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day05_pressure_2

# day05_pressure_2 - Fluid Mechanics 3502 Day 5(Fall 2008...

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9/16/2008 1 Fluid Mechanics 3502 Day 5 (Fall, 2008) Chapter 3: Fluid Statics Part 2 y Pressure on a solid surface y Buoyancy A “typical” pressure on flat solid surface problem y Determine the force F app necessary to just start opening the 2 m–wide rectangular gate. For now, neglect its weight. y A problem we need to solve address first: What is the resultant force due to the pressure on one side of the plate and where does it “act”? F app Forces on submerged surfaces: Plane surfaces y Consider a submerged surface, with one axis (x) parallel to the surface and the other (y) at an angle α with the horizontal α y H V y Problem: What is the resultant force (F p ) due to the pressure on one side of the plate and where (y cp ) does it act? cp F p x y centroid y Alternate derivation: The vertical magnitude can be equated to the total weight resting above the surface, i.e., Q1: Q1: what is the magnitude of the what is the magnitude of the force on a submerged surface α F H V Base c h ) cos A h ( ) h x Base ( plane) above lquid of x( F c Liq c Liq Liq V α γ = γ = γ = Vertical Depth of centroid (1) y y The magnitude of the vertical component is y Equating (1) and (2): p centroid Projection of Plane area: Base = A cos α α = cos F F p V α γ = α cos A h cos F c p Pressure at centroid (2) A h F or c p γ = A sin y F or p α γ = A p F or p “slant distance” to centroid From Fig. A1(in the Appendix) Q2: what is the line of action of the pressure on a submerged surface y Warm-up question: y Why have I drawn the “center pressure”, the location of the of action of the force, below the centroid ? y A uniformly loaded beam can be balanced at its centroid α cp y F This is exactly the case on a submerged plane The pressure force decreases toward the water surface y If the force increases “down-beam”, the fulcrum needs to be shifted y The Moments about the fulcrum must balance, i.e.,

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day05_pressure_2 - Fluid Mechanics 3502 Day 5(Fall 2008...

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