conjunction with shaft sleeves in order to avoid damage to the shaft by aggressive fluids or due to improper treatment of the packed gland.

The packed gland is still widely used for stem sealing of various types of valves including gate valves, globe valves, and ball valves (figure 19).
The packed gland provides a low cost option with the capabilities of sealing under a wide range of operating conditions with a wide range of fluids by selecting appropriate packing materials. A packed gland is often used in conjunction with another type of seal or fluid containment e.g an o-ring seals, bellows containment etc.
FIG 19


The gland packing generally creeps over time and therefore needs to be regularly tightened to maintain the seal. The packing can be continuously spring loaded using disc springs or similar to extend the maintenance period.

2-2 ROTARY SEALS
Rotary seals are used on pumps and motors to prevent fluid leaking out through the gap between the shaft and the shaft bearing. They are designed with a spring loaded lip which presses to the shaft. Oil leaking into the space behind the seal will force the lip even tighter but this space should be drained to prevent the seal being blown out by pressure.
FIG 20


labyrinth Seals

A labyrinth is defined as a complicated network of passages. A labyrinth is provided the prevent the easy passage from the entry to the exit.
The labyrinth seal provides the same function.The Labyrinth Seal restricts the passage of solid, liquid and gaseous contaminants into the sealed area and also restricts the leakage of fluid out of the sealed containment.
Non-contacting rotary and stationary elements provide a restricted flow path and utilize centrifugal force and gravity to prevent leakage.
Unlike other rotating e.g lip seals, the Labyrinth Seal will not damage shafts and has a virtually unlimited life, is frictionless, is largely unaffected by high or low temperatures and can be used for high shaft rotating speeds.
Sealing depends on the form of the labyrinth gap and the length of the leakage path. Rings on the shaft and grooves in the housing provide the basic labyrinth. At least three groves should be used to provide adequate sealing; clearances vary between 0.25 to 1.0 mm, depending on the speed and temperature the seal is operating in.
More efficient forms of labyrinth seal use alternating teeth of alternating serrations. Smaller gaps produce less leakage but the gap has to be large enough to avoid contact.
The obvious disadvantage of the labyrinth seal is that there is an engineered gap. This type of seal does not work well if the shaft is not rotating and is not really effective at sealing across high pressure differentials.
FIG 21


Lip Seals

This is an assembly consisting of a rubbing elastomer ring seal element held in place by spring.
The seal friction is reduced as an oil film is generated between the lip of the seal and the shaft. Any damage to the shaft where the seal runs will cause leakage because the optimum oil film thickness will be exceeded locally. Therefore the shaft finish is especially important, as leakage will occur if an irregular surface is present.

The lubricated rubbing provides the sealing action. This sealing action cannot be maintained at high speeds if the shaft is not running perfectly true. To maintain oil film thickness the seal must follow any shaft movement. This becomes difficult when the shaft is subject to eccentric running or vibration at high speeds. Typically these seals will operate in the region of 18 m/s and the seals are affected by friction.
FIG 22
The standard shaft seals include the most recent profiles(figure 23), standardised by ISO 6194, DIN 3760 or DIN 3761. 
They are generally pressure-free and come in different design shapes depending on the type of fluid, level of external pollution, qualities of the shaft and housing (hardness, surface roughness, material), speed, temperature,
FIG 23
V-Rings. 

The use of V-rings is rather limited in hydraulic systems; however, they are used in some shock struts. A V-ring can seal in only one direction and can be used to seal surfaces regardless of whether there is movement between the parts
FIG 24
Circumferential seals 

Circumferential seals are designed to provide a close fitting ring (a bush) to limit leakage along the shaft. The most common form is a series of segments that are held together to form a bush, typically known as a segmented ring sea
FIG 25
Axial Mechanical Seals

Axial mechanical seals (figure 26) are face type seals which create an axial seal interface between matched, radially mounted components. In operation, one contact face is usually stationary in the housing while the other moves with the shaft. Sealing pressure is applied in the axial direction through a spring mechanism. The spring force keeps the surfaces together.
Axial mechanical seals are generally used where pressure and/or surface speeds exceed the capabilities of radial shaft seals. Typical applications are water pumps and most types of pumps used in chemical processing plants or refineries. 
FIG 26

Felt Seals

Felt seals are mainly used with as oil or grease seals for retaining lubrication and at the same time preventing dirt or dust entering the bearing.
Felt has long been used for sealing duties because of numerous favourable properties such as wicking and oil absorption properties, fine filtering and resilience. This allows the felt to maintain a constant sealing pressure and as the seal wears the felt surface remains unchanged.
Felt seals are usually pre-saturated with lubricants of a higher viscosity than the bearings offering positive bearing protection. If the seal does run dry it will tend to protect and polish the shaft rather than cause damage. Through normal operating temperatures and conditions the felt seal is highly economical, normally requiring replacement when the machine is overhauled.
When the seal is correctly installed the seal is effective over a variety of operating conditions and a wide range of speeds.
Normal maximum rubbing speed is 10 m/s but can be as high as 20m/s if the rubbing surfaces are highly polished and lubricant is always present.
Felt Seals are not suitable for oils with extremely low viscosity or the lubricant is pressurised.
FIG 27

Ferrofluid Seals

This is a very specialised rotary seal type which has very superior theoretical benefits.
The seal is fluid ring which is retained in place between the rotating and fixed members under the action of magnetic forces (figure 28).
Ferrofluidic sealing technology takes advantage of the response of a fluid, containing a uniform distribution of magnetic particles, to an applied magnetic field. It uses a magnet with magnetically permeable north and south pole pieces and a magnetically permeable shaft to create a permanent magnetic circuit. The magnetic flux is concentrated in the gap under each pole and when ferrofluid is applied to this gap it assumes the shape of a liquid o-ring and produces a hermetic seal.
Ferrofluidic seals offer provide hermetic sealing, long life, virtually frictionless sealing and smooth operation. They are non-contaminating, highly reliable and can operate at high speeds. This type of seal can be used over a wide temperature range, which can be increased by use of cooling, or heating circuits.
The seals have to be regularly maintained as the fluid properties deteriorate over time.
These bearings are used for very specialised applications.
FIG 28

BRUSH SEALS

Brush seals are an alternative for labyrinths in gas turbine engine applications, reducing leakage by a factor up to five or tenfold, although relatively expensive. The brush seal comprises a bundle of metal filaments welded at the base. The filaments are angled circumferentially at about 45 degrees, filament length is chosen to give an interference of 0.1–0.2 mm with the sealing counterface. Filaments are typically about 0.7 mm diameter and manufactured from such materials as high temperature alloys of nickel or cobalt. Suitable counterface materials include hardfacings of chromium carbide, tungsten carbide or alumina
FIG 29
Finger seals 

Finger seals (FS) (figure 30) represent a compliant seals technology. They can be mounted on stationary members as well as on rotating ones. They belong to the same class of seals as brush seals, foil seals, and leaf seals. While their compliance allows both axial and radial adjustment to rotor excursions without damage to the integrity of the seal, their potential lifting capability maintains seal integrity but largely eliminates the wear factor, thus increasing their life span relative to that of brush seals and labyrinth seals.
FIG 30

Selection Factors for Seals

The primary factors affecting seal selection are temperature, wear resistance, abrasion, sealed pressure, face materials, vibration, and expected life. Usually, bellow seals are needed for high-temperature applications.

1- Temperature
Temperature affects all seal materials, but its most important effects are on the secondary seals. The general limitation on temperature for standard synthetics is about 225°F although some are available for uses up to 600°F. PTFE can be used over a temperature range of -400 to 550°F, although most manufacturers rate PTFE seals on the basis of 500°F maximum temperature.
Asbestos elements have been used up to 650°F. Above 650°F, metal bellows, U-cups, or piston rings can be used, but these seals are considered specials.

2- Lubrication 
 Lubrication can reduce heat generation at the seal interface, but care must be taken to prevent coking. Direct cooling with a cooling chamber and heat exchanger can help control thermal problems. In this method, an integral pumping ring on the rotating seal element circulates coolant through an inner chamber in the stuffing box.

3- Wear resistance 
Wear resistance depends largely on temperature and chemical factors, and on abrasives. To minimize wear, the sealed fluid should be a good lubricant for the materials of the seal head and seat. Furthermore, all seal materials should be virtually impervious to corrosion by the sealed fluid.

4- Face materials
Face materials  subject to dry running because of malfunctioning equipment can fail prematurely. Double seals with isolated liquid circulation avoid this hazard. For systems with external circulation, pressure drops can be detected with a pressure-sensitive switch.

5- Abrasion 
Abrasion is the bane of face seals. Faces should be cleaned before initial start-up to prevent premature failures. With liquids that form abrasives on contact with air, a buffer zone or quench gland should be provided between the atmosphere and the seal faces. With liquids that form abrasives at certain temperatures, heating or cooling is necessary to dissolve abrasives near the seal faces. With liquids that are inherently abrasive, a neutral clean liquid can sometimes be injected into the seal chamber. If the sealed liquid cannot be contaminated, a double-seal design can be used, or a centrifugal separator should be inserted ahead of the seal.

6-High sealed pressure
High sealed pressure can drastically shorten the life of the sealing faces and should be compensated by seal balancing.

7- Face materials
Face materials must be compatible with each other and the sealed fluid. Because of their good mechanical and thermal properties, graphites are generally used as one of the primary sealing elements. The opposing element can be made of ceramics, iron, bronze, stainless steel, tool steel, and various other metals plated with dense chrome. The ceramics are some of the hardest face materials available and have excellent wear and corrosion properties. However, they cannot stand tensile stress and are subject to cracking by thermal shock.

8- Vibration
Vibration can shorten the life of a seal, particularly if imposed vibration during operation has a frequency near the natural frequency of the seal. The basic precaution is to ensure the seal's natural frequency is higher than the highest imposed frequency. This precaution is particularly necessary with metal bellows.

9- Life expectancy
Life expectancy depends on both shelf life and operational life. The shelf life of metal bellows is practically unlimited, whereas organic secondary seals may have shorter shelf life, particularly at elevated temperatures. Within their temperature limits, elastomeric bellows have better operational life than metal bellows. However, metals withstand higher temperatures.

Theory of the leak-rate of seals
Seals are extremely useful devices to prevent fluid leakage. However, the exact mechanism of roughness induced leakage is not well understood
Seals play a crucial role in many modern engineering devices, and the failure of seals may result in catastrophic events
 In spite of its apparent simplicity, it is still not possible to predict theoretically the leak-rate and (for dynamic seals) the friction forces for seals.
The main problem is the influence of surface roughness on the contact mechanics at the seal-substrate interface. Most surfaces of engineering interest have surface roughness on a wide range of length scales, e.g, from cm to nm, which will influence the leak rate and friction of seals, and accounting for the whole range of surface roughness is impossible using standard numerical methods, such as the Finite Element Method. 
Here will analyze the role of surface roughness on seals. 
It will use a recently developed contact mechanics theory to calculate the leak-rate of static seals. It is recommended to assume that purely elastic deformation occurs in the solids, which is the case for rubber seals. For metal seals, strong plastic deformation often occurs in the contact region. 

FIG 31
Rubber seal (figure 31). The liquid on the left-handside is under the hydrostatic pressure Pa and the liquid to the right under the pressure Pb (usually, Pb is the atmospheric pressure). The pressure difference ∆P = Pa − Pb results in liquid flow at the interface between the rubber seal and the rough substrate surface. The volume of liquid flow per unit time is denoted by  , and depends on the squeezing pressure P0 acting on the rubber seal.


Thus for an incompressible Newtonian fluid, the volumeflow per unit time through the critical constriction will be


where :
Q˙ = The volume of liquid flow per unit time
 η :       is the fluid viscosity
 u1(ζ) : the (average) height separating the surfaces which appear to come into contact when the                      magnification decreases from ζ to ζ − ∆ζ,
where
∆ζ      is a small (infinitesimal) change in the  magnification.
u1(ζ)  is a monotonically decreasing function of  ζ,  and can be calculated from  the average interfacial separation ¯u(ζ) and A(ζ) using
         
FIG 32
            

The rubber-countersurface apparent contact area is rectangular Lx × Ly. SO “divide” it into 
 N = Ly/Lx square areas with side L = Lx and area A0 = L ²
FIG 33
The contact region at different magnifications (schematic 34). Note that at the point where the                  non-contact area (white area) percolate A(ζc) ≈ 0.4A0, while there appear to be complete                      contact between the surfaces at the lowest magnification ζ = 1: A(1) = A0
          
FIG 34
A first rough estimate of the leak-rate is obtained by assuming that all the leakage occurs                    through the critical percolation channel, and that the whole pressure drop ∆P = Pa−Pb 
(where     Pa and Pb is the pressure to the left and right of the seal) occurs over the critical constriction  [of width and length λc ≈ L/ζc and height uc = u1(ζc)]


It should assumed laminar flow and that uc << λc, which is always satisfied in practice. Here  have introduced a factor α which depends on the exact shape of the critical constriction, but which is expected to be of order unity. Since there are N = Ly/Lx square areas in the rubbercountersurface (apparent) contact area, it get the total leak-rate
 Seal Materials Specification 

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