Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_164

⚡ Mecademy AIENG정역학 · ch5  Problem Statement When the sea-water level inside the hemispherical chamber reaches the 0.6-m level shown in the figure, the plunger is lifted, allowing a surge of sea water to enter the vertical pipe. For this fluid level (a) determine the average pressure supported by the seal area of the valve before force is applied to lift the plunger and (b) determine the force (in addition to the force needed to support its weight) required to lift the plunger. Assume atmospheric pressure in all airspaces and in the seal area when contact ceases under the action of . Problem 5/164 (a) Average pressure supported by the seal area 1. Formula: The average contact pressure on the seal area is the net downward fluid force divided by the seal area. We use gauge pressure () as atmospheric pressure acts on both the top of the stem and the bottom center of the plunger. where the net downward fluid force from the sea water is: and the seal area is: 2. Substitution: Density of sea water: (standard value for such problems) Gravitational acceleration: Water level (depth): Outer seal/flange diameter: Inner seal diameter: Stem/pipe diameter: σ P P σ σ p = atm 0 σ= A seal F fluid, net F = fluid, net p × base A = top_flange (ρgh)× ( d − 4 π outer 2 d ) stem 2 A = seal ( d − 4 π outer 2 d ) inner 2 ρ= 1030kg/m 3 g= 9.81m/s 2 h=0.6m d = outer 0.6m d = inner 0.4m d = stem 75mm=0.075m 3. Calculation: Net downward fluid force: Average pressure: 4. Result: ● Final Conclusion: The a