Hydrostatic forces on plane surfaces

Fluid mechanics

1. Ministry of Higher Education & Scientific Research
Foundation of Technical Education
Technical College of Basrah
CH.3: Hydrostatic Forces on Plane Surfaces
Training Package
in
Fluid Mechanics
Modular unit 3
Hydro static Force on Plane Surface

By
RisalaA. Mohammed
M.Sc. Civil Engineering
Asst. Lect.
Environmental & Pollution Engineering Department
2011

2. 1-Over view
1-1 Target population
CH.3: Hydrostatic Forces on Plane Surfaces
Forthestudentsofsecondclassin
EnvironmentalengineeringDepartmentin
TechnicalCollege

3. 1-2 Rationale
CH.3: Hydrostatic Forces on Plane Surfaces
Thestudyofforceinfluidmechanicsisvery
importantinappliedfieldtocalculatetheamountof
forceonthewallsofthereservoirs,surfaceswhich
exposedtotheeffectsofwindsuchasaircraftandhigh
buildings.Inadditiontotheapplicationinthefieldof
hydraulicstructurestocalculatetheforcesthat
exposedondamsandgates.

4. 1-3 Central Idea
CH.3: Hydrostatic Forces on Plane Surfaces
The main goal of this chapter are:
1-Define the hydrostatic force.
2-Applied of the hydrostatic force on surface
plane .

5. 1-4 Instructions
CH.3: Hydrostatic Forces on Plane Surfaces
1-Study over view thoroughly
2-Identify the goal of this modular unit
3-Do the Pretest and if you :-
*Get 9 or more you do not need to proceed
*Get less than 9 you have to study this modular
4-After studying the text of this modular unit , do the post test
and if you :-
*Get 9 or more , so go on studying modular unit four
*Get less than 9 , go back and study the modular unit three

6. 1-5 Performance Objectives
CH.3: Hydrostatic Forces on Plane Surfaces
Attheendofthismodularunitthestudentwillbeableto:-
1-Define the hydrostatic force
2-calculate the magnitude and direction and it position of
hydrostatic pressure on vertical, inclined and curved
surfaces.

7. 2-Pre test
-
CH.3: Hydrostatic Forces on Plane Surfaces
Q1)) ( 5 mark)
The tank in Fig. below is 40cm wide. Compute
the hydrostatic forces on horizontal panels BE
and AD. Neglect atmospheric pressure .
Q2)) ( 5 mark)
the net hydrostatic force per unit width on
rectangular panel AB in Fig. below and
determine its line of action.
Not
Check your answers in key answer page

8. Hydrostatic Forces on Plane Surfaces
CH.3: Hydrostatic Forces on Plane Surfaces
Onaplanesurface,the
hydrostaticforcesforma
systemofparallelforces
For many applications,
magnitudeandlocationof
application,whichiscalled
centerofpressure,mustbe
determined.
AtmosphericpressureP
atmcan
beneglectedwhenitactson
bothsidesofthesurface.

9. Hydrostatic Forces on Inclined Plane Surfaces
CH.3: Hydrostatic Forces on Plane Surfaces
ThemagnitudeofF
Ractingonaplanesurfaceofacompletelysubmerged
plateinahomogenousfluidisequaltotheproductofthepressureP
Cat
thecentroidofthesurfaceandtheareaAofthesurface

10. Hydrostatic Forces on Inclined Plane Surfaces
CH.3: Hydrostatic Forces on Plane Surfaces
Lineofactionofresultantforce
F
R=P
CAdoesnotpassthrough
thecentroidofthesurface.In
general,itliesunderneath
wherethepressureishigher.
VerticallocationofCenterof
Pressureisdeterminedby
equationthemomentofthe
resultantforcetothemomentof
thedistributedpressureforce.,xx C
pC
c
I
yy
yA


11. Example(1)
CH.3: Hydrostatic Forces on Plane Surfaces

12. Example(2)
CH.3: Hydrostatic Forces on Plane Surfaces

13. Hydrostatic Forces on CurvedSurfaces
CH.3: Hydrostatic Forces on Plane Surfaces
F
Ron a curved surface is more involved since it requires
integration of the pressure forces that change direction
along the surface.
Easiest approach: determine horizontal and vertical
components F
Hand F
Vseparately.

14. Hydrostatic Forces on CurvedSurfaces
CH.3: Hydrostatic Forces on Plane Surfaces
Horizontalforcecomponentoncurvedsurface:F
H=F
x.Lineofaction
onverticalplanegivesycoordinateofcenterofpressureoncurved
surface.
Verticalforcecomponentoncurvedsurface:F
V=F
y+W,whereWis
theweightoftheliquidintheenclosedblockW=rg.Xcoordinateof
thecenterofpressureisacombinationoflineofactiononhorizontal
plane(centroidofarea)andlineofactionthroughvolume(centroidof
volume).
MagnitudeofforceF
R=(F
H
2
+F
V
2
)
1/2
Angleofforceisa=tan
-1
(F
V/F
H)

15. Example(3)
CH.3: Hydrostatic Forces on Plane Surfaces

16. Example(3)
CH.3: Hydrostatic Forces on Plane Surfaces

17. Example(4)
CH.3: Hydrostatic Forces on Plane Surfaces

18. Example(5)
CH.3: Hydrostatic Forces on Plane Surfaces

19. Example(6)
CH.3: Hydrostatic Forces on Plane Surfaces

20. Example(7)
CH.3: Hydrostatic Forces on Plane Surfaces

21. Post test
-
CH.3: Hydrostatic Forces on Plane Surfaces
Q1)) (5 marks)
Gate AB in Fig. below is 16 ft long and 8 ft wide.
Neglecting the weight of the gate, compute the
water level h for which the gate will start to fall.
Q2)) (5 marks)
Gate AB in Fig. below a is 16 ft long and 8 ft
wide. Neglecting the weight of the gate,
compute the water level h for which the gate
will start to fall.

22. Answer key
CH.3: Hydrostatic Forces on Plane Surfaces
Pretest
Q1))

23. Answer key
CH.3: Hydrostatic Forces on Plane Surfaces
Pretest
Q2))

24. Answer key
CH.3: Hydrostatic Forces on Plane Surfaces
Post test
Q1))

25. Answer key
CH.3: Hydrostatic Forces on Plane Surfaces
Post test
Q2))

26. References
CH1: Fluid Properties
1.Evett,J.,B.andLiu,C.1989“2500solvedproblemsinfluidmechanicsand
hydraulics”LibraryofCongressCataloging-in-PublicationData,(Schaum's
solvedproblemsseries)ISBN0-07-019783-0
2.Rajput,R.,K.2000“ATextBookofFluidMechanicsandHydraulic
Machines”.S.Chand&CompanyLTD.
3.White,F.,M.2000“FluidMechanics”.McGraw-HillSeriesinMechanical
Engineering.
4.Wily,S.,1983“FluidMechanics”.McGraw-HillSeriesinMechanical
Engineering.