Hydrostatic Forces On Plane Surfaces Static Surface Forces
Hydrostatic Forces onPlane SurfacesStatic Surface Forces Forces on plane areasForces on curved surfacesBuoyant forceStability of floating and submerged bodiesForces on Plane Areas:Horizontal surfacesForces on Plane Areas Two types of problems– Horizontal surfaces (pressure is )constant– Inclined surfaces dp Two unknownsdz– Totalforce– Lineof action Two techniques to find the line of action ofthe resultant force– Moments– Pressure prismWhat is the force on the bottom of thistank of water?FR pdA p dA pAhSide viewp hFR hAFR weight of overlying fluid!h Vertical distanceto free surfaceF is normal to the surface and towardsthe surface if p is positive.F passes through thecentroid of the area.ATop view
Forces on Plane Areas: InclinedSurfacesForces on Plane Areas: InclinedSurfacesFree surface Direction of force Normal to the plane Magnitude of forceFR ?hc– integrate the pressure over the area– pressure is no longer constant!A’xcxRB’O– Moment of the resultant force must equal themoment of the distributed pressure forcecenter of pressureMagnitude of Force on InclinedPlane Areap h y sin FR sin ydAyc 1ydAA Axcentroid Line of actionFR pdAOyy RRyccThe origin of the yaxis is on the freesurfaceExample yFR Ayc sin Concrete(23.6 kN/m3)F pA ( y sin ) Ay 1.22m (23,600 *1.22 *1) * (1.22 * 2.44)F 85.8 kN2.44 mFFR hc Ahc is the vertical distance between freesurface and centroidFR pc Acentroid of the areapc is the pressure at thePlywood Form(2.44m x 1.22m)
Forces on Plane Areas:Center of Pressure: xRCenter of Pressure: xR The center of pressure is not at the centroid(because pressure is increasing with depth)xR 1xydAyc A AxR I xyyc AxR xc yc A I xycyc A– x coordinate of center of pressure: xRxR FR xpdAAMoment of resultant force sum ofmoment of distributed forcesp y sin FR yc A sin 1xpdAFR A1xR xy sin dAyc A sin A1xR xydAyc A AxR xR A1ypdAFR yc A sin FR A1yR y 2 sin dAyc A sin A1yR y 2 dA Ayc AyR yR p y sin Ixc aIxcI x y dA2I x I xc yc2 AI xc yc2 Ayc AyR I xc yyc A cParallel axis theoremParallel axis theoremyI xyc xcyc AbycxIxcA abyc a2a3b dxc 3I xc ba 312I xyc 0I xc ba 336I xyc p R4I xyc 0yc aabyc A 2bdAIxyc AProduct of inertiaProperties of AreasSum of the momentsyR AI xy xc yc A I xycCenter of Pressure: yRy R FR ypdAI xy xydARycA p R 2 yc RI xc 4ba 2(b - 2d )72
Properties of AreasInclined Surface Findings0IxcycRA p R22yc 4R3pI xc baycIxcRycA p abA p R24yc ayc I xc 4R3pI xc p R48p ba 34I xyc 0I xyc 0p R416I The horizontal center of pressure and thexR xyc xcyc Acoincide when the surfacehorizontal centroidhas either a horizontal or vertical axis ofsymmetry 0 The center of pressure is alwaysbelow the y I xc yRcyc Acentroid The vertical distance between the centroid andthe center of pressuredecreases as the surfaceis lowered deeper into the liquid (yc increases) What do you do if there isn’t a free surface?ExampleMagnitude of the ForceAn elliptical gate covers the end of a pipe 4 m in diameter. If thegate is hinged at the top, what normal force F applied at thebottom of the gate is required to open the gate when water is 8 mdeep above the top of the pipe and the pipe is open to theatmosphere on the other side? Neglect the weight of the gate.FR pc A8mA abwaterFRRFhc 10 m Depth to the centroidSolution Scheme Magnitude of the forceapplied by the water hcpc 8m Location of the resultant force Find F using moments about hingewaterFhinge4mFR hc abNFR 9800 3 10 m π 2.5 m 2 m m FR 1.54 MNa 2.5 mb 2mhinge4m
Location of Resultant ForceyR I xc ycyc A8mFrrFyc hcyc 12.5 my R yc ba 34 yc aba2y R yc 4 ycmy R yc 0.125waterForce Required to Open Gatehinge4mI xc 4A ab 2.5 m 2y R yc 4 12.5 m xcxR 8mF a 2.5 mcpFR lcpltotwaterFrrFMoments about the hinge M hinge 0 Fltottot - FRRlcpcpSlant distanceto surfacep ba 3How do we find therequired force?lcp 2.625 mcp 1.54 x 10 N 2.625 m F 6Forces on Plane Surfaces Review The average magnitude of the pressure forceis the pressure at the centroid The horizontal location of the pressure forcegate was symmetricalwas at xc (WHY?) Theabout at least one of the centroidal axes. The vertical location of the pressure force isPressurebelow the centroid. (WHY?)increases with depth.F 809 kN4m2.5 m 5 m b 2mhingeb 2mForces on Plane Areas:Pressure Prism A simpler approach that works well forareas of constant width ( )rectangles If the location of the resultant force isrequired and the area doesn’t intersect thefree surface, then the moment of inertiamethod is about as easyltot
Forces on Plane Areas: PressurePrismyR 1yd Example : Pressure PrismO8m 8 m 12 m5m4mx5m4m(rectangular conduit) hy hSolution : Pressure Prismh1 h22FR (9800 N/m3 )(10 m)(5 m)(4 m)hingeDamFRR VolumeFRR (h/cos )( h)(w)/2FRR (10 m/0.9135)(9800 N/m33*10 m)(50 m)/2FRR 26 MNMagnitude of forcewater 24º h1 h2MNFR 1.965ma41xd FRwmxR h 10 mForce Volumeof pressure prismCenter of pressureis at centroid ofpressure prismh/cos w h 21xpdAFR A F h A F Ap hxR wideh1 mh2Ois50 h1DamFree surfaceExample : Pressure PrismLocation of resultant force measured from hingea aw h1 2a aw h2 y R FR 3 2 3 2 5 m 8 m 12 m yR 10 m 63 yR a 2 w h1 h2 aw 10 m 6 3 FRR2.667 myR
Exercise:First Moments2.61, 2.67, 2.71, 2.77xdAMoment of an area A about the y axisxc 1xdAA ALocation of centroidal axisyc 1ydAA òA A13hFor a plate of uniform thickness the intersection of the centroidalaxes is also the center of gravitySecond MomentsProduct of Inertia A measure of the asymmetry of the areamoment of inertia of the areaAlso calledI xy xydAAI x y 2 dAI xy xc yc A I xycAI x I xc AycProduct of inertia2Ixc is the 2nd moment with respect to anaxis passing through its centroid andparallel to the x axis.Parallel axis theoremyIxyc 0Ixyc 0yxxIf x xc or y yc is an axis of symmetry then the product ofinertia Ixyc is zero.
Hydrostatic Forces on Plane Surfaces Static Surface Forces Forces on plane areas Forces on curved surfaces Buoyant force Stability of floating and submerged bodies Forces on Plane Areas Two types of problems – Horizontal surfaces (pressure is
Hydrostatic Forces on Curved Surfaces Static Surface Forces Forces on plane areas Forces on curved surfaces Buoyant force . The vertical component of pressure force on a curved surface is equal to the weight of liquid vertically above the curved surface and extending up to the (virtual or real) free .File Size: 211KBPage Count: 6Explore furtherHydrostatic Force acting on Submerged Surfacewww.engineeringtoolbox.com(PDF) Compressible Fluid Flow Calculation Methodswww.researchgate.netSURFACE TENSION IN FLUID MECHANICS - Mechanical .www.hkdivedi.comFluid Mechanics II Viscosity and shear stresseswww.homepages.ucl.ac.ukFluid Flow: Conservation of Momentum, Mass, and Energywww.comsol.comRecommended to you b
Experiment (1): Hydrostatic force on a plane surface Introduction: The study of pressure forces acting on plane submerged surfaces is a fundamental topic in the subject of hydrostatic involving assessment of the value of the net thrust and the concept of center . Liquid pressures on the curved surfac
HYDROSTATIC FORCES ON SURFACES Remember the second law of Pascal – In a container, pressure acts perpendicular to the boundary In this lecture we will investigate how forces act on surfaces – Nature of plane or curved surface Total force Center of force
Hydrostatic Force on a Curved Surfaces Henryk Kudela 1 Hydrostatic Force on a Curved Surface On a curved surface the forces pδA on individual elements differ in direction, so a simple summation of them may not be made. Instead, the resultant forces in certain directions may be determined, and these forces may then be combined vectorially.File Size: 279KB
Hydrostatic Forces On Submerged Surfaces hydrostatic forces acting on a plane or curved surface submerged in a multilayered fluid of different dens ities can be determine d by cons idering different parts of surfaces in different fluids as different surfaces, findi ng the force
Hydrostatic pressure is, the pressure exerted by a fluid at equilibrium due to the force of gravity. A fluid in this condition is known as a hydrostatic fluid. So our Hydrostatic pressure lab was to determine the hydrostatic pressure
A.6 Surface tension B Hydrostatics B.1 The hydrostatic equation B.2 Pressure in fluid of uniform density B.3 Absolute, gauge and vacuum pressure B.4 Applications to pressure measurements B.4 Hydrostatic force on plane surfaces B.5 Hydrostatic force on curved surfaces Tutorial Recommended Re
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