Hyperbolic Process

           A process, in which the gas is heated or expanded in such a way that the product of its pressure and volume (i.e *v ) remains constant, is called a hyperbolic process.

          It may be noted that the hyperbolic process is governed by Boyle,s law i.e p v = constant. If we plot a graph for pressure and volume, during the process as shown in fig we shall get a rectangular hyperbola. Hence, this process is terned as hyperbolic process. It is merely a theoretical case, and has a little importance from the subject point of view. Its practical application is isothermal process, which is discussed below.

General Laws for Expansion and Compression

     The general law of expansion or compression of a perfect gas is pVn = Constant. It gives the relationship between pressure and volume of a given quantity of gas. The value of n depends upon the nature of gas., and condition under which the changes take place. The value of n may be between zero and infinity. But the following values of n are important from the subject point of view.

1. when n = 0. This means pV0 = constant, i.e.p = constant. In other words, for the expansion or constant of a perfect gas at constant pressure, n = 0.

2. when n = 1 ; then pv = constant, i.e the expansion or compression is isothermal or hyperbolic.
3. when n lies between 1 and n, the expension or compression is polytropic, i.e. pVn = Constant.
4. when n = & the expension or compression is adiabatic

5. when n = infinity the expansion or compression is at constant volume, i.e. v - Constant.

Importance of Critical Steel Ratio in Calculating Thermal Reinforcement

The fulfillment of critical steel ratio means that in construction joints or planes of weakness of concrete structure, steel reinforcement will not yield and concrete fails in tension first. This is important in ensuring formation of more cracks by failure of concrete in tension, otherwise failure in steel reinforcement would produce a few wide cracks which is undesirable. 

   What is the difference in arranging pumps in series and in parallel… solved example extracted from the topic Pumping Station of steel structures based on civil engineering… identical pumps with similar functions, if the pumps arranged in series, the total head is increased without a change to maximum discharge...

Functions of Cap Block, Drive Cap and Pile Cushion
   What are the functions of cap block, drive cap and pile cushion in driven piles… Solved example based on the topic piles and foundation Marine Piles of Reinforced Concrete Design of civil engineering subject… Cap block is installed between the hammer end and the drive cap to control the hammer blow in order to protect both the hammer and the pile from damage.

Relation of Bearing Pressure
   What is the relation of bearing pressure on soil nail head to the ratio La/Lb, where La is the length of soil nail before the potential slip circle…sample problem based on the topic Soils & Rocks from the Soil Mechanics of Civil Engineering subject… unstable soil mass before the potential circular slip is resisted by two components: soil nail head bearing pressure and friction of soil nail in the unstable soil mass...

Acetylene Gas Cylinders used for Gas Welding
   Why should acetylene gas cylinders used for gas welding be erected in upright position… Solved Example based on the topic Steel Structural Analysis of structure from the subject Civil Engineering… Acetylene gas is commonly used for gas welding because of its simplicity of production and transportation and its ability to achieve high temperature in combustion...

Major Problems in Using Pumping
   What are the major problems in using pumping for concreting works… solved example extracted from the topic Composite Steel-Concrete Construction of steel structures based on civil engineering… The main problems associated with pumping are the effect of segregation and bleeding…

SAFETY PRECAUTIONS AND OPERATING INSTRUCTIONS

When engineering personnel work outside of the engineering department, the responsibility for training and enforcing safety precautions rests with the head of the  department  controlling  the  operation.  For  example, weapons and ammunition handling requires special instructions by the weapons officer. The   engineer   officer   has   the   following responsibility  for  safety  in  the  engineering  department: l l l Be  sure  safety  precautions  are  posted  in  a conspicuous  and  accessible  places. Be sure all persons in the department and others who  may  be  concerned  with  engineering  matters observe safety precautions. Drill personnel in the safety procedures that apply to their work. Each   division   officer   has   the   following responsibilities for safety in his division: l l l Instruct  subordinates  in  all  safety  precautions that  apply. Require  subordinates  to  observe  all  safety precautions that apply. Post   safety   precautions   and   warnings   in conspicuous  places.  This  includes  posting warnings on dangerous equipment and in areas of the ship where there are particular hazards. Each  member  of  the  engineering  department  has the  following  responsibilities: l l l l l Report  unsafe  conditions  and  correct  the conditions  where  possible. Warn  others  of  unsafe  conditions. Use  approved  protective  clothing  and  equipment where it is called for. Report injury or ill health to supervisors. Use caution in emergency conditions or other dangerous  situations. WARMING-UP SCHEDULES Warming-up schedules for propulsion machinery and boilers are chronological checklists of the key steps used to light boiler fires and warm up the ship’s main engineering plant.

Types of Air compresser

Centrifugal

in service. Where capacity or horsepower rather than numbers is considered as a measure, the centrifugal,

without a doubt, heads the compressor field. During the past 30 years, the centrifugal compressor,

because of its smaller relative size and weight compared to the reciprocating machine, became

much more popular for use in process plants, which were growing in size. The centrifugal compressor

does not exhibit the inertially induced shaking forces of the reciprocator and therefore does not need

the same massive foundation. Initially, the efficiency of the centrifugal was not as good as that of a

well maintained reciprocating compressor. However, the centrifugal established its hold on the market

in an era of cheap energy when power cost was rarely, if ever, evaluated.

The smaller compressor design was able to penetrate the general-process plant market, which had

historically belonged to the reciprocating compressor. As the compressor grew in popularity, developments

were begun to improve reliability, performance, and efficiency. With the increase in energy

cost in the mid-1970s, efficiency improvements became a high priority. Initially, most development

had concentrated on making the machine reliable, a goal that was reasonably well achieved. Run

time between overhauls currently is three years or more, with six-year run times not unusual. As

plant size increased, the pressure to maintain or improve reliability was very high because of the

large economic impact of a nonscheduled shutdown.

Centrifugal compressors are dynamic types with rotating impellers that impart velocity and pressure

to air (Fig. 61.6). Their design is simple and straightforward, consisting of one or more highspeed

impellers with cooling sections. The only lubrication required is in the drive system, which is

sealed off from the air system.

Integral gear-type centrifugal air compressors are generally used in central plant air applications

requiring volumes ranging from 1000-30,000 cfm and discharge pressures from 100-125 psig.

Centrifugal air compressors are normally specified on the basis of required air-flow volume.

However, there are several ways to calculate volume and serious problems can result unless both

user and manufacturer use the same method. At the very least, the user can have problems comparing

bids from competing manufacturers. At worst, he may choose the wrong compressor.

These problems can be avoided by specifying capacity in terms of actual inlet conditions and by

understanding how compressor capacity is affected by variable ambient conditions such as inlet

pressure, temperature, and relative humidity. Factors such as cooling water temperature and motor

load must be considered before a compressor and its drive motor can be sized.

A multistage arrangement for integral gear-type compressors is shown in Fig. 61.7. The flow path

is straight through the compressor, moving through each impeller and cooler in turn. This type of

centrifugal compressor is probably the most common of any found in process service, with applications

ranging from air to gas.

compressors are second only to reciprocating compressors in numbers of machines

Sliding-vane

61.8). As the rotor turns, the vanes slide out against the stator or housing. Air compression occurs

when the volume of the space between the sliding vanes is reduced as the rotor turns. Single- and

multistage versions are available.compressors consist of a vane-type rotor mounted eccentrically in a housing (Fig.

• Oxidation

• Condensation

• Viscosity

• Outgassing in the inlet

• Foaming

• Separation performance

• Chemical reaction

Some problems can be solved with specially selected oil grades. Another solution is synthetic oils,

but cost is a problem, particularly with silicone oils. Alternatives need to be reviewed to match

service life of the lubricant with lubrication requirements in the compressor.

One consideration for flooded compressors is the recovery of liquid. In conventional arrangements,

the lubricating oil is separated at the compressor outlet, cooled, filtered, and returned to the compressor.

This is fine for air service, where oil in the stream is not a major problem, but when oilfree

air is needed, the separation problem becomes more complex. Because the machine is flooded

and the discharge temperature is not high, separation is much easier relative to compressors that send

small amounts of fluid at high temperature down stream. Usually part of the lubricant is in a vaporized

form and is difficult to condense except where it is not wanted. To achieve quality oil-free air, such

as that suitable for a desiccant-type dryer, separators that operate at the tertiary level should be

considered. Here, the operator must be dedicated to separator maintenance, because these units require

more than casual attention. Separation by refrigeration is not as critical if direct expansion chillers

are used. In these applications, the oil moves through the tubes with the refrigerant and comes back

to the compressor with no problem, if the temperature is not too low for the lubricant.

Advantages of helical screw compressors include smooth and pulse-free air output, compact size,

high output volume, low vibration levels, and long life.

Air Compressor

material is also a factor in setting the temperature limit. While 30O

should be remembered that this is an average outlet temperature and the cylinder will have hot spots

exceeding this temperature.

Lubricated compressors use either a full-pressure or splash-lubricating system with oil in the

crankcase. Oil-free compressors have a crosshead or distance piece between the crankcase and cylinders.

Nonlubricated compressors use nonmetallic piston rings, guides, and sealed bearings with no

lubricating oil in the crankcase.

0F may not seem all that hot, it

Reciprocating double-acting

used for heavy-duty, continuous service. Discharge pressures range from above atmospheric to several

thousand psig. The largest single application is continuous-duty, supplying air at 100 psig. This design

is available with the same modifications as single-acting compressors.

Double-acting crosshead compressors, when used as single-stage, have horizontal cylinders. The

double-acting cylinder compressor is built in both the horizontal and the vertical arrangement. There

is generally a design tradeoff to be made in this group of compressors regarding cylinder orientation.

From a ring-wear consideration, the more logical orientation is vertical; however, taking into account

size and the ensuing physical location as well as maintenance problems, most installations normally

favor a horizontal arrangement (Fig. 61.3).

designs compress air on both strokes of the piston and are normally

Rotary screw

machines. Oil or water injection is normally used to seal clearances and remove the heat of

compression. Oil-free designs have reduced clearances and do not require any other sealing medium.

In single-screw designs, the rotor meshes with one or two pairs of gates (Fig. 61.4). The screw

and casing act as a cylinder, while the gates act like the piston in a reciprocating compressor. The

screw also acts as a rotary valve, with the gates and screw cooperating as a suction valve and the

screw and a port in the casing acting as a discharge valve. Single-stage sizes range from 10-1200

cfm with pressures up to 150 psig. 250-psig designs, supplying 700-1200 cfm, are available.

Dual rotor designs use two intermeshing rotors in a twin-bore housing (Fig. 61.5). Air is compressed

between the convex and concave rotors. The trapped volume of air is decreased along the

rotor, increasing pressure. Single- and multistage versions are available with and without lubrication.

The power consumption of rotary screw compressors during unloaded operation is normally higher

than that of reciprocating types. Recent developments have produced systems where the unloaded

horsepower is 15-25% of loaded power. These systems are normally used with electric motor,

constant-speed drives. Use as a base load compressor is recommended to avoid excessive unloaded

power costs.

A dry screw compressor may be selected for applications where a high air-flow rate is required

but space does not allow a reciprocating compressor, or where the flow requirement is greater than

can be supplied by a single-unit, oil-flooded screw compressor. Packaged versions of dry screw

compressors require a minimum of floor space.

Dry screw compressors generate high frequency pulsations that affect system piping and can cause

acoustic vibration problems. These would be similar to the type of problems experienced in reciprocating

compressor applications, except that the frequency is higher. While volume bottles work

with the reciprocator, dry-type screw compressors require a manufacturer-supplied proprietary silencer

to take care of the problem.

There is one problem this compressor can handle quite well: unlike most other compressors, it

will tolerate a moderate amount of liquid. Injection for auxiliary cooling can be used, normally at a

lower level than would be used in a flooded compressor. The compressor also works well in fouling

service, if the material is not abrasive. The foulant tends to help seal the compressor and, in time,

may improve performance.compressors use one or two rotors or screws and are constant-volume, variablepressure

NUMERICAL CALCULATIONS.

addition to the name and the date, all calculations shouldaccompanied by a complete record of the object and purpose

of

the calculation, the apparatus, the assumptions made, the

data

used, reference to other calculations or data employed,

etc.,

to

in short, they should include all the information requiredmake the calculation intelligible to another engineer without

further

information besides that contained in the calculations,

or in the references

given therein. The small amount of time

and

increased

work required to do this is negligible compared with theutility of the calculation.

Tables

and curves belonging to the calculation should in

the

same way be completely identified with it and contain

sufficient

data to be intelligible.

d.

167.

Reliability of Numerical Calculations.The most important and essential requirement of

numerical

engineering calculations is their absolute reliability.

When

making a calculation, the most brilliant ability, theoretical

knowledge and

practical experience of an engineer are

made

useless, and even worse than useless, by a single error in

an

important calculation.

Reliability

of the numerical calculation is of vastly greater

importance

in engineering than in any other field. In pure

mathematics

example which

an error in the numerical calculation of anillustrates a general proposition, does not detract

from the

interest and value of the latter, which is the main

purpose; in physics, the general

the'

law which is the subject ofinvestigation remains true, and the investigation of interest

and

use, even if in the numerical illustration of the law an

error

is made. With the most brilliant engineering design,

however,

if in the numerical calculation of a single structural

member

an error has been made, and its strength thereby calculated

wrong,

the rotor of the machine flies to pieces by centrifugal

forces,

engineer.

or the bridge collapses, and with it the reputation of theThe essential difference between engineering and

purely

scientific caclulations is the rapid check on the correctnessof the calculation, which is usually afforded by the per

In

be

ENGINEERING MATHEMATICS.

be used visually also, in determining the frequency

of

hunting of synchronous machines, etc. In the phenomenon

of

frequency,

hunting, frequently two periods are superimposed, forcedresulting from the speed of generator, etc., and the

natural

frequency of the machine. Counting the number of

impulses,

/, per minute, and the number of nodes, n, gives the

two

frequencies :/+- and/ ; and as one of these frequencies

2i 2i

is

the impressed engine frequency, this affords a check.

Not

infrequently wave-shape distortions are met, which

are

but

not due to higher harmonics of the fundamental wave,are incommensurable therewith. In this case there are

two

entirely unrelated frequencies. This, for instance, occurs

in

the secondary circuit of the single-phase induction motor;

two

sets of currents, of the frequencies / and (2ffs) exist

(where

/ is the primary frequency and / the frequency of

slip).

Of this nature, frequently, is the distortion produced by

surges,

oscillations, arcing grounds, etc., in electric circuits;

it is

a combination of the natural frequency of the circuit

with the impressed

frequency. Telephonic currents commonly

show

such multiple frequencies, which are not harmonics ofeach

Engineering

work leads to more or less extensive

numerical

investigation

calculations, when applying the general theoreticalto the specific cases which are under consideration.

Of importance

in such engineering calculations are;

(a)

The method of calculation.

(6)

The degree of exactness required in the calculation.

(c)

(d)

a.

Method of Calculation.

Before

carefully

beginning a more extensive calculation, it is desirableto scrutinize and to investigate the method, to find

the simplest

system

way, since frequently by a suitable method andof calculation the work can be reduced to a small fraction

of

what it would otherwise be, and what appear to be

hopelessly

complex calculations may thus be carried out

quickly

and expeditiously by a proper arrangement of the

work.

The most convenient way usually is the arrangement

in

tabular form.

As

example, consider the problem of calculating the regulation

of

a 60,000-volt transmission line, of r=60 ohms resistance,

x

= 135 ohms inductive reactance, and fe 0.0012 condensive

susceptance,

for various values of non-inductive, inductive,

and

condensive load.

Starting

transmission

with the complete equations of the long-distanceline, as given in "Theory and Calculation of

Transient

Electric Phenomena and Oscillations," Section III,

paragraph

power-factors,

2.

90 PER CENT POWER-FACTOR, LAG.

cos

0=09; sin0=Vl-0.92

=0.436;

j

sin 0)

=

i (0 9+0.436j);

Si

= (0.919- 0.03Gj> + (56.8- 131.8/K0.9 +0.436j>o

=

(0.919- 0.036j>o + (108.5

-

93.8/H

=

4 + '

:

/i

=

(0.919-0.036j)(0.9

+0.436j)io- (0.0144 +U

'

=

(0.843

+0.366j>

-

(0.0144

+1.168j> 10-3 =C/ -D,

and

now the table is calculated in the same manner as under 1.

Then

manner,

corresponding tables are calculated, in the samefor power-factor, =0.8 and =0.7, respectively, lag,

and

for power-factor -0.9, 0.8, 0,7, lead; that is, for

cos

0+] sin 0=0.8 +0.6]';

0.7+0.714]';

0.9-0.436]';

0.8-0.6]';

0.7-0.714].

Then

curves are plotted for all seven values of power-factor,

from

0.7 lag to 0.7 lead.

From

these curves, for a number of values of i

,

for instance,

to

taken,

=20, 40, 60, 80, 100, numerical values of ii, e^ cos Q, aroand plotted as curves, which, for the same voltage

ei

= 60 at the step-up end, give i\ } eo, and cos 6, for the same

value

IQ, that is, give the regulation of the line at constantcurrent output for varying power-factor.9; and considering that for every one of the variouslag, and lead, a sufficient number of valuesThe intelligibility of the results,The reliability of the calculation.other.

frequently