Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_161

⚡ Mecademy AIENG정역학 · ch5  Problem Statement The aquarium in the Dubai mall boasts one of the largest acrylic viewing panels in the world. The panel measures approximately and is thick. If salt water rises to a height of above the top of the panel, compute the resultant force which the salt water exerts on the panel. The aquarium is open to the atmosphere. Problem 5/161 (a) Magnitude of the Resultant Hydrostatic Force ● Calculation Process 1. Present Final Formula: The resultant force on a submerged plane surface is equal to the pressure at the centroid of the surface () multiplied by the surface area ( ). Since the aquarium is open to the atmosphere, we consider the gauge pressure: where: is the density of the fluid (salt water). is the acceleration due to gravity. is the depth of the centroid of the rectangular panel from the free surface of the water. is the area of the panel face. 2. Substitute Values: From typical properties for sea water (as noted in Problem 5/168 on the same page), we use . The area of the panel is . The top of the panel is at a depth of . The centroid of the high rectangular panel is at its geometric center, so its depth is: Substituting these values: 33 m×8.5 m750 mm 0.5 m R p c A R=p A= c ρgAh ˉ ρ g h ˉ A ρ= 1030 kg/m 3 A= 33 m×8.5 m0.5 m 8.5 m =h ˉ 0.5 m+ = 2 8.5 m 4.75 m R= (1030 kg/m)(9.81 m/s)(4.75 m)(33 m× 32 8.5 m) 3. Partial Operations: Calculate area: Calculate specific weight of salt water: Calculate average pressure at the centroid: 4. Fi