Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_165

⚡ Mecademy AIENG정역학 · ch5  Problem Statement One of the critical problems in the design of deep-submergence vehicles is to provide viewing ports which will withstand tremendous hydrostatic pressures without fracture or leakage. The figure shows the cross section of an experimental acrylic window with spherical surfaces under test in a high-pressure liquid chamber. If the pressure is raised to a level that simulates the effect of a dive to a depth of 1 km in sea water, calculate the average pressure supported by the gasket A. Problem 5/165 (a) Calculation of the average pressure supported by gasket A ● Calculation Process 1. Present Final Formula: The hydrostatic pressure at depth is given by: The total axial force exerted by this pressure on the window is the pressure multiplied by the projected area of the surface exposed to the pressurized liquid: where is the outer diameter of the window assembly. This force is resisted by the reaction from gasket A. The average pressure on the gasket is the total force divided by the gasket's contact area: 2. Substitute Values: From Table D/1 for sea water, the specific weight is . Depth Hydrostatic pressure: Outer diameter: p σ ph p=ρgh=γh F F=p⋅A = projected p⋅ 4 πD o 2 D o σ σ= = A gasket F = (D −D ) 4 π o 2 i 2 p⋅ 4 πD o 2 p D −D o 2 i 2 D o 2 γ= 10.05 kN/m 3 h=1 km=1000 m p= 10.05 kN/m× 3 1000 m=10,050 kPa= 10.05 MPa D = o 350 mm Inner diameter of the hull opening: Substituting into the formula for : 3. Partial Operations: Calculate