Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_170

⚡ Mecademy AIENG정역학 · ch5  Problem Statement A vertical section of an oil sump is shown. The access plate covers a rectangular opening which has a dimension of 400 mm normal to the plane of the paper. Calculate the total force exerted by the oil on the plate and the location of . The oil has a density of . Problem 5/170 (a) Total force exerted by the oil on the plate 1. Formula: The total hydrostatic force on a submerged plane surface is given by: where is the density, is the acceleration due to gravity, is the vertical depth to the centroid of the plate, and is the surface area of the plate. 2. Substitution: Density of oil: Gravity: Length of plate: Width of plate: Area: Depth of the top edge: Inclination angle: Vertical depth to centroid: 3. Calculation: Pressure at centroid: Total force: 4. Result: R xR 900 kg/m 3 R R=p A= avg ρgAh ˉ ρgh ˉ A ρ= 900 kg/m 3 g= 9.81 m/s 2 L=600 mm=0.6 m w=400 mm=0.4 m A=L⋅w=0.6⋅0.4=0.24 m 2 h = 1 500 mm=0.5 m θ=30 ∘ =h ˉ h + 1 sinθ= 2 L 0.5+ sin30= 2 0.6 ∘ 0.5+0.3(0.5)=0.65 m R= (900 kg/m)(9.81 m/s)(0.65 m)(0.24 m) 32 2 p = c ρg=h ˉ 900⋅9.81⋅0.65=5738.85 Pa R=5738.85⋅0.24=1377.324 N R=1377 N ● Final Conclusion: The total force exerted by the oil on the access plate is (or ). (b) Location of the resultant force 1. Formula: The resultant force acts through the center of pressure. The distance from the intersection of the plate line and the free surface along the plate is: The distance from the top edge of the plate is: where is the distance fr