Microsoft Word - Mode of Failure

8/2/2019 Microsoft Word - Mode of Failure

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The yield strength or yield point of a material is defined in engineering and materials

science as the stress at which a material begins to deform plastically. Prior to the yield

point the material will deform elastically and will return to its original shape when the

applied stress is removed. Once the yield point is passed some fraction of the

deformation will be permanent and non-reversible.

In the three-dimensional space of the principal stresses (1,2,3), an infinite numberof yield points form together a yield surface.

Knowledge of the yield point is vital when designing a component since it generally

represents an upper limit to the load that can be applied. It is also important for the

control of many materials production techniques such as forging, rolling, orpressing.

In structural engineering, this is a soft failure mode which does not normally cause

catastrophic failure orultimate failure unless it acceleratesbuckling.

Definition

Typical yield behavior for non-ferrous alloys.

1: True elastic limit

2: Proportionality limit

3: Elastic limit

4: Offset yield strength

It is often difficult to precisely define yielding due to the wide variety ofstressstrain

curves exhibited by real materials. In addition, there are several possible ways to

define yielding:[1]

True elastic limit

The lowest stress at which dislocations move. This definition is rarely used, since

dislocations move at very low stresses, and detecting such movement is very difficult.Proportionality limit

Up to this amount of stress, stress is proportional to strain (Hooke's law), so the stress-

strain graph is a straight line, and the gradient will be equal to the elastic modulus of

the material.

Elastic limit (yield strength)

Beyond the elastic limit, permanent deformation will occur. The lowest stress at

which permanent deformation can be measured. This requires a manual load-unload

procedure, and the accuracy is critically dependent on equipment and operator skill.

Forelastomers, such as rubber, the elastic limit is much larger than the proportionality

limit. Also, precise strain measurements have shown that plastic strain begins at low

stresses.


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Yield point

The point in the stress-strain curve at which the curve levels off and plastic

deformation begins to occur

Offset yield point (proof stress)

When a yield point is not easily defined based on the shape of the stress-strain curvean offset yield pointis arbitrarily defined. The value for this is commonly set at 0.1 or

0.2% of the strain. The offset value is given as a subscript, e.g., Rp0.2=310 MPa. High

strength steel and aluminum alloys do not exhibit a yield point, so this offset yield

point is used on these materials

Upper yield point and lower yield point

Some metals, such as mild steel, reach an upper yield point before dropping rapidly to

a lower yield point. The material response is linear up until the upper yield point, but

the lower yield point is used in structural engineering as a conservative value. If a

metal is only stressed to the upper yield point, and beyond, Lders bands can develop.

In practice, buckling is characterized by a sudden failure of a structural member

subjected to high compressive stress, where the actual compressive stress at the point

of failure is less than the ultimate compressive stresses that the material is capable of

withstanding. For example, during earthquakes, reinforced concrete members may

experience lateral deformation of the longitudinal reinforcing bars. This mode of

failure is also described as failure due to elastic instability. Mathematical analysis of

buckling makes use of an axial load eccentricity that introduces a moment, which

does not form part of the primary forces to which the member is subjected. When load

is constantly being applied on a member, such as column, it will ultimately become

large enough to cause the member to become unstable. Further load will cause

significant and somewhat unpredictable deformations, possibly leading to complete

loss of load-carrying capacity. The member is said to have buckled, to have deformed.

In materials science, fatigue is the progressive and localized structural damage that

occurs when a material is subjected to cyclic loading. The nominal maximum stress

values are less than the ultimate tensile stress limit, and may be below the yield stress

limit of the material.

Fatigue occurs when a material is subjected to repeated loading and unloading. If the

loads are above a certain threshold, microscopic cracks will begin to form at the

surface. Eventually a crack will reach a critical size, and the structure will suddenlyfracture. The shape of the structure will significantly affect the fatigue life; square

holes or sharp corners will lead to elevated local stresses where fatigue cracks can

initiate. Round holes and smooth transitions or fillets are therefore important to

increase the fatigue strength of the structure.

Poisson's ratio (), named afterSimon Poisson, is the ratio, when a sample object isstretched, of the contraction or transverse strain (perpendicular to the applied load), to

the extension or axial strain (in the direction of the applied load).


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When a material is compressed in one direction, it usually tends to expand in the other

two directions perpendicular to the direction of compression. This phenomenon is

called the Poisson effect. Poisson's ratio (nu) is a measure of the Poisson effect. ThePoisson ratio is the ratio of the fraction (or percent) of expansion divided by the

fraction (or percent) of compression, for small values of these changes.

Conversely, if the material is stretched rather than compressed, it usually tends to

contract in the directions transverse to the direction of stretching. Again, the Poisson

ratio will be the ratio of relative contraction to relative stretching, and will have the

same value as above. In certain rare cases, a material will actually shrink in the

transverse direction when compressed (or expand when stretched) which will yield a

negative value of the Poisson ratio.

The Poisson's ratio of a stable, isotropic, linearelastic material cannot be less than

1.0 nor greater than 0.5 due to the requirement that Young's modulus, the shear

modulus andbulk modulus have positive values.[1] Most materials have Poisson's

ratio values ranging between 0.0 and 0.5. A perfectly incompressible material

deformed elastically at small strains would have a Poisson's ratio of exactly 0.5. Most

steels and rigid polymers when used within their design limits (before yield) exhibit

values of about 0.3, increasing to 0.5 for post-yield deformation (which occurs largely

at constant volume.) Rubber has a Poisson ratio of nearly 0.5. Cork's Poisson ratio is

close to 0: showing very little lateral expansion when compressed. Some materials,

mostly polymer foams, have a negative Poisson's ratio; if these auxetic materials are

stretched in one direction, they become thicker in perpendicular directions.

Anisotropic materials can have Poisson ratios above 0.5 in some directions.

Assuming that the material is stretched or compressed along the axial direction (the xaxis in the diagram):

where

is the resulting Poisson's ratio,is transverse strain (negative for axial tension (stretching), positive for

axial compression)is axial strain (positive for axial tension, negative for axial compression).


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Young's modulus

Young's modulus is a measure of the stiffness of an elastic material and is a quantityused to characterize materials. In solid mechanics, the slope of the stress-strain curve

at any point is called the tangent modulus. The tangent modulus of the initial, linear

portion of a stress-strain curve is called Young's modulus, also known as the tensile

modulus. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the

range of stress in which Hooke's Law holds.[1] It can be experimentally determined

from the slope of a stress-strain curve created during tensile tests conducted on a

sample of the material. In anisotropic materials, Young's modulus may have different

values depending on the direction of the applied force with respect to the material'sstructure.

It is also commonly, but incorrectly, called the elastic modulus ormodulus of

elasticity, because Young's modulus is the most common elastic modulus used, but

there are other elastic moduli measured, too, such as thebulk modulus and the shear

modulus.

Young's modulus is named afterThomas Young, the 19th century British scientist.

However, the concept was developed in 1727 by Leonhard Euler, and the first

experiments that used the concept of Young's modulus in its current form were

performed by the Italian scientist Giordano Riccati in 1782, predating Young's work

by 25 years

Stiffness is the resistance of an elastic body to deformation by an applied force along

a given degree of freedom (DOF) when a set of loading points and boundaryconditions are prescribed on the elastic body. It is an extensive material property.


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Calculations

The stiffness, k, of a body is a measure of the resistance offered by an elastic body to

deformation. For an elastic body with a single Degree of Freedom (for example,

stretching or compression of a rod), the stiffness is defined as

where

Fis the force applied on the body

is the displacement produced by the force along the same degree of freedom (for

instance, the change in length of a stretched spring)

In the International System of Units, stiffness is typically measured in newtons permetre. In English Units, stiffness is typically measured in pound force (lbf) per inch.

Generally speaking, deflections (or motions) of an infinitesimal element (which is

viewed as a point) in an elastic body can occur along multiple Degrees of Freedom

(maximum of six Degrees of Freedom at a point). For example, a point on a

horizontalbeam can undergo both a vertical displacement and a rotation relative to its

undeformed axis. When the Degrees of Freedom is M, for example, a M x M matrix

must be used to describe the stiffness at the point. The diagonal terms in the matrix

are the direct-related stiffnesses (or simply stiffnesses) along the same degree of

freedom and the off-diagonal terms are the coupling stiffnesses between two different

degrees of freedom (either at the same or different points) or the same degree offreedom at two different points. In industry, the term influence coefficient is

sometimes used to refer to the coupling stiffness.

It is noted that for a body with multiple Degrees of Freedom, Equation (1) generally

does not apply since the applied force generates not only the deflection along its own

direction (or degree of freedom), but also those along other directions (or Degrees of

Freedom). For example, for a cantilevered beam, the stiffness at its free end is

12*E*I/L^3 rather than 3*E*I/L^3 if calculated with Equation (1).

For a body with multiple Degrees of Freedom, to calculate a particular direct-related

stiffness (the diagonal terms), the corresponding Degree of Freedom is left free while

the remaining Degrees of Freedom should be constrained. Under such a condition,

Equation (1) can be used to obtain the direct-related stiffness for the degree of

freedom which is unconstrained. The ratios between the reaction forces (or moments)

and the produced deflection are the coupling stiffnesses.

The inverse of stiffness is compliance, typically measured in units of metres per

newton. In rheology it may be defined as the ratio of strain to stress,[1] and so take the

units of reciprocal stress, e.g. 1/Pa.

Rotational stiffness


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A body may also have a rotational stiffness, k, given by

where

Mis the applied moment

is the rotation

In the SI system, rotational stiffness is typically measured in newton-metres perradian.

In the SAE system, rotational stiffness is typically measured in inch-pounds per

degree.

Further measures of stiffness are derived on a similar basis, including:

shear stiffness - ratio of applied shearforce to shear deformation

torsional stiffness - ratio of applied torsion moment to angle of twist

Relationship to elasticity

In general, elastic modulus is not the same as stiffness. Elastic modulus is a property

of the constituent material; stiffness is a property of a structure. That is, the modulus

is an intensive property of the material; stiffness, on the other hand, is an extensiveproperty of the solid body dependent on the material andthe shape and boundary

conditions. For example, for an element in tension orcompression, the axial stiffness

is

where

A is the cross-sectional area,Eis the (tensile) elastic modulus (orYoung's modulus),

L is the length of the element.

Similarly, the rotational stiffness is

where

"I" is the moment of inertia,"n" is an integer depending on the boundary condition (=4 for fixed ends)


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For the special case of unconstrained uniaxial tension or compression, Young's

moduluscan be thought of as a measure of the stiffness of a material.

Use in engineering

The stiffness of a structure is of principal importance in many engineering

applications, so the modulus of elasticity is often one of the primary properties

considered when selecting a material. A high modulus of elasticity is sought when

deflection is undesirable, while a low modulus of elasticity is required when

flexibility is needed.


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Factor of safety.

Factor of safety (FoS), also known as safety factor (SF), is a term describing the

structural capacity of a system beyond the expected loads or actual loads. Essentially,

how much stronger the system is than it usually needs to be for an intended load.

Safety factors are often calculated using detailed analysis because comprehensivetesting is impractical on many projects, such as bridges and buildings, but the

structure's ability to carry load must be determined to a reasonable accuracy.

Many systems are purposefully built much stronger than needed for normal usage to

allow for emergency situations, unexpected loads, misuse, or degradation.

Two definitions of factor of safety

There are two distinct uses of the factor of safety: One as a ratio of absolute strength

(structural capacity) to actual applied load. This is a measure of the reliability of aparticular design. The other use of FoS is a constant value imposed by law, standard,

specification, contract orcustom to which a structure must conform or exceed.

Careful engineers refer to the first sense (a calculated value) as afactor of safety or, to

be explicit, a realized factor of safety, and the second sense (a required value) as a

design factor, design factor of safety orrequired factor of safety, but usage is

inconsistent and confusing.

The cause of much confusion is that reference books and standards agencies use the

term factor of safety differently. Design Codes and Structural and Mechanical

engineering textbooks often use the term to mean the fraction of total structural

capability over that needed[1][2][3] (first sense). Many undergraduate Strength of

Materials books use "Factor of Safety" as a constant value intended to be a minimum

target for design[4][5][6] (second sense).

Calculating safety factors

There are several ways to compare the factor of safety for structures. All the different

calculations fundamentally measure the same thing, how much extra load beyond

what is intended a structure will actually take (or be required to withstand). The

difference between the methods is the way in which the values are calculated andcompared. Safety factor values can be thought of as a standardized way for comparing

strength and reliability between systems.

There is a near universal push towards conservatism in the calculation of safety

factors, i.e. in the absence of highly accurate data, using the worst case configuration

possible to make sure the system is adequate (to err on the side of caution).[citation needed]

Design factor and safety factor

The difference between the safety factor and design factor (design safety factor) is as

follows: The safety factor is how much the designed part actually will be able to


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withstand. The design factor is what the item is required to be able to withstand. The

design factor is defined for an application (generally provided in advance and often

set by regulatory code or policy) and is not an actual calculation, the safety factor is a

ratio of maximum strength to intended load for the actual item that was designed.

This may sound similar, but consider this: Say a beam in a structure is required tohave a design factor of 3. The engineer chose a beam that will be able to withstand 10

times the load. The design factor is still 3, because it is the requirement that must be

met, the beam just happens to exceed the requirement and its safety factor is 10. The

safety factor should always meet or exceed the required design factor or the design is

not adequate. Meeting the required design factor exactly implies that the design meets

the minimum allowable strength. A high safety factor well over the required design

factor sometimes implies "overengineering" which can result in excessive weight

and/or cost. In colloquial use the term, "required safety factor" is functionally

equivalent to the design factor.

For ductile materials (e.g. most metals), it is often required that the factor of safety bechecked against both yield and ultimate strengths. The yield calculation will

determine the safety factor until the part starts toplastically deform. The ultimate

calculation will determine the safety factor until failure. On brittle materials these

values are often so close as to be indistinguishable, so is it usually acceptable to only

calculate the ultimate safety factor.

The use of a factor of safety does not imply that an item, structure, or design is "safe".

Many quality assurance, engineering design, manufacturing, installation, and end-use

factors may influence whether or not something is safe in any particular situation.

Design load being the maximum load the part should ever see in service.Margin of safety

Many government agencies and industries (such as aerospace) require the use of a

margin of safety (MoS orM.S.) to describe the ratio of the strength of the structure

to the requirements. There are two separate definitions for the margin of safety so careis needed to determine which is being used for a given application. One usage of M.S.

is as a measure of capacity like FoS. The other usage of M.S. is as a measure of

satisfying design requirements (requirement verification). Margin of safety can be

conceptualized (along with the reserve factor explained below) to represent how much

of the structure's total capacity is held "in reserve" during loading.

M.S. as a measure of structural capacity: This definition of margin of safety

commonly seen in textbooks[7][8] basically says that if the part is loaded to the

maximum load it should ever see in service, how many more loads of the same force

can it withstand before failing. In effect, this is a measure of excess capacity. If the

margin is 0, the part will not take any additional load before it fails, if it is negative


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the part will fail before reaching its design load in service. If the margin is 1, it can

withstand one additional load of equal force to the maximum load it was designed to

support (i.e. twice the design load).

Margin of Safety = Factor of Safety 1

M.S. as a measure of requirement verification: Many agencies such asNASA[9]

and AIAA[10] define the margin of safety including the design factor, in other words,

the margin of safety is calculated after applying the design factor. In the case of a

margin of 0, the part is at exactly the required strength (the safety factor would equal

the design factor). If there is a part with a required design factor of 3 and a margin of

1, the part would have a safety factor of 6 (capable of supporting two loads equal to

its design factor of 3, supporting six times the design load before failure). A margin of0 would mean the part would pass with a safety factor of 3. If the margin is less than 0

in this definition, although the part will not necessarily fail, the design requirement

has not been met. A convenience of this usage is that for all applications, a margin of

0 or higher is passing, one does not need to know application details or compare

against requirements, just glancing at the margin calculation tells whether the design

passes or not.

Design Safety Factor = [Provided as requirement]

For a successful design, the realized Safety Factor must always equal or exceed the

required Safety Factor (Design Factor) so the Margin of Safety is greater than or equal

to zero. The Margin of Safety is sometimes, but infrequently, used as a percentage,

i.e., a 0.50 M.S is equivalent to a 50% M.S. When a design satisfies this test it is said

to have a "positive margin," and, conversely, a negative margin when it does not.

Reserve factor

A measure of strength frequently used in Europe is the Reserve Factor (RF). With

the strength and applied loads expressed in the same units, the Reserve Factor is

defined as:

RF = Proof Strength / Proof Load

RF = Ultimate Strength / Ultimate Load

The applied loads have any factors, including factors of safety applied.


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Choosing design factors

Appropriate design factors are based on several considerations, such as the accuracy

of predictions on the imposed loads, strength, wearestimates, and the environmental

effects to which the product will be exposed in service; the consequences of

engineering failure; and the cost of over-engineering the component to achieve that

factor of safety. For example, components whose failure could result in substantial

financial loss, serious injury, or death may use a safety factor of four or higher (often

ten). Non-critical components generally might have a design factor of two. Risk

analysis, failure mode and effects analysis, and other tools are commonly used.

Design factors for specific applications are often mandated by law, policy, or industry

standards.

Buildings commonly use a factor of safety of 2.0 for each structural member. The

value for buildings is relatively low because the loads are well understood and most

structures are redundant. Pressure vessels use 3.5 to 4.0, automobiles use 3.0, andaircraft and spacecraft use 1.2 to 3.0 depending on the application and materials.

Ductile, metallic materials tend to use the lower value whilebrittle materials use the

higher values. The field ofaerospace engineering uses generally lower design factors

because the costs associated with structural weight are high (e.g. an aircraft with an

overall safety factor of 5 would probably be too heavy to get off the ground). This low

design factor is why aerospace parts and materials are subject to very stringent quality

control and strict preventative maintenance schedules to help ensure reliability. The

usually applied Safety Factor is 1.5, but for pressurized fuselage it is 2.0, and for main

landing gear structures it is often 1.25.

In aerospace, there are additional requirements. Before and up to Limit Load, thestructure may not have failed nor have permanent deformation. In excess of this,

plastic deformation is allowed, but failure is not. Reaching the Ultimate Load (usually

the Limit Load multiplied by the Safety Factor), the structure is allowed to fail.

Civilian aircraft structures are required to meet both Limit Load and Ultimate Load

criteria.

For loading that is cyclical, repetitive, or fluctuating, it is important to consider the

possibility ofmetal fatigue when choosing factor of safety. A cyclic load well below a

material's yield strength can cause failure if it is repeated enough.


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Pressure drop is a term used to describe the decrease inpressure from one point in a

pipe or tube to another point downstream. "Pressure drop" is the result of frictional

forces on the fluid as it flows through the tube. The frictional forces are caused by a

resistance to flow. The main factors impacting resistance to fluid flow are fluid

velocity through the pipe and fluid viscosity. The flow of any liquid or gas will

always flow in the direction of least resistance(less pressure). Pressure drop increasesproportional to the frictional shear forces within the piping network. A piping network

containing a high relative roughness rating as well as many pipe fittings and joints,

tube convergence, divergence, turns, surface roughness and other physical properties

will affect the pressure drop. High flow velocities and / or high fluid viscosities result

in a larger pressure drop across a section of pipe or a valve or elbow. Low velocity

will result in lower or no pressure drop. [1]

Pressure Drop can be calculated by 2 values the Reynolds Number, NRe, (determining

laminar or turbulent flow) and the relative roughness of the piping, /D. NRe = Dv/

Where D is the pipe diameter in meters, v is the velocity of the flow in meters per

second, is the density in kilograms per cubic meter, and is in kilograms per meter-second. The relative roughness of the piping is usually known and then these two

values can be cross referenced.

Hydraulic head orpiezometric head is a specific measurement ofwater pressure

above a geodetic datum.[1][2] It is usually measured as a water surface elevation,

expressed in units of length, at the entrance (or bottom) of apiezometer. In an aquifer,

it can be calculated from the depth to water in a piezometric well (a specialized water

well), and given information of the piezometer's elevation and screen depth.

Hydraulic head can similarly be measured in a column of water using a standpipe

piezometer by measuring the height of the water surface in the tube relative to a

common datum. The hydraulic head can be used to determine a hydraulic gradient

between two or more points.

Head" in fluid dynamics

In fluid dynamics, headis a concept that relates the energy in an incompressible fluid

to the height of an equivalent static column of that fluid. From Bernoulli's Principle,

the total energy at a given point in a fluid is the energy associated with the movement

of the fluid, plus energy from pressure in the fluid, plus energy from the height of the

fluid relative to an arbitrary datum. Head is expressed in units of height such as

meters or feet.

Thestatic headof apump is the maximum height (pressure) it can deliver. The

capability of the pump can be read from its Q-H curve (flow vs. height).

Head is equal to the fluid's energy per unit weight. Head is useful in specifying

centrifugal pumps because their pumping characteristics tend to be independent of the

fluid's density.

There are four types of head used to calculate the total head in and out of a pump:

Velocity headis due to the bulk motion of a fluid (kinetic energy).


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Elevation headis due to the fluid's weight, the gravitational force acting on acolumn of fluid.

Pressure headis due to the static pressure, the internal molecular motion of afluid that exerts a force on its container.

Resistance head(orfriction headorHead Loss) is due to the frictional forcesacting against a fluid's motion by the container.

Components of hydraulic head

A mass free falling from an elevation (in a vacuum) will reach a speed

when arriving at elevationz=0, or when we rearrange it as a

head:

where

gis the acceleration due to gravity

The term is called the velocity head, expressed as a length measurement. In a

flowing fluid, it represents the energy of the fluid due to its bulk motion.

The total hydraulic head of a fluid is composed ofpressure headand elevationhead.[1][2] The pressure head is the equivalent gaugepressure of a column of water at

the base of the piezometer, and the elevation head is the relativepotential energy in

terms of an elevation. The head equation, a simplified form of the Bernoulli Principle

for incompressible fluids, can be expressed as:

where

h is the hydraulic head (Length in m or ft), also known as the piezometric head.

is thepressure head, in terms of the elevation difference of the water columnrelative to the piezometer bottom (Length in m or ft), and

zis the elevation at the piezometer bottom (Length in m or ft)

In an example with a 400 m deep piezometer, with an elevation of 1000 m, and a

depth to water of 100 m:z= 600 m, = 300 m, and h = 900 m.

The pressure head can be expressed as:


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where

Pis the gauge pressure (Force per unit area, often Pa or psi),

is the unit weight of water (Force per unit volume, typically Nm3 orlbf/ft),

is the density of the water (Mass per unit volume, frequently kgm3

), andgis the gravitational acceleration (velocity change per unit time, often ms2)

Fresh water head

The pressure head is dependent on the density of water, which can vary depending on

both the temperature and chemical composition (salinity, in particular). This means

that the hydraulic head calculation is dependent on the density of the water within the

piezometer. If one or more hydraulic head measurements are to be compared, they

need to be standardized, usually to theirfresh water head, which can be calculated as:

where

is the fresh water head (Length, measured in m or ft), and

is the density of fresh water (Mass per unit volume, typically in kgm3)

Hydraulic gradient

The hydraulic gradientis a vector gradient between two or more hydraulic head

measurements over the length of the flow path. It is also called theDarcy slope, since

it determines the quantity of aDarcy flux, or discharge. A dimensionless hydraulic

gradient can be calculated between two piezometers as:

where

i is the hydraulic gradient (dimensionless),dh is the difference between two hydraulic heads (Length, usually in m or ft),and

dlis the flow path length between the two piezometers (Length, usually in mor ft)

The hydraulic gradient can be expressed in vector notation, using the deloperator.

This requires a hydraulic head field, which can only be practically obtained from a

numerical model, such as MODFLOW. In Cartesian coordinates, this can be

expressed as:


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This vector describes the direction of the groundwater flow, where negative values

indicate flow along the dimension, and zero indicates no flow. As with any otherexample in physics, energy must flow from high to low, which is why the flow is in

the negative gradient. This vector can be used in conjunction with Darcy's law and a

tensorofhydraulic conductivity to determine the flux of water in three dimensions.

Hydraulic head in groundwater

The distribution of hydraulic head through an aquiferdetermines where groundwater

will flow. In a hydrostatic example (first figure), where the hydraulic head is constant,

there is no flow. However, if there is a difference in hydraulic head from the top to

bottom due to draining from the bottom (second figure), the water will flow

downward, due to the difference in head, also called the hydraulic gradient.

Atmospheric pressure

Even though it is convention to use gauge pressure in the calculation of hydraulic

head, it is more correct to use total pressure (gauge pressure + atmospheric pressure),

since this is truly what drives groundwater flow. Often detailed observations of

barometric pressure are not available at each well through time, so this is often

disregarded (contributing to large errors at locations where hydraulic gradients are

low or the angle between wells is acute.)

The effects of changes in atmospheric pressure upon water levels observed in wells

has been known for many years. The effect is a direct one, an increase in atmospheric

pressure is an increase in load on the water in the aquifer, which increases the depth to

water (lowers the water level elevation). Pascal first qualitatively observed these

effects in the 17th century, and they were more rigorously described by the soil

physicistEdgar Buckingham (working for the USDA) using air flow models in 1907.

Head loss

In any real moving fluid, energy is dissipated due to friction; turbulence dissipates

even more energy for high Reynolds numberflows. Head loss is divided into two

main categories, "major losses" associated with energy loss per length of pipe, and

"minor losses" associated with bends, fittings, valves, etc. The most common equation

used to calculate major head losses is the DarcyWeisbach equation. Older, more

empirical approaches are the Hazen-Williams equation and the Prony equation.

For relatively short pipe systems, with a relatively large number of bends and fittings,

minor losses can easily exceed major losses. In design, minor losses are usually

estimated from tables using coefficients or a simpler and less accurate reduction of

minor losses to equivalent length of pipe.


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Microsoft Word - Mode of Failure