Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_169

⚡ Mecademy AIENG정역학 · ch5  Problem Statement The rectangular gate shown in section is 10 ft long (perpendicular to the paper) and is hinged about its upper edge B. The gate divides a channel leading to a fresh-water lake on the left and a saltwater tidal basin on the right. Calculate the torque on the shaft of the gate at B required to prevent the gate from opening when the salt-water level drops to . Problem 5/169 (a) Torque required at the hinge B ● Calculation Process 1. Present Final Formula: To prevent the gate from opening, the sum of moments about the hinge must be zero. The required torque must balance the net moment produced by the hydrostatic pressures of the fresh water and salt water. where and are the magnitudes of the moments about due to the fresh water and salt water, respectively. The moment due to a hydrostatic force on a vertical rectangular surface of width is given by: 2. Substitute Values: Width of the gate: Height of the gate: Specific weight of fresh water: Specific weight of salt water: Fresh water depth relative to : Surface is above . For a point below , depth is . Salt water depth relative to : Surface is above , which is below . For , depth is . M h=3 ft M BM M = ∑ B 0⟹M+M − sw M = fw 0⟹M=M − fw M sw M fw M sw B w M = B y d F = ∫y (p⋅ ∫wdy) w=10 ft H=12 ft γ = fw 62.4 lb/ft 3 γ = sw 64.0 lb/ft 3 B3 ftBy Bd = fw y+3 B3 ftA12−3= 9 ftBy∈[9,12]d = sw y−9 3. Partial Operations: Calculate : Calculate : 4. Final Calculation: Convert to kip-feet: ● Final