Pressure and Manometers

There is a simplest explaination of fluid mechanics

1. Dr. Eng. Ezzat El-Sayed G. Saleh
Civil Engineering Dept.
Minia University
Lec (2-3)
Fluid Statics ”Manometers”

3. A Life ruled by time, a
life powered by new
opportunities

4. Pressure
Pressure:isdefinedastheamountofforceexerted
onaunitareaofasubstance.Thiscanbestatedby
theequation:A
F
P

5. Direction of Fluid Pressure on
Boundaries
Closed Duct
Pipe
Dam

6. Mercury Barometer

7. Barometer
Apparatususedtomeasurepressure;derivedfromtheGreek“baros”
meaning,“weight”.CreatedbyEvangelistaTorricelliin1646who
invertedatubefilledwithmercury(Hg)intoadishuntiltheforceofthe
Hginsidethetubebalancedtheforceoftheatmosphereonthesurface
oftheliquidoutsidethetube.

8. Thetwopoints“o”,and“a”areinthesame
elevation,then
P
o= P
vap.+ 
mer.g y
P
o= P
a= P
atm
P
atm= 
mer.g y
P
vap.
Can be neglected

9. Comparison between Absolute and Gage Pressures
Absolute Zero
Pressure
Absolute
Pressure (2)
Absolute
Pressure (1)


Vacuum or Negative
gage pressure (2)
gage
pressure (1)
Atmospheric
Pressure

10. Absolute and Gage Pressure
Asimpleequationrelatesthetwopressuremeasuring
systems:
where
P
abs Absolute pressure
P
gage Gage pressure
P
atm Atmospheric pressure.PPP
atmgageabs 

11. Aperfectvacuumisthelowestpossiblepressure.
Therefore,anabsolutepressurewillalwaysbepositive.
Agagepressureaboveatmosphericpressureis
positive.
Agagepressurebelowatmosphericpressureis
negative,sometimescalledvacuum.
GagepressurewillbeindicatedintheunitsofP
a(gage)
orpsi(g).

12. AbsolutepressurewillbeindicatedintheunitsofP
a
(abs)
orpsi
(a).
Atsealevel,thestandardatmosphericpressureis
101.3kp
a(abs),or14.70psia.
Unlesstheprevailingatmospherepressureisgiven,
wewillassumeittobe
101 kp
a(abs)
, or 14.7 psi.

14. Gagepressure:iscommonlymeasuredbyaBourdongage.
Differenceinpressureismeasuredbyamanometers.
Localatmosphericpressure:(i.e.theabsolutepressureofthe
atmosphereataplace)ismeasuredbyamercurybarometer.
Thelocalatmosphericpressurevarieswiththeelevationabovemean
seelevelandlocalmeteorologicalconditions.
Forengineeringapplication,astandardatmosphericpressureat
meansealevelat15
o
Cisoftenused.Thevalueofthisstandard
atmosphericpressure(called1atmosphere)is:
1 atm. = 760 mm of mercury =10.34 m of water
= 101.33 KPa = 101.33 m bar

15. Amanometerisoneoftheearliestandsimplestdevicesused
formeasurementofgaugepressureanddifferentialpressures.
Manometerhasmyriadusesindifferentfields. (ددعلاصىيحنمتامادخت سالا)
Usedinthemaintenanceofheating,ventilation,andair
conditioning(HVAC)systems,lowpressurepneumatic
(ئياوه) orgassystems.
Constructionofbridges,installingswimmingpoolsandother
engineeringapplications.
Climateforecasting.
Clinicalapplicationslikemeasuringbloodpressureandin
physiotherapy.
Piezometersareusedtomeasurethepressureinpipeswhere
theliquidisinmotion.

16. Manometers

17. Piezometer
As shown in the figure, one end of the piezometer is open to
atmospheric pressure, and the other end is connected to the
point A, where pressure is to be measured.

19. Twophotosshowinghowtomeasuretheheadinagatedpipesystem.
Theheadisthedistancebetweenthewaterlevelinthetubeandthe
centerofthepipe.

21. Itconsistsofaglasstubebent
liketheletter'U'.Inthistypeof
manometer,balancingacolumn
ofliquidisdonebyanother
columnofsameorotherliquid.
OneendoftheU-tubeisattached
tothepointwherepressureisto
bemeasured,whiletheotherend
isopentoatmosphericpressure.
U-Tube Manometer

22. U-tube-Manometer

24. 2matm1wwater hgPhgP  BAPP Sincethepressures
atequalelevations
inacontinuous
massoffluidatrest
mustbethesame,)gage0P(hghgP
.atm1w2mwater 
A U-tube Manometer

25. P
A= -ve P
A= +vex.gy.gPPP
mAAQP  x.gy.gPPP
mAAQP 
AU-tube Manometer for Measurements of
Positive and Negative Pressures
The indicated Liquid B,in this case, is mercury

26. AU-tube Manometer for Measurements of
Positive and Negative Pressures
P
1= P
2
P
A+ 
L g h
L+ 
I g h
i = P
atm
P
A = + ve
P
A = -ve
P
atm
P
atm
P
1=P
2
P
A+ 
L g (h
L+ h
i) = P
atm+ 
igh
i

27. Inverted U-tube Differential Manometer
U-tube Differential Manometer

28. Digital Manometer
Adigitalmanometerusesamicroprocessorandpressure
transducertosenseslightchangesinpressure.Itgives
thepressurereadoutonadigitalscreen.Itmeasures
differentialpressureacrosstwoinputs.Ananalog/digital
outputinproportiontotheinstantaneouspressurecanbe
obtained.
Digitalmanometersreportpositive,negative,or
differentialmeasurementsbetweenpressures.

29. A Differential Manometer is connected to a pipe at two
Points to measure the pressure difference
P
3= P
4& P
1+
Lg (h + h
i) = P
2+ 
Lg ((Z
2–Z
1) + h ) + 
i
g h
i

30. The well-typeorcistern
manometer,issimilartoaU-tube
manometerbutonehalfofthe
tubeismadeverylargesothatit
formsawell.
Thechangeinthelevelofthe
wellasthemeasuredpressure
variesisnegligible.Therefore,
theliquidlevelinonlyonetube
hastobemeasured,which
makestheinstrumentmuch
easiertousethantheU-tube
manometer.
Well -Type
Manometer

33. A Differential Manometer is connected to a pipe at
two points to measure the pressure difference
P
1= P
2+ 
Lg{h + h (d/D)
2 }

34. 
l
P
A= 
i g (l sin )
Analysis of Inclined-Tube Manometer:
AnInclinedDifferentialManometerisconnectedtoapipeattwopoints
tomeasurethepressuredifference.

35. Thefactthattheshearstressinthefluidisdirectly
proportionaltothevelocitygradientcanbestated
mathematicallyas








dy
dV
wheretheconstantofproportionalityµ(theGreek
lettereta)iscalledthedynamicviscosityofthefluid.
……………… .. (1)
Dynamic Viscosity

36. Thedefinitionofdynamicviscositycanbederivedby
solvingforµ 









dydV
Theunitsofµcanbederivedbysubstitutingthe
SIunitsintoEq.(2)asfollows
……………… .. (2)2
2
mS.N
sm
m
m
N

Thedimensionsofforcemultipliedbytimedividedby
lengthsquaredareevident.
Units of Dynamic Viscosity

37. InternationalSystem  N.s / m
2
, P
a.s, or kg
/(m.s)
B.GSystem Ib.s / ft
2
or Slug/ (ft.s)
c.g.sSystemPoise=dyne.s/cm
2
=g/(cm.s)=0.1
P
a.s
Dynamic Viscosity Units in the three most widely used systems

38. BecauseP
a
isanothernameofN/m
2s.P
a
IntermsofkgratherthanN
……………… .. (3)s.m
kg
m
s
s
m.kg
m
s
N
222

Units of Dynamic Viscosity

41. 41#
Any Questions???

43. h hgP AhgAPF  hA
I
hh
cg
cp

 Forces on a Sluice Gateh

44. Radial Gate

47. Thispropellermeterisinstalledinsideapipesection.

49. Siphon