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CHAPTER: 1

 

PROJECT PURPOSE OR ABSTRACT

The pressure at any level in the atmosphere may be interpreted as the total weight of the air

above a unit area at any elevation. At higher elevations, there are fewer air molecules above

a given surface than a similar surface at lower levels. For example, there are fewer

molecules above the 50 km surface than are found above the ! km surface, which is why

the pressure is less at 50 km. "hat this implies is that atmospheric pressure decreases with

increasing height. #ince most of the atmosphere$s molecules are held close to the earth$s

surface by the force of gravity, air pressure decreases rapidly at first, then more slowly at

higher levels. Air pressure decreases with altitude from an average of about 0%h&a at the

surface to 0h&a in space ' which is not that far up. Temperature decreases with altitude in

the troposphere, increases in the stratosphere. (ecreases in the mesosphere and increases in

the thermosphere until the molecules are so far apart on the edge of space that temperature becomes immeasurable. At higher altitudes, less air means less weight and less pressure.

&ressure and density of air decreases with increasing elevation. )y using and calculating

the given formula we can easily find out the pressure at an altitude of some height in *arth$s

atmosphere, estimate the pressure at an altitude e+uivalent to the height of ountain, the

ambient air pressure at altitude is roughly estimated by assuming an exponential drop with

altitude and a sea'level pressure of atm. -n some circumstances this method can give large

errors, so should not be relied on.

  CHAPTER: 2

  PROJECT BACKGROUND OR LITERATURE REVIEW

Air pressure is the pressure

exerted by the weight of air in

the atmosphere of *arth or that of

another planet/. -n most

circumstances air pressure is closely

approximated by the h!r"s#$#i%

pressure caused by the &ei'h# of

$ir above the measurement

 point. n a given plane, low'

 pressure areas have less

atmospheric mass above their

location, whereas high'pressure

areas have more atmospheric mass

above their location.

Fraction of 

atm

Average altitude

m/ ft/

0 0

1! 5234.% 3000

1% 3%5.3 !230

10 4%.6 5!6!4

100 %0600.6 0%3

1000 2324.! 560%

10000 4624%.4 !!366

100000 64!3.4 !3%04

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7ikewise, as elevation increases, there is less overlying atmospheric mass, so that

atmospheric pressure decreases with increasing elevation. n average, a column of air one

s+uare centimeter in cross'section, measured from sea level to the top of the atmosphere,

has a mass of about .0% kg and weight of about 0. 8 !.!3 lbf /. A column one s+uare

inch in cross'section would have a weight of about 2. lbs or about 45.2 8./ This giventable compiled by 8A#A gives a rough idea of air pressure at various altitudes as a

fraction of one atmosphere/.

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De#er(i)i)' $#("spheri% pressure:

 P  9−¿

 P0e¿

h

h0

/

where:

 p = atmospheric pressure

(measured in bars)

h = height (altitude)

 p0 = is pressure at height h = 0 (surface pressure)

h0 = scale height

This e+uation shows that the atmospheric pressure decays exponentially from its value at

the surface of the body where the height h is e+ual to 0.

"hen h0 = h, the pressure has decreased to a value of e' times its value at the surface.

"e are actually living near the bottom of an ocean of air. At sea level, the weight of the air

 presses on us with a pressure of approximately 2. lbs1in!

. At higher altitudes, less airmeans less weight and less pressure. &ressure and density of air decreases with increasing

elevation. &ressure varies smoothly from the earth$s surface to the top of the mesosphere.

The fundamental procedure is a subroutine called Atmosphere that accepts altitude as an

input argument and returns non'dimensional values of temperature, pressure, and density

which are ratios of the +uantity at altitude to that at sea'level. The standard atmosphere is

defined as a set of layers and the routine determines which layer contains the specified

altitude. The temperature is then computed by linear interpolation. Then the pressure is

computed from the hydrostatic e+uations and the density follows from the perfect gas law.

&ressure varies smoothly from the *arth$s surface to the top of the mesosphere. Although

the pressure changes with the weather, 8A#A has averaged the conditions for all parts of

the earth year'round. As altitude increases, atmospheric pressure decreases. ne can

calculate the atmospheric pressure at a given altitude. Temperature and humidity also affect

the atmospheric pressure, and it is necessary to know these to compute an accurate figure.

The graph at right was developed for a temperature of 5 ;< and a relative humidity of

0=.At low altitudes above the sea level, the pressure decreases by about .! k&a for every

00 meters. The highest ad>usted'to'sea level barometric pressure ever recorded on *arth

above 50 meters/ was ,035. hectopascals %!.04 in?g/ measured in Tosontsengel,

ongolia on 6 (ecember !00. The highest ad>usted'to'sea level barometric pressure ever 

recorded below 50 meters/ was at Agata, *venhiyskiy, @ussia 44;5%B8, 6%;!3B*,elevation: !4 m 354.% ft/C on % (ecember 643 of ,03%.% hectopascals %.66 in?g/.

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The discrimination is due to the problematic assumptions assuming a standard lapse rate/

associated with reduction of sea level from high elevations. The lowest non'tornadic

atmospheric pressure ever measured was 30 h&a !5.46 in?g/, set on ! ctober 66,

during Typhoon Tip in the western &acific cean. The measurement was based on an

instrumental observation made from a reconnaissance aircraft. The normal high barometric pressure at the (ead #ea, as measured by a standard mercury manometer and blood gas

analyDer, was found to be 66 mm?g 045 h&a/.

Atmospheric pressure reduces with altitude for two reasons ' both related to gravity.

. The gravitational attractionE/ between the earth and air molecules is greater for

those molecules nearer to earth than those further away ' they have more weight '

dragging them closer together and increasing the pressure force per unit area/

 between them.

!. olecules further away from the earth have less weight because gravitationalattraction is less/ but they are also $standing$ on the molecules below them, causing

compression. Those lower down have to support more molecules above them and

are further compressed pressuriDed/ in the process.

E/ #trictly it is the gravitational force minus the effect of the *arth$s spin an effect that is

greatest at the e+uator/.

The concept of pressure $*#i#u!e allows us to take into consideration any variation in the

ambient pressure. "e know that standard pressurethe pressure most likely to be

encounteredis !6.6!G?g inches of mercury/ at sea level. "e also know that the pressureof the air normally decreases G?g with an 000B increase in altitude. Therefore, if we are

at an airport with sea level elevation, and the current altimeter setting is !3.6!G?g, we can

 predict that the aircraft during the takeoff, for example, will perform as if it is doing the

same takeoff at an airport with an elevation of 000B, and performance will be degraded

accordingly. <onversely, if the altimeter setting were %0.6!G?gi.e., the pressure of the

air is higher than normal or standardthe takeoff performance of the aircraft would be

enhancedas if the takeoff were conducted at an airport situated 000B under sea level

where thick dense air not waterH/ would provide better conditions for lift from the wing

surfaces and thrust from the propeller and engine.

<alculation of pressure is done by calculating the difference between the current altimeter

setting and the standard altimeter setting. This difference is then converted into feet, based

on the given that G?g 9 000Bthis is referred to as the #tandard &ressure 7apse @ate.

Accordingly, if the current altimeter setting is %0.!G?g., we would calculate as follows:

%0.! I !6.6! 9 .!. Jsing the standard lapse rate, .! is converted into !00B. "hat do we do

with this !00BK The answer is that if we want to determine the pressure altitude for an

airport, we must add or subtract the !00B relative to the airportBs elevation. -f we want to

determine the pressure altitude of an intended altitude that we want to cruise at, we must

add or subtract the !00B relative to the planned cruising altitude. The +uestion of adding orsubtracting the Lcorrection valueG is determined by whether the current air pressure is

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higher or lower than standard. #ince pressure decreases with altitude, and the current

altimeter setting is higher than standard, we should subtract the !00B. Thus, if the airport

elevation were %2!B, we can say that the airportBs pressure altitude is %!!B for the purpose

of determining takeoff performance, and if the planned cruising altitude were 4500B we

know that when we level off with 4500B indicated on the altimeter, the aircraft will burnfuel and produce an indicated airspeed as if it had leveled off at 4%00B.

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  CHAPTER: +

 Resu*#s $)! Dis%ussi")s

a/

 

P

30

P= 30e−3.23×10−5

h

h

b/ The definition of a tangent line is defined as a line passing through a given point of a

function whose slope is e+ual to the derivative of the function at that point.

The e+uation of the tangent line is of the form y 9 mx M b, where m is the slope and b is the

y'intercept. Niven function is not in terms of x and y, it is in terms of & and h, so the

e+uation of the tangent line will look like & 9 mh Mb. This e+uation can be found after

calculating the slope of & at h90, and the value of & at h 9 0

The slope of & at h 9 0 is e+ual to the derivative of & d&1dh evaluated at h 9 0:

d&

9 %0e

O%.!%P0O5h

O%.!% P 0

O5

/dh

  #o , 9 O%0P%.!% P 0O5

/ 9 O6.46 P 0O29 m

h90

?ence, at h90, the slope of the tangent line is '6.46P0 '2

#o far we have

& 9 O6.46 P 0O2 h M b

we need to find b, the y intercept, to completely solve for the tangent line. "e know that

this point passes through & h90/, or 0, %0/

&ut this point into the e+uation for the tangent line, and solve for b:

%0 9 O6.46 P 0O2 P0 M b

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solve for b, b 9 %0Q

& 9 O6.46 P 0O2 Ph M %0

& 9 %0 O .000646h

c/ At h 9 0,

the air pressure is %0 inches of mercury. At 000 feet, it would be %0

0001000 PQ at !000 feet, it would be %0 ' !0001000 P ,

The rule of thumb says, (rop in pressure from sea level to height h9 h1000

)ut since the pressure at sea level is %0 inches of mercury,

This drop is pressure is also %0'p/, so

  %0'p 9h

1000

#o, examining the pattern:

& 9 %0 ' h1000

d/ The e+uations in b/ and c/ are almost the same: both have & intercepts of %0, and the

slopes are almost the same 6.46 P 0O2 R 0.00/. The rule of thumb calculates values of &

which are very close to the tangent lines, and therefore yields values very close to the

curve.

(e) The tangent line is slightly below the curve, and the rule of thumb line, having a slightlymore negative slope, is slightly below the tangent line for h S 0/. Thus, the rule of thumbvalues are slightly smaller.

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  CHAPTER: , 

CONCLUSION

The implementation of the chain rule using rule of thumbs can be considered highly

successful in terms of the ob>ectives and the scope of work. <onclusions concerning

activities and findings can be drawn as follows:

1. The given formula indicates that the air pressure rapidly increases whenthe altitude tends to zero and that relation sketched in a graph to see thereal fact.

2. When the altitude (h) tends to zero the equation shows the air pressurevalue in its increasing stage and with the change of altitudes higher valuethe air pressure will e reduced.

!. At higher altitudes, less air means less weight and less pressure. &ressure and density

of air decreases with increasing elevation.

". The gravitational attraction between the earth and air molecules is greater for those

molecules nearer to earth than those further away ' they have more weight ' dragging

them closer together and increasing the pressure force per unit area/ between them.

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  CHAPTER: -

  Re.ere)%es

A +uick derivation relating altitude to air pressure by &ortland #tate Aerospace #ociety,

Uol.%23/:6!%'6!5, doi:0.041>.renene.!003.!.006

Vapour Pressure, ?yperphysics.phy'astr.gsu.edu, retrieved !0!'0'

 www.npl.co.uk1reference1fa+s1why'does'atmospheric'pressure'change'with'altitude'

=!3fa+'pressure=!6, available access in 02.02.!05

en.wikipedia.org1wiki1AtmosphericVpressure, available access in 02.02.!05

www.!00.atmos.uiuc.edu1=!3Nh=!61guides1mtr1prs1hght.rxml, available access in

0%.02.!05

www.regentsprep.org1regents1math1algtrig1atp3b1exponentialresource.html, available access

in 04.02.!05

www.>iskha.com1display.cgiKid9%50664%%, available access in 04.02.!05

www.pdas.com1atmos.html, available access in 04.02.!05