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Static Surface Forces

Static Surface Forces. Forces on plane areasForces on curved surfacesBuoyant forceStability of floating and submerged bodies. ?. ?. Forces on Plane Areas. Two types of problemsHorizontal surfaces (pressure is _______)Inclined surfacesTwo unknowns________________________Two techniques to find the line of action of the resultant forceMomentsPressure prism.

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Static Surface Forces

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    1. Static Surface Forces

    2. Static Surface Forces Forces on plane areas Forces on curved surfaces Buoyant force Stability of floating and submerged bodies

    3. Forces on Plane Areas Two types of problems Horizontal surfaces (pressure is _______) Inclined surfaces Two unknowns ____________ ____________ Two techniques to find the line of action of the resultant force Moments Pressure prism

    4. Forces on Plane Areas: Horizontal surfaces

    5. Forces on Plane Areas: Inclined Surfaces Direction of force Magnitude of force integrate the pressure over the area pressure is no longer constant! Line of action Moment of the resultant force must equal the moment of the distributed pressure force

    6. Forces on Plane Areas: Inclined Surfaces

    7. Magnitude of Force on Inclined Plane Area

    8. First Moments

    9. Second Moments

    10. Product of Inertia A measure of the asymmetry of the area

    11. Properties of Areas

    12. Properties of Areas

    13. Forces on Plane Areas: Center of Pressure: xR The center of pressure is not at the centroid (because pressure is increasing with depth) x coordinate of center of pressure: xR

    14. Center of Pressure: xR

    15. Center of Pressure: yR

    16. Inclined Surface Findings The horizontal center of pressure and the horizontal centroid ________ when the surface has either a horizontal or vertical axis of symmetry The center of pressure is always _______ the centroid The vertical distance between the centroid and the center of pressure _________ as the surface is lowered deeper into the liquid What do you do if there isn’t a free surface?

    17. Example using Moments

    18. Magnitude of the Force

    19. Location of Resultant Force

    20. Force Required to Open Gate How do we find the required force?

    21. Forces on Plane Surfaces Review The average magnitude of the pressure force is the pressure at the centroid The horizontal location of the pressure force was at xc (WHY?) ____________________ ___________________________________ The vertical location of the pressure force is below the centroid. (WHY?) ___________ ___________________

    22. Forces on Plane Areas: Pressure Prism A simpler approach that works well for areas of constant width (_________). It works especially well if the surface intersects with the free surface. If the location of the resultant force is required and the area doesn’t intersect the free surface, then the moment of inertia method is about as easy.

    23. Forces on Plane Areas: Pressure Prism

    24. Example 1: Pressure Prism

    25. Example 2: Pressure Prism

    26. Solution 2: Pressure Prism

    27. Forces on Plane Areas: Pressure Prism A simpler approach that works well for areas of constant width (rectangles). Use pressure prism method if the rectangles intersect the free surface. If the location of the resultant force is required and the area doesn’t intersect the free surface, then the moment of inertia method is about as easy.

    28. Forces on Curved Surfaces Horizontal component Vertical component

    29. Forces on Curved Surfaces: Horizontal Component What is the horizontal component of pressure force on a curved surface equal to? The center of pressure is located using the moment of inertia or pressure prism technique. The horizontal component of pressure force on a closed body is _____.

    30. Forces on Curved Surfaces: Vertical Component What is the magnitude of the vertical component of force on the cup?

    31. Forces on Curved Surfaces: Vertical Component 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 surface. Streeter et al.

    32. Example: Forces on Curved Surfaces

    33. Example: Forces on Curved Surfaces

    34. Example: Forces on Curved Surfaces

    35. Example: Forces on Curved Surfaces

    36. Cylindrical Surface Force Check All pressure forces pass through point C. The pressure force applies no moment about point C. The resultant must pass through point C.

    37. Find force F required to open the gate. All the horizontal force is carried by the hinge The pressure forces and force F pass through O. Thus the hinge force must pass through O! Hinge carries only horizontal forces! (F = ________) Curved Surface Trick

    38. Curved Surface Trick

    39. Static Surface Forces Summary Forces caused by gravity (or _______________) on submerged surfaces horizontal surfaces (normal to total acceleration) inclined surfaces (y coordinate has origin at free surface) curved surfaces Horizontal component Vertical component (________________________) Virtual surfaces…

    40. The resultant force exerted on a body by a static fluid in which it is fully or partially submerged The projection of the body on a vertical plane is always ____. The vertical components of pressure on the top and bottom surfaces are _________ Buoyant Force

    41. Buoyant Force: Thought Experiment Place a thin wall balloon filled with water in a tank of water. What is the net force on the balloon? _______ Does the shape of the balloon matter? ________ What is the buoyant force on the balloon? _____________ _________ Where is the line of action of the buoyant force? __________

    42. Buoyant Force: Line of Action The buoyant force acts through the centroid of the displaced volume of fluid (center of buoyancy)

    43. Buoyant Force: Applications Using buoyancy it is possible to determine: _______ of an object _______ of an object _______________ of an object

    44. Buoyant Force: Applications

    45. A sailboat is sailing on Lake Bryan. The captain is in a hurry to get to shore and decides to cut the anchor off and toss it overboard to lighten the boat. Does the water level of Lake Bryan increase or decrease? Why?_______________________________ ____________________________________ ____________________ Buoyant Force (Just for fun)

    46. Rotational Stability of Submerged Bodies A completely submerged body is stable when its center of gravity is _____ the center of buoyancy

    47. End of Chapter Question Write an equation for the pressure acting on the bottom of a conical tank of water. Write an equation for the total force acting on the bottom of the tank.

    48. End of Chapter What didn’t you understand so far about statics? Ask the person next to you Circle any questions that still need answers

    49. Grand Coulee Dam

    50. Gates

    51. Gates

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