The tank in Fig. P 2.89 contains benzene and is pressurized...

The tank in Fig. $\mathrm{P} 2.89$ contains benzene and is pressurized to 200 kPa (gage) in the air gap. Determine the vertical hydrostatic force on circular-arc section $A B$ and its line of action.

Key Concepts

Resultant Force and Line of Action

Once the differential forces on the surface are integrated, the resultant hydrostatic force is obtained. The point where this resultant force effectively acts is known as the line of action or the center of pressure. Identifying the line of action is crucial in engineering applications because it determines the moment produced by the force, which is essential for stability and structural analysis.

Hydrostatic Pressure Distribution

This concept refers to the fact that the pressure within a static fluid increases linearly with depth due to the weight of the fluid. The basic relation, P = P? + ?gh, where ? is the density of the fluid and g is the acceleration due to gravity, characterizes how pressure varies at different depths. This is a foundational idea in fluid mechanics, used to analyze forces exerted by fluids on submerged or partially submerged surfaces.

Integration of Pressure Over Curved Surfaces

To determine the force on a curved surface, the pressure distribution must be integrated over the surface area. For curved surfaces, special techniques, such as using the horizontal projection method, simplify the integration by transforming the problem into an equivalent flat surface analysis. This process allows for the evaluation of the resultant force due to pressure, accounting for the variable orientation of the surface elements.

Please give Ace some feedback