1

2

Objectives:-

1. Explain the meaning of fluid power.

2. List the various applications of fluid power.

3. List the advantages and disadvantages of fluid power.

4. Explain the industrial applications of fluid power.

5. Differentiate between mechanical ,electrical, pneumatic and

hydraulics systems.

6. Energy losses in hydraulic systems.

7. Types of hydraulic fluids & properties

8. ISO symbols

Unit-I

3

Introduction-All machines require some type of power source

and a way of transmitting this power to the

point of operation.

The three methods of transmitting power are:

1. Mechanical

2. Electrical

3. Fluid Power

In this course we are going to deal with the

third type of power transmission which is the

Fluid Power.

4

Methods for transmitting power

Mechanical transmission Electrical transmission Fluid powereg: shafts, gears, chains, belts eg: wires, transformers eg: liquids or gas

Fluid Power: Def: The technology that deals with the generation, controland transmission of forces and movement of mechanicalelement or system with the use of pressurized fluids.

- Both liquids and gases are considered as fluids

5

Advantages of a Fluid Power System:

1. Fluid power systems are simple, easy to operate

and can be controlled accurately

2. Multiplication and variation of forces

3. Multifunction control

4. Low-speed torque

5. Economical

6. Low weight to power ratio

7. Fluid power systems can be used where safety is of

vital importance

6

7

Fluid power system includes –

1. Hydraulic system (hydra in Greek meaning water)

- use liquid to transfer force from one point to

another.

2. Pneumatic system (pneuma in Greek meaning air)

- use air to transfer force from one point to another.

8

Air is Compressible:(This describes whether it is possible to force an object

into a smaller space than it normally occupies.

For example, a sponge is compressible because it can

be squeezed into a smaller size).

Liquid is Incompressible:(The opposite to compressible. When a “squeezing” force

is applied to an object, it does not change to a smaller

size.

For example hydraulic fluid, possesses this physical

property).

9

Applications can be classified into two major segments:

Stationary hydraulics:

fixed in one position

valves are mainly solenoid

operated

Applications:1. Machine tools and transfer

lines.

2. Lifting and conveying

devices.

3. Metal-forming presses.

4. Plastic machinery such as

injection-molding machines.

5. Rolling machines.

6. Lifts.

7. Food processing machinery.

8. Automatic handling

equipment and robots.

Mobile hydraulics:

move on wheels or tracks

valves are frequently

manually operated

Applications:

1. Automobiles, tractors ,

aéroplanes, missile, boats

, etc.

2. Construction machinery.

3. Tippers, excavators and

elevating platforms.

4. Lifting and conveying

devices.

5. Agricultural machinery.

10

Hydraulic systems are commonly used where mechanisms require large forces and precise control. Examples include vehicle power steering and brakes, hydraulic jacks and heavy earth moving machines.

1. Vehicle brake hydraulic systems-The function of a vehicle braking system isto stop or slow down a moving vehicle.

When the brake pedal is pressed asillustrated in Fig. , the hydraulic pressure istransmitted to the piston in the brakecaliper of the brakes.

The pressure forces the brake pads againstthe brake rotor, which is rotating with thewheel.

The friction between the brake pad and therotor causes the wheel to slow down andthen stop.

Brake pedal

Master cylinder

Brake lines

Front

brake calipers

Rear wheel

cylinder pistons

Pads Rotor

Hydraulic pump

Control valve Power cylinder

11

2. Vehicle power steering

The vehicle power steering

system uses hydraulic oil, the

hydraulic pump supplies the oil

through the control valves to the

power cylinder as shown in Fig. .

The major advantage of using

this system is to turn the

vehicle’s wheels with less effort.

12

3. Hydraulic jack

In a hydraulic jack, a

small piston (pumping

piston) transmits

pressure through the

oil to a large piston

(power piston) through

a check valve,

resulting in the weight

being lifted as shown

in Fig..

Pumping piston Power piston

Weight

Outlet check valve

(allows the oil to move

in only one direction)

Inlet check

valve (allows

the oil to

move in only one direction)

Oil reservoir Handle

13

4. Aircraft hydraulic systems

All modern aircraft contain hydraulic

systems to operate mechanisms, such

as: Flaps, Landing gear .

The hydraulic pump that is coupled to

the engine provides hydraulic power

as illustrated by Fig.

Power is also distributed to systems

through the aircraft by transmission

lines.

Hydraulic power is converted to

mechanical power by means of an

actuating cylinder or hydraulic motor.

14

S. No. Hydraulics System Pneumatics System

1It employs a pressurized liquid

as a fluid

It employs a compressed gas, usually

air, as a fluid

2An oil hydraulic system operates at

pressures up to 700 bar

A pneumatic system usually operates

at 5–10 bar

3 Generally designed as closed system Usually designed as open system

4The system slows down when leakage

occurs

Leakage does not affect the system

much

5 Valve operations are difficult Valve operations are easy

6 Heavier in weight Lighter in weight

7Pumps are used to provide

pressurized liquids

Compressors are used to provide

compressed gases

8 The system is unsafe to fire hazards The system is free from fire hazards

9 Automatic lubrication is provided Special arrangements for lubrication

are needed

10 Response speed-Good -Response speed- fair

11 Application- Hydraulic jack, power steering Application- jack hammer,

15

Differences in Principles and Properties

Air is Compressible.

Oil is considered Incompressible.

Actuator demand is measured in m3 per hour or operation

Compressor output is measured in m3 per hour Free Air

Delivery (FAD)

Gas laws such as Boyle’s and Charles’s Laws govern medium

behaviour

Both Hydraulics and Pneumatics are described with Pascal’s Law and F=PA

Bernoulli’s and other Fluid Flow Laws govern medium

behaviour

Actuator demand is measured litres per minute for a specific speed

Pump output is measured litres per minute

Pneumatic systems rely on a supply of Compressed air flowing through

Pipes to Actuators. The Force for work is produced due to the Pressure of the

Air acting on the Area of the actuator.

Hydraulic systems rely on a supply of incompressible fluid flowing

through Hoses to Actuators. The Force for work is produced due to the

Pressure of the Oil acting on the Area of the actuator.

16

Differences in Pressure and Force

Pneumatic Pressures and

Forces

Hydraulic Pressures and

Forces

Force Calculator

Force

Pressure

Area

Produced at 10Bar

Used at 0~10 Bar

Forces up to 5000Kg

Produced and used at 200~700Bar

Forces up to Thousands of tonnes

17

Differences in ConstructionThe hydraulic

Power Pack

contains the Pump,

Tank (Reservoir),

Filters and

commonly a Relief

Valve for protection

of the system.

The unit is usually

local to the

machine that is

using it.

Hydraulic pumps

are usually

Positive

Displacement

devices which

means they

displace all the oils

they pump.

The

Pneumatic

Compressor

installation

usually

includes a

Dryer and

Receiver.

The unit is

usually

remote from

the machine

that is using

it.

18

Differences in ConstructionValves and Actuators-

Pneumatic valves and

actuators are generally of

light construction as they

need to deal with pressure

up to a maximum of 10 Bar.

The cost of these

components is cheap when

compared to the much more

heavily constructed hydraulic

components.

Hydraulic valves and actuators

are much more heavily

constructed than pneumatic

components. This is because the

components must deal with

pressures up to 400 Bar+.

Hydraulic actuators can be very

large when compared with

common pneumatic actuators.

Hydraulic components are much

more expensive than standard

pneumatic components.

19

20

21

22

23

Pneumatic and Hydraulic Dangers:-

The dangers of the use of compressed air include:

Air Embolism

Hose/Pipe Whipping

Noise

Crushing/Cutting

The dangers of working

with high pressure oil can

be infinitely more drastic:

High Pressure Oil Injection

Oil Burns

Crushing/Cutting

Carcinogens

This injury is a result of placing the

hand in front of a jet of leaking

hydraulic fluid at around 180 Bar

24

Types of hydraulic systems-

1.Hydrostatic Systems: uses fluid pressure to transmit power, Creates high pressure and

through a transmission line and control elements this pressure drives

an actuator (linear or rotational)

The pump used is a positive displacement pump

An example of pure hydrostatics is the transfer of force in

hydraulics.

2. Hydrodynamic Systems: use fluid motion to transmit power, Power transmission by

kinetic energy of the fluid

The pump used is a non-positive displacement pump.

An example of pure hydrodynamics is the conversion of flow

energy in turbines in hydroelectric power plants.

25

Advantages of Hydrostatic drives-

Simple method to create linear movements

Creation of large forces and torques, high energy density

Continuously variable movement of the actuator

Simple turnaround of the direction of the movement, startingpossible under full load from rest

Low delay, small time constant because of low inertia

Simple overload protection (no damage in case of overload)

Simple monitoring of load by measuring pressure

Arbitrary positioning of prime mover and actuator

Large power density (relatively small mass for a given powercompared to electrical and mechanical drives)

Robust (insensitive against environmental influences)

26

Disadvantages of hydrostatic drives-

Working fluid is necessary (leakage problems, filtering, etc.)

It is not economic for large distances

27

Types of hydraulic systems-

1. Fluid transport system-

Objective - Delivery of fluid from one place to other

Eg - pumping of water

2. Fluid Power system-

Objective - Design to perform work

Eg - cylinder produces force resulting linear motion

28

Electro-Pneumatic and Hydraulic Systems

Control of Electro-Pneumatic and Hydraulic systems using

Electrical control systems is similar for both media types.

Both systems would use Solenoid actuated valves, either

Directly Actuated or Indirectly Actuated.

An Electronic system would commonly incorporate Push

Button Switches (for human input), Reed Switches (to

detect cylinder position), Proximity Sensors and Photocells

(to detect machine/component position).

An Electronic system would also commonly incorporate

Relays and computer controlled systems such as

Programmable Logic Controllers.

29

30

Structure of a Hydrostatic drive

31

Basic Components of Hydraulic system

32

1.Power Input Device – A pump that provides hydraulic power

to the system. The pump draws the oil from the reservoir and

pumps it into the supply line.

2.Control Devices – Valves control direction, pressure, and flow

rate of pressurized oil in the hydraulic system.

3.Power Output Device – This is where the hydraulic power is

converted back to mechanical power. The output devices are call

actuators. There are two types of actuators:

Motors : Create rotary motion as the oil flows through it.

Cylinders: Create straight line motion when oil flows into it.

4.Conductors – To transmit the liquid, conductors (pipes, tubing,

or hoses) are used. There are two main lines in a hydraulic

system:

Supply line: Provides flow to the actuators.

Return line: Allows oil leaving the actuators to return to the

reservoir.

5.Liquid – The power conducting medium. Typically oil, but other

liquids are used sometimes.

Basic Components-

33

A typical Hydraulics system

34

1 – pump2 – oil tank3 – flow control valve4 – pressure relief valve5 – hydraulic cylinder6 – directional control valve7 – throttle valve

35

Hydraulic fluids Tasks:-Primary tasks:

Power transmission (pressure and motion transmission)

Signal transmission for control

Secondary tasks:

Lubrication of rotating and translating components toavoid friction and wear

Heat transport, away from the location of heatgeneration, usually into the reservoir

Transport of particles to the filter

Protection of surfaces from chemical attack, especiallycorrosion

36

PROPERTIES OF FLUID:

A drop forms when liquid

is forced out of a small tube.

The shape of the drop is

determined by a balance of

pressure, gravity, and

surface tension forces.

37

INTRODUCTION TO PROPERTIES-

38

The various properties required for an ideal

hydraulic fluid are as follows: 1. Ideal viscosity.

2. Good lubrication capability.

3. Demulsibility.

4. Good chemical and environmental stability.

5. Incompressibility.

6. Fire resistance.

7. Low flammability.

8. Foam resistance.

9. Good heat dissipation.

10. Low density.

11. System compatibility.

DENSITY AND SPECIFIC GRAVITY

40

Surface tension:The cohesive forces between liquid molecules are responsible for

the phenomenon known as surface tension.

The magnitude of this force per unit length Is called surface

tension (or coefficient of surface tension) and is usually expressed in

the unit N/m.

41

Viscosity:The viscosity of a fluid is a measure of its resistance to shear or

angular deformation.

42

Viscosity index (VI) :

It is a relative measure of the change in the viscosity of

an oil with respect to a change in temperature.

An oil having a low VI is one that exhibits a large

change in viscosity with a small change in temperature.

A high VI oil does not change appreciably with a

change in temperature.

43

Lubrication Capability:Hydraulic fluids must have good lubricity to prevent friction and wear

between the closely fitted working parts such as vanes of pumps, valve

spools, piston rings and bearings.

44

DemulsibilityThe ability of a Hydraulic fluid to separate rapidly from

moisture and successfully resist emulsification is known as

“demulsibility.”

If an oil emulsifies with water, the emulsion promotes the

destruction of lubricating and sealant properties.

Highly refined oils are basically water resistant by nature.

45

Good Chemical and Environmental Stability (Oxidation

and Corrosion Resistance) :

1. Most fluids are vulnerable to oxidation, as they come in

contact with oxygen in air.

2. Mineral oils or petroleum-based oils (widely used in

hydraulic systems) contain carbon and hydrogen

molecules, which easily react with oxygen.

3. The oxidation products are highly soluble in oil and

being acidic in nature they can easily corrode metallic

parts.

46

Neutralization Numbers :Measure of the acidity or alkalinity of hydraulic oil.

This is referred to as the pH value of the oil.

High acidity causes the oxidation rate in oil to increase

rapidly.

Incompressibility:Hydraulic fluids as incompressible, in practice, they are relatively

compressible.

Most mineral oils undergo reduction in the volume of about 0.7%

for every 100 bar rise in pressure.

The compressibility of a fluid is greatly influenced by

temperature and pressure.

47

Types of Hydraulic Fluids :1. Petroleum-based fluid

2. Emulsions

3. Water glycol

4. Synthetic fluids

5. Vegetable oils

6. Biodegradable hydraulic fluids

48

1. Petroleum-based fluid:

Mineral oils are the petroleum-based oils

Advantage:

1. they are easily available and economical

2. they offer the best lubrication ability

3. least corrosion problems and are compatible with most

seal materials

Disadvantage:

Flammability:

They pose fire hazards, mainly from the leakages, in high-

temperature environments such as steel industries, etc.

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2.Emulsions:A mixture of two fluids that do not chemically react with

others

Emulsions of petroleum-based oil and water are commonly used.

An emulsifier is normally added to the emulsion, which keeps

liquid as small droplets and remains suspended in the other liquid.

Two types of emulsions are in use:

a) Oil-in-water emulsions:

Water as the main phase, while small droplets of oil are

dispersed in it

The oil dilution is limited, about 5%; hence, it exhibits the

characteristics of water.

Limitations: poor viscosity, leading to leakage problems, loss in

volumetric efficiency and poor lubrication properties.

These problems can be overcome to a greater extent by using

certain additives. Such emulsions are used in high-displacement,

low-speed pumps (such as in mining applications).

50

b) Water-in-oil emulsions/inverse emulsions:

Basically oil based in which small droplets of water are

dispersed throughout the oil phase.

The commonly used emulsion has a dilution of 60% oil and 40%

water

popular fire-resistant hydraulic fluids

exhibit more of an oil-like characteristic; hence, they have good

viscosity and lubrication properties.

These emulsions are good for operations at 25°C, as at a higher

temperature, water evaporates and leads to the loss of fire-resistant

properties.

51

3. Water glycol:

Nonflammable fluid commonly used in aircraft hydraulic

systems.

has a low lubrication ability as compared to mineral oils and

is not suitable for high-temperature applications.

It has water and glycol in the ratio of 1:1.

Because of its aqueous nature and presence of air, it is prone to

oxidation and related problems.

It needs to be added with oxidation inhibitors.

Enough care is essential in using this fluid as it is toxic and

corrosive toward certain metals such as zinc, magnesium and

aluminum.

52

4. Synthetic fluids:based on phosphate ester, is another popular fire-resistant

fluid.

It is suitable for high-temperature applications, since it

exhibits good viscosity and lubrication characteristics.

It is not suitable for low-temperature applications.

It is not compatible with common sealing materials such as

nitrile.

5. Vegetable oils: biodegradable and are environmental safe.

They have good lubrication properties, moderate viscosity and

are less expensive good fire resistance characteristics with certain

additives,

tendency to easily oxidize and absorb moisture.

The acidity, sludge formation and corrosion problems are more

severe

in vegetable oils than in mineral oils.

Hence, vegetable oils need good inhibitors to minimize oxidation

problems

53

6. Biodegradable hydraulic fluids / bio-based hydraulic

fluids :

Bio-based hydraulic fluids use sunflower, soybean, etc.,

as the base oil and hence cause less pollution in the case

of oil leaks or hydraulic hose failures.

These fluids carry similar properties as that of a mineral

oil–based anti-wear hydraulic fluid,

54

Factors Influencing the Selection of a Fluid:

1. Operating pressure of the system.

2. Operating temperature of the system and its variation.

3. Material of the system and its compatibility with oil used.

4. Speed of operation.

5. Availability of replacement fluid.

6. Cost of transmission lines.

7. Contamination possibilities.

8. Environmental condition (fire proneness, extreme

atmosphere like in mining, etc.).

9. Lubricity.

10. Safety to operator.

11. Expected service life.

Hydraulic fluids - requirements

55

Functional-

Good lubrication characteristics

Viscosity should not depend strongly on temperatureand pressure

Good heat conductivity

Low heat expansion coefficient

Large elasticity modulus

Economic-

Low price

Slow aging and thermal and chemical stability long life cycle

Hydraulic fluids - requirements (contd.)

56

Safety-

High flash point or in certain cases not inflammable at all

Chemically neutral (not aggressive at all against all materials it touches)

Low air dissolving capability, not inclined to foam formation

Environmental friendliness-

No environmental harm

No toxic effect

57

Ideal and real fluid

58

Types of Fluid Flow-

1.Laminar flow/streamlineIn streamline flow, the fluid appears to move by sliding

of laminations of infinitesimal thickness relative to

adjacent layers; that is, the particles move in definite and

observable paths or streamlines.

2.Turbulent flow: It is characterized by a fluid flowing in random way.

The movement of particles fluctuates up and down in a

direction perpendicular as well as parallel to the mean flow

direction.

60

61

Reynolds Number

If Re is less than 2000, the flow is laminar.

If Re is greater than 4000, the flow is turbulent.

Reynolds number between 2000 and 4000 covers a critical

zone between laminar and turbulent flow.

Governing laws

62

e) Continuity

b) Pascals’s law

g) Bernoulli equation

f) Flow resistance

a) Hydrostatic pressure c) Transmission of power

d) Transmission of pressure

63

Pascal’s Law-

• “The pressure in a

confined fluid is

transmitted equally to

the whole surface of its

container ”.

• When force F is exerted on

area A on an enclosed

liquid, pressure P is

produced. The same

pressure applies at every

point of the closed system

as shown in Fig.

64

65

66

67

The continuity equation-

Hydraulic systems commonly have a pump that produces a

constant flow rate.

If we assume that the fluid is incompressible (oil), this situation

is referred to as steady flow. This simply means that whatever

volume of fluid flows through one section of the system must also

flow through any other section.

Fig. shows a system where flow is constant and the diameter

varies

A2 V2

A1 V1

Q1 Q2 21QQ

2211AVAV

69

Distribution of fluid power:Types of Hoses

1) Steel Pipes:

Extensively used in fluid power systems, although they are

rapidly being supplemented by steel or plastic tubing.

Disadvantages of steel pipes are their weight and the large

number of fitting requirement for connection .

Advantage is its mechanical strength and particularly its ability

to withstand abuse.

70

Screwed Connections :

Steel piping in fluid power systems is most often joined by

threaded connections.

Steel Tubing :

widely used material for hydraulic system conductors.

it can be easily formed to fit irregular paths so that fewer

fittings are required.

lessened chance of leakage since every connection is a

potential leak point.

It is also relatively small and light, thus making it easy to use.

71

Compression Joints :

comprise a loose ring having a cone-shaped nose that must

face the open end of a tube, a mating tapered barrel and a

retaining nut.

The end of the tube must always be cut square and deburred

before assembly.

When the tube is pushed fully in the fitting and the retaining

nut is tightened, the compressive action forces the nose of the

ring into the surface of the metal tube,

creating a permanent and very strong interference fit that is

capable of withstanding pressure in excess of 350 bar.

72

Plastic Conductors:available in polyethylene, polypropylene, polyvinyl chloride and nylon

compatible with most hydraulic fluids, however, and could safely be

used in low-pressure applications.

Flexible Hoses :A hose is manufactured from natural and synthetic rubbers and

several plastics.

This material is supported by fabric or by wire cloth, and wire braid

may be used between plies or as an outside casing for high-pressure

applications

73

Quick Disconnect Couplings :

This type of coupling in conjunction with flexible hoses connects movable

components together hydraulically.

Used to connect and/or disconnect hydraulic or pneumatic lines quickly

and easily without the use of tools

Typical applications are mobile trailers and agriculture machinery.

usually comprise a plug and socket arrangement that provides a leak-proof

joint when two parts are connected together

Each half of the coupling contains a spring-loaded ball or poppet that

automatically closes on disconnection, so that two completely leak-free

joints are obtained.

Leaking during the process of disconnecting or connecting coupling is

negligible

74

Types of Quick Couplings:

There are three basic types of quick couplings;

1. single shut-off,

2. double shut-off, and

3. straight-through

75

1.Single shut-off couplings/One-Way shut-off or Pneumatic

couplings:

This design locates the shut-off of fluid source connections but

leaves actuators unblocked

installed with the valved half on the pressure side of the circuit to

provide automatic shut-off flow when the coupling is disconnected.

low working pressure capabilities ranging from 100 to 300 PSI.

The are commonly made from brass or steel.

Applications -lubrication, paint spray, and carpet cleaning

equipment.

76

2. Double Shut-off Couplings /Two-way shut-off / Hydraulic

Couplings:

This design enables shutoff of both ends of pressurized lines when

disconnected.

77

BENDS:

78

Seals:Functions:Used to prevent both internal and external leakage of fluid

Prevent dirt, Dust enters into system

Maintenance of system pressure

Control of fluid loss

Classification of Seals:a) Classification by location

Static : no relative movement occurs between mating parts

Dynamic : movement occurs

b)Classification by method of sealing

1.Positive sealing- prevent minute leakage

2.Non- Positive sealing- allow small leakage for lubrication

c)Classification by geometric shape :

1. O-ring

2. Quad-ring

3. T-ring

4. V-cup ring

5. Hat ring

6. U-cup ring

79

According to seal materials-1. Leather seals

2. Metal seals

3. Polymers

4. Elastomers

5. Plastic seals

Factors influencing the selection of seals- Operating pressure and its variation

Ambient conditions

Operating temperature of system

Working fluid

Application of seal such as static or dynamic

Operational reliability expected

Expected service life

80

1. O-ring:

widely used seal for hydraulic

systems.

It is a molded synthetic rubber

seal that has a round cross-

section in its free state

used for the most static and

dynamic conditions.

It gives effective sealing through a

wide range of pressures, temperatures

Movements with the added advantages of sealing pressure

in both directions and providing low running friction on

moving parts.

81

Figure : Relative position of O-ring packings in different grooves at increasing

pressure.

82

2.Quad-ring/ X-Rings

•Static and dynamic sealing applications

•The four-lobed design provides twice the sealing

s/f in comparison to a standard o-ring

83

3.T-ring:Dynamic seal that is extensively used to seal cylinder-

pistons, piston rods and other reciprocating parts

Made of synthetic rubber molded in the shape of the cross-

section T and reinforced by backup rings on either side

The sealing edge is rounded and seals very much like an

O-ring.

84

4.V-ring seal and U-ring seal:

This are compression-type seals used in virtually in all types of

reciprocating motion applications like, piston rods and piston

seals in pneumatic and hydraulic cylinder, press rank, jacks

and seals on plungers and piston in reciprocating pumps.

Figure (a)V-ring seal and (b) U-ring seal

85

86

5. Piston cup packings:

Designed specifically for pistons in reciprocating pumps and

pneumatic and hydraulic cylinders.

Best service life for this type of application, require a

minimum recess space and minimum recess machining, and

can be installed easily and quickly.

87

Sources of Hydraulic System Contamination

New Fluid – most new fluid is not acceptable for use

in hydraulic systems and must be filtered first

Built-In – contamination introduced into the

system during the manufacture, assembly and

testing of components

Ingressed – external ingression of atmospheric

contamination; air condenses and water is released

into the reservoir

Induced – particles introduced during normal

maintenance or system operation

88

In-Operation – wear generation contamination

caused by the pump, actuators, cylinder or the

hydraulic motor

Rubber and Elastomers – degradation of rubber

compounds and elastomers products

High Water Based Fluids – supports biological

growth

Replacement of Failed Components – failure to

thoroughly clean conductor lines after replacing a

failed pump

89

ENERGY LOSSES IN HYDRAULIC SYSTEMS:

Energy losses in Pump, Hoses, connectors, Cylinders

Darcy–Weisbach Equation :

Head losses in a long pipe in which the velocity

distribution has become fully established or uniform

along its length can be found by Darcy’s equation as

Where, f is the Darcy friction factor,

L is the length of pipe (m),

D is the inside diameter of the pipe (m),

v is the average velocity (m/s) and

g is the acceleration of gravity (m/s2).

90

Frictional Losses in Laminar Flow:

Darcy’s equation can be used to find head losses in pipes

experiencing laminar flow by noting that for laminar flow,

the friction factor equals the constant 64 divided by the Reynolds

number:

Substituting this into Darcy’s equation gives the Hagen–Poiseuille

equation:

91

Equivalent Length :

length of pipe that for the same flow rate would produce the same

head loss as a valve or fitting.

where , Le is the equivalent length of a valve or fitting.

92

Effect of Pipe Roughness

The relative roughness of pipe is defined as the ratio of inside surface

roughness to the diameter:

Here, (ε) is surface roughness

93

Frictional Losses in Valves and Fittings

Where, K is called the loss coefficient of valve or fittings