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The Principles of Hydraulics by ttACAG


									                           Principles of Hydraulics
Hydraulics is a branch of engineering that deals with the practical application of
water or other liquids at rest or in motion. The two major divisions of hydraulics
are hydrostatics and hydrodynamics.

Hydrostatics is the study of liquids at rest and the forces exerted on them or by
them. Equilibrium is the condition when all forces and torques are balanced by
equal and opposite forces and torques. Most hydraulic systems apply
hydrostatic principles. For example, the fluid in a automotive braking system is at
rest and the pressure throughout the system is in equilibrium. The brake system
is activated by applying pressure to the foot pedal. The fluid in the system
transmits the applied force from the foot pedal to the slave cylinder piston. The
slave cylinder piston transmits the force to brake pad which applies pressure to
the brake drum (rear wheel on newer vehicles). The pressure is equal in all parts
of the system, but higher than the pressure of the fluid when the system is at

Simplified auto brake system

Hydrodynamics is the study of force exerted on a solid body by the motion or
pressure of a fluid. For example, fluids are transferred through a non-positive
displacement pump by angular velocity. A non-positive displacement pump is a
pump that is not sealed between its inlet and outlet. Angular velocity forces are
produced by a rotating object. The fluid is force to the discharge (outlet) port by
rotating impeller blades. The output of the pump may be reduced or completely

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blocked if the pressure of the discharge circuit is increased because there is no
positive displacement of fluid.

                                                Hydrodynamic pump, non-
                                                positive displacement pump

Hydraulic History (abbreviated)
Early hydraulic systems consisted of diverting streams for village irrigation and
water supply and digging wells. There exists evidence of hydraulic principle use
in early Mesopotamia (currently geography encompassed by Iraq). This record
predates the existence of Christianity by over a thousand years. One of the first
recorded machines for hydrostatic use is the Archimedes water-screw.
Developed by the Greek Archimedes, it believed that earlier Egyptian technology
influenced the development of this invention.

Archimedes screw, a spiral screw turned inside
a cylinder, was once commonly used to lift water
from canals. The screw is still used to lift water in
the Nile delta in Egypt, and is often used to
shift grain in mills and powders in factories.

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Liquid Characteristics
In hydraulics the term fluid refers to gases as well as liquids. A fluid is a
substance that tends to conform to the outline or shape of its container (such as
a liquid or gas). Fluids yield easily to pressure. A liquid is a fluid that can flow
readily and assume the shape of its container. Fluids have no independent
shape but do have a definite volume. Liquids do not expand indefinitely and are
only slightly compressible. A gas is a fluid that has neither independent shape
nor volume and tends to expand indefinitely. Oxygen, hydrogen, nitrogen, etc.
are gases.

Liquids make convenient fluids for transmitting force because they are not highly
compressible like gases. The term fluid is used in reference to a liquid because
liquids are specifically used in hydraulic systems. Work produced in a hydraulic
system is dependent on the pressure and flow of the fluid in the system.

Transmission of Hydraulic Force
To understand the principals of hydraulics it is necessary to understand Blaise
Pascal’s theorem upon which all hydraulics are based. Pascal realized that
enclosed fluids under pressure follow a definite law. Pascal’s theorem is now
stated as a law of physics; pressurized fluid within a closed container—such as a
cylinder or pipe—exerts equal force on all surfaces of the container and is the
same in every direction. Force is the energy that produces movement. Although
this law and its potential for technology were realized in the 17th century, it was
not until the 20th century that fluid power became a means of energy

                           Pascal’s law of equal pressure
                           of enclosed fluids on all surfaces
                           in all directions

Pressure is the force per unit area. Pressure is expressed as atmospheric,
gauge and absolute. Atmospheric pressure is the force exerted by the weight of
the atmosphere (air) on the Earth’s surface. The weight of the atmosphere,
acting over a height of several hundred thousand feet above the Earth’s surface
varies slightly with weather conditions and variation in gravity. For practical
purposes and to establish a standard for weight of the atmosphere at sea level is

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determined to be 14.7 pounds per square inch (psi). Atmospheric pressure is
expressed in psi and is measured with a mercury barometer. A mercury
barometer is an instrument that measures atmospheric pressure using a column
of mercury.
                                              Torricelli’s Mercury Barometer

A mercury barometer consists of a glass tube that is closed on one end and
completely filled with mercury. The tube is inverted and the open end is
submerged in a dish of mercury. A vacuum (low pressure) is created at the top
of the tube as the mercury tries to run out of the tube. Vacuum is a pressure
lower than atmospheric pressure. The pressure of the atmosphere on the
mercury in the open dish prevents the mercury in the tube from running out of the
tube. The height of the mercury in the tube corresponds to the pressure of the
atmosphere on the mercury in the open dish.

A mercury barometer is commonly calibrated in inches of mercury (in. Hg). At
sea level, the atmosphere can support 29.92” Hg in the tube. A barometric
pressure of 29.92” equals one atmosphere or 14.7 psi. Pressures above one
atmosphere are generally expressed in psi and pressures below one atmosphere
are generally expressed in in. of Hg. Minute pressure changes are expressed in
inches of water column (in.WC). Atmospheric pressure at sea level should be
able to hold water in a column 33.9’ (407.37”) high because atmospheric
pressure is able to hold mercury in a column 29.92” high and water is 13.6 times
lighter than mercury.

Gauge pressure is pressure above atmospheric pressure that is used to express
pressure inside a closed system. Gauge pressure assumes that atmospheric
pressure is zero (0 psi). Most pressures are measured as gauge pressure
unless otherwise specified. Gauge pressure is expressed in pounds per square
inch (psig).

Absolute pressure is pressure above a perfect vacuum. Absolute pressure is the
sum of gauge pressure plus atmospheric pressure. Absolute pressure is
expressed in pounds per square inch absolute (psia).

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Pressure outside a closed system (such as normal air pressure) is expressed in
pounds per square inch absolute. The difference between gauge pressure and
absolute pressure is the pressure of the atmosphere at standard conditions
(14.7psi). A pressure gauge reads 0 psi at normal atmospheric pressure. To
find absolute pressure when gauge pressure is known, the atmospheric pressure
of 14.7 psi is added to the gauge pressure. Absolute pressure is found by
applying the formula:

psia = psig + 14.7
psia = pounds per square inch absolute
Psig = pounds per square inch gauge
14.7 = constant (atmospheric pressure at standard conditions)
Pressure other than atmospheric pressure is considered to be artificial and is
produced to transfer or amplify force in hydraulic systems. This transferred or
amplified force is used to do work such as lifting a car with a hydraulic jack,
running a conveyor with a hydraulic motor, or stamping steel in automotive

Area, force and pressure are the basis of all hydraulic systems. The force
exerted by a liquid is based on the size of the area on which the liquid pressure is
applied. In hydraulic systems this area usually refers to the face of the piston,
which is circular in shape. Area is always expressed in square units such as sq.
in. or sq. mm.

A circle with a diameter the same as a square has less area. The area of a circle
is exactly 78.54% of the area of a square with the same measurements.

                                   78.54% of square

The area of a piston can be found if the force and pressure applied to a cylinder
is known. The applied pressure on a piston can be found if the amount of force
and the piston area are known. Also the force produced by a piston can be

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found if the area and pressure applied to a piston are known. Two of the values
must be known to find the unknown value.

The relationship between force, pressure and area can be recalled using the
force, pressure, and area formula pyramid from the standard calculations
handout sheet.

                                 Force                    F
                      Pressure = Area
                                                      P A
By covering the letter of the unknown value, the formula for finding the solution is

Head pressure
Head is the difference in the level liquid (fluid) between two points. Head is
expressed in feet. Head pressure is the pressure at any point below the surface
of the fluid.

In an open cylinder, the pressure of the fluid at any depth in the cylinder is
proportional to the height of the column of fluid. The pressure in a column of fluid
is determined by the columns height and the fluid’s weight, not the shape of the
vessel. The pressure at the same level in each vessel is identical if the pressure
surrounding the different surrounding the different-shaped vessels is the same
and the fluid in each vessel is the same. The pressure of the fluid at any level in
a vessel is based on the height of the fluid above that level and is the same at
that level regardless of the shape of the vessel.

In a hydraulic system, head pressure is the energy or pressure that supplies a
hydraulic pump. Atmospheric pressure and head pressure combine to feed the
intake (suction) line connecting a hydraulic pump to a reservoir.

Head is classified as static or dynamic. Static head is the height of a fluid above
a given point in column at rest. Static head pressure is a force over and area
created by the weight of the fluid itself. Static head pressure is potential energy.
The pressure of water per foot of static head is calculated by using .0361 lb/cu in.
or 2.31’ head of water for each psi.

Dynamic head is the head of a fluid in motion. Dynamic head represents the
pressure necessary to force a fluid from a given point to a given height. Dynamic
head pressure is the pressure and velocity of a fluid produced by a liquid in
motion. Dynamic head pressure results when a valve is opened and fluid is

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allowed and open flow. Dynamic head pressure may be used to direct an open
flow of fluid. For example, dynamic head pressure was used in early prospecting
days to wash away the sides of mountains to retrieve gold. This was
accomplished by piping water from higher lakes and using dynamic head
pressure to produce a high pressure and high velocity.

Hydrostatic head. The fluid height in
columns A and B is identical, but the
pressure reading on the gauges
differs because of the different fluid
densities. Hydrostatic head refers to
the vertical column height;
hydrostatic pressure refers to the
force exerted by the fluid.

Fluid flow is the movement of fluid caused by a difference in pressure between
two points. In a hydraulic system, fluid flow is produced by the action of a pump
and expressed as a measurement of gallons per minute (gpm) or liters per
minute (lpm). Fluid flow in a hydraulic system is affected by friction and the
viscosity of the fluid. Fluid flow is based on the volume and capacity of the
system and the velocity of the fluid in the system. Fluid flow also affects the
speed of a hydraulic system. In a system with flowing fluid, pressure is caused
by total resistance to fluid flow from a pump. Pressure results only when there is
resistance to flow. Resistance to flow is comprised of friction throughout the
system and actuator loads. A pressure change occurs to a fluid due to its flow is
generally expressed in psi.

Friction is generated throughout a hydraulic system between the piping wall and
the fluid, and within the fluid as fluid layers slide by one another. The faster the
fluid flows, the greater the friction. Any friction generated becomes a resistance
to fluid flow. Pressure must be increased to overcome the friction. Each

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component in a hydraulic system offers resistance and reduction of available
working pressure.

A fluid flows because of a difference in pressure. The pressure of a moving fluid
is always higher upstream. Pressure drop is the pressure differential between
upstream and downstream fluid flow cause by resistance. The pressure
developed in a hydraulic system is designed to be used as hydraulic leverage.
Pressure and fluid flow are independent of each other, but both assist in the
output. Pressure provides the force and flow rate is used to provide speed. Flow
rate is expressed in gpm and is typically determined by the capacity of the pump.

Fluids follow the path of least resistance. For example, a hydraulic system
consisting of a telescoping cylinder for lifting purposes will extend the largest
portion first. Force = pressure times area determines which section of the
cylinder will extend first. The larger area of the telescope’s base cylinder will
provide greater lifting power for a given pressure, and will extend initially. The
larger force from the base cylinder area begins to move the weight as a lighter
resistance compared to the other cylinders smaller area.

Fluid flow in a telescoping cylinder

Volume is the three-dimensional size of an object measured in cubic units.
Regardless of the shape of the figure, volume is expressed in cubic units (cu in.,
cu ft, mm3, m3, etc.). The volume of a figure is found by calculating the area of
the figure and multiplying by the length. The volume of a cylinder is found by
applying the procedure:

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Find the area of cylinder.
A = .7854 x D2
A = area (in sq units)
.7854 = constant
D2 = diameter squared

Find volume of cylinder.

V = volume
A = area (in square units)
L = length (in units)

Capacity is the ability to hold or contain something. Capacity is expressed in
cubic units and is calculated from a containers volume. Fluids are measured in
ounces, pints, quarts, gallons, liters, etc.

Fluid measurements can also be expressed in cubic units (cu in., cu ft, etc.)
because fluids occupy three dimensions. For example, one gallon of fluid equals
231 cu in.

The quantity of fluid required to fill a specific volume is determined by calculating
the volume and dividing by 231.

Less hydraulic fluid is required to retract a piston than is required to extend a
piston. This is due to the rod taking up part of the cylinder volume (reduced
capacity). The volume that the piston rod occupies must be subtracted from the
total volume of the cylinder when determining the volume of fluid that a cylinder
displaces when retracting.

                                           Single acting cylinder. Deduct the
                                           volume of the rod from the total
                                           cylinder volume to determine fluid
                                           capacity of rod end.

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Velocity is the distance a fluid travels in a specified time. Velocity generally
means the change in position of a fluid particle during a certain time interval.
This may be represented as a distance in feet per second (ft/sec).

Velocity is measured as a vector. A vector is a quantity that has a magnitude
and direction. A vector is commonly represented by a line segment whose length
represents its magnitude and whose orientation represents its direction.

The velocity of a fluid particle is determined by subtracting it’s initial position from
its final position and dividing by the value of value of the initial time subtracted
from the final time. Velocity is found by applying the equation:

V = x2 – x1
    t2 – t1

V = velocity (in ft/sec)
x2 = final position (in ft)
x1 = initial position (in ft)
t2 = final time (in sec)
t1 = initial time (in sec)
The velocity of the hydraulic fluid in a system should not exceed recommended
values because turbulent conditions result with loss of pressure and excessive
heating. The concept for predicting turbulence (non laminar flow) is based upon
the Reynolds number. More about Reynolds numbers and their calculation will
be covered in later lessons.

Flow Rate
Flow is the movement of fluid. Flow rate is the volume of fluid flow. A fluid in
motion is always flowing but its rate of flow may change. Fluid velocity depends
on the rate of flow in gallons per minute (gpm) and the cross-sectional area of a
pipe or component.

The velocity of a fluid increases at any restriction in a pipe or component if the
flow rate remains the same in the system. Common restrictions include valves,
elbows, pipes, reducers, etc. Also the velocity of a fluid decreases as the cross-
sectional area of a pipe or component increases.

The law of conservation of matter states that the mass or volumetric flow rate of
an incompressible fluid through a pipe is constant at every point in the pipe. The
velocity must increase at any restriction if there are no leaks in the system and

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the flow rate remains constant. The velocity increases four times to maintain a
constant rate of flow, if the original pipe diameter is changed to one-half of its
original size.

The speed of a cylinder rod is determined by volume, capacity, and fluid flow
velocity. To determine the speed at which a cylinder rod moves, the flow rate at
which hydraulic fluid is directed into the cylinder must be known.

The speed of a cylinder rod is independent of pressure (yup it’s true). The speed
of rod extension is usually expressed in inches per minute (in. /min). The speed
of rod extension is directly proportional to the flow rate.

Two methods of increasing speed at which a load (or cylinder rod) in a hydraulic
system moves are by using a smaller diameter cylinder or by increasing the rate
of fluid flow to the cylinder. A small diameter cylinder produces an increase in
speed and a decrease in applied force as compared to a larger cylinder. Two
cylinders of different diameters having the same length have different fluid
capacities and if both receive the same rate of fluid flow, the rate of travel and
pressure output are different.

Flow rate must be kept below
the rate at which turbulence
occurs in the system, derived by
the calculation of a Reynolds

Mechanical Advantage
Mechanical advantage is the ratio of the output force of a device to the input
force. Mechanical advantage is achieved when an applied force is multiplied,
resulting in a larger output force. Devices that produce mechanical advantage
include levers, block and tackles, gears etc.

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Mechanical advantage results from a force applied a certain distance from a
fulcrum. A fulcrum is a support on which a lever turns or pivots and is located
somewhere between the effort force and the resistance force. In determining the
force needed to balance a lever/fulcrum mechanism, the effort force must be
farther from the fulcrum than the resistance force or must have and effort force
equal to or greater than the resistance force.

Pascal’s law states that pressure exerted on enclosed fluid is transmitted
undiminished in every direction. This is demonstrated by a fluid filled bottle. As
a cork is pressed further into the bottle, the pressure throughout the bottle is
increases until the incompressible fluid bursts the bottle. The bottle bursts
because the force applied to one area (the cork) is equal to the pressure
multiplied by the larger area (the body of the bottle). The resulting force within a
vessel is a product of the input force and the input pressure area divided by the
output pressure area.

Fluids are well suited for being transmitted through pipes, hoses and passages
because of these force characteristics. This force is energy, which can produce
movement, work, or leverage when applied to a hydraulic application. For
example, interconnected hydraulic cylinders of different diameters produce
hydraulic leverage in a typical hydraulic car jack.

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                                                               multiplication with
                                                               cylinders of
                                                               different sizes.

At times, system pressure must be determined before calculating either input
force or the output force. This may be required when determining the input force
required to produce a given output force with given size cylinders. The required
input force is determined by calculating the area of the output cylinder,
calculating the pressure in the system, and determining the input force based on
the system pressure and area of the input cylinder.

Hydraulics is the branch of engineering that deals with the practical application of
water or other liquids at rest or in motion. Hydrostatics is the study of fluids at
rest and the forces exerted on them or by them. Hydrodynamics is the study of
the forces exerted on a solid body by the motion or pressure of a fluid. A liquid is
a fluid that can flow readily and assume the shape of its container. Fluid flow is
the movement of fluid caused by a difference in pressure between two points. In
a hydraulic system, fluid flow is produce by the action of a pump and is
expressed as a measurement of gallons per minute or liters per minute.

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