Hydrostatic Forces On Curved Surfaces Static Surface Forces
Hydrostatic Forces onCurved SurfacesStatic Surface Forces Forces on Curved Surfaces Horizontal component Vertical componentwaterForces on plane areasForces on curved surfacesBuoyant forceStability of floating and submerged bodiesForces on Curved Surfaces:Horizontal Component What is the horizontal component ofpressure force on a curved surface equalto? The pressure force on the vertical plane projection The center of pressure is located usingthe moment of inertia or pressure prismtechnique. The horizontal component of pressureforce on a closed body is .zero
Forces on Curved Surfaces:Vertical ComponentPressure on Curved Surface F 0 What is the magnitude of thevertical component of force onthe cup? FAC FxFxFyhF pAxycp F 0yp hF h r2FAC Fx Fy FCB WFy W FCB W!rWhat if the cup had sloping sides?Forces on Curved Surfaces:Vertical ComponentThe vertical component of pressure force on acurved surface is equal to the weight of liquidvertically above the curved surface andextending up to the (virtual or real) freesurface.F pi AAC WF V ABCD W
Example: Forces on CurvedSurfacesExample: Forces on CurvedSurfacesThe vertical component line of action goes throughthe centroid of the volume of water above the surface.Find the resultant force (magnitude and location)on a 1 m wide section of the circular arc.FV W11 W223m22 (3 m)(2 m)(1 m) 1/4 (2 m) (1 m) water 58.9 kN 30.8 kN 89.7 kN2mW1Take moments about a verticalaxis through A.4R2mxR FV (1 m)W1 W2xR pc hc (4 m)(2 m)(1 m) 78.5 kN2mW2W1aI xc (1 m)(2 m)33/12 0.667 m44yc 4 m0.667 m 4yR (4 m ) 4.083 m(4 m )([ 2 m)(1 m)]water4.083 m2my78.5 kN horizontal89.7 kN verticalW22m0.948 mA3mbExample: Forces on CurvedSurfacesxba 3I xc 122myThe location of the line of action of the horizontalcomponent is given byI xc yyc A c4( 2 m )(30.8 kN)3 (89.7 kN)(1 m)(58.9 kN) waterW1 0.948 m (measured from A) with magnitude of 89.7 kNExample: Forces on CurvedSurfacesyR 3p3mxFH p c A4(2 m)W23 A119.2 kN resultant
Cylindrical Surface Force Check0.948 mC1.083 m78.5kN89.7kN All pressure forces passthrough point C. The pressure forceapplies no moment aboutpoint C. The resultant must passthrough point C.Static Surface Forces Summary Forces caused by gravity (or)total acceleration on submerged surfaces– horizontal surfaces (normal to totalacceleration) FR g hALocation where p pref– inclined surfaces (y coordinate has origin atfree surface) FR hc A y I xc ycRyc A– curved surfaces Horizontal component FR hc A Vertical component ( )weight of fluid above surface(78.5kN)(1.083m) - (89.7kN)(0.948m) 0Buoyant Force The resultant force exerted on a body by astatic fluid in which it is fully or partiallysubmerged– The projection of the body on a vertical plane iszeroalways .– The vertical components of pressure on the topdifferentand bottom surfaces are–Archimedes Principle Archimedes PrincipleFB weight displaced fluid Line of action passes through thecentroid of displaced volume
Buoyant Force: Line of ActionExample The buoyant force acts through the centroidof the displaced volume of fluid (center ofbuoyancy)Seawater( 10.1 kN/m3)BuoyCableSpherical buoy has a diameter of 1.5 m, weighs 8.50 kN, and isanchored to the sea floor with a cable as shown. The buoy normallyfloats on the surface, at other times the water depth increases so thatthe buoy is completely immersed as shown. What is the tension in thecable? Fy 0 FB W TyFB T FB W volume d distributed forceFBWxcc centroid of volume–––Weight of an objectVolume of an objectSpecific gravity ofan object6 d 3 (10,100 N / m 3 ) (1.5 m) 3 17,850 N6 17,850 8,500 N 9,350 NTHydrometerBuoyant Force: Applications Using buoyancy it ispossible todetermine: F11 11 22 11W F22Buoyant forceFB weight of the hydrometer 22WForce balance(With F1, F2 , 1, and 2 given)must remain constant Hydrometer floats deeper or shallowerdepending on the specific weight of thefluid
A sailboat is sailing on Caspian sea. Thecaptain is in a hurry to get to shore anddecides to cut the anchor off and toss itoverboard to lighten the boat. Does the waterlevel of Caspian sea ----------increase ordecrease?Why? The anchor displaces less water whenit is lying on the bottom of the lake than itdid when in the boat.ExampleA hydrometer weighs 0.0216 N and has a stem at theupper end that is cylindrical and 2.8 mm in diameter.hHow much deeper will it float in oil of S 0.78 thanin alcohol of S 0.821?For position 1:1Whydrometer Wdisplaced water20.0216 0.821* 9810 *V1V1 2.68 x10 6 m 3For position 2:S 0.821S 0.780Whydrometer Wdisplaced water0.0216 0.780 * 9810 * (V1 Ah) 0.780 * 9810 * [2.68 x10 6 4(0.0028) 2 h]h 0.0232 m 23.2 mmExercise:Rotational Stability ofSubmerged Bodies A completelysubmerged bodyis stable when itscenter of gravity isbelow the centerof buoyancyBG2.89, 2.84, 2.95, 2.104BG
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
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 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 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 Surface General theory of plane surfaces does not apply to curved surfaces Many surfaces in dams, pumps, pipes or tanks are curved No simple formulas by integration similar to those for plane surfaces A new method must be used Isolated Volume Bou
Hydrostatic Forces on Submerged Curved Surfaces Universidad San Ignacio de Loyola Eusebio Ingol Blanco, Ph.D. 1. The horizontal component of the hydrostatic force acting on a curved surface is equal (in both magnitude and the line of action) to the hydrostatic force acting on the verti
Forces on a curved surface 7 Forces on Curved Surfaces So the magnitude of the force can be determined using the expression for a vertically oriented surface submerged in a fluid. A zy 1.0m 2.5m 2.5m2 z c 1.0m 2 0.5m F h R h ρgz c A zy 1000 kg m3 9.81 m s2 (0.5m)(2.5m2) R h 12262.5N 12.26kN Forces .File Size: 1MB
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
“Cost accounting is a quantitative method that accumulates, classifies, summarizes and interprets information for three major purposes: (in) Operational planning and control ;( ii) Special decision; and (iii) Product decision.” -Charles T. Horngren. 2 “Cost accounting is the process of accounting for costs from the point at which the expenditure is incurred of committed to the .
