Exam Question

### 1. Introduction and Fundamental Principles
This problem requires the calculation of hydrostatic forces (loads) exerted by fresh water on the top and a short side of a ballast tank under two distinct scenarios. The principles of hydrostatic pressure are fundamental to marine engineering and naval architecture, critical for structural integrity and stability assessments.
* **Hydrostatic Pressure**: The pressure at any point within a fluid at rest is directly proportional to its depth ($$h$$) from the free surface, the density of the fluid ($$\rho$$), and the acceleration due to gravity ($$g$$). This relationship is given by the formula: $$P = \rho \cdot g \cdot h$$
* **Hydrostatic Force (Load)**: The total force exerted by a fluid on a submerged plane surface is the product of the average pressure acting on the surface and the area of that surface. For a horizontal surface, the pressure is uniform, so $$F = P \cdot A$$. For a vertical or inclined surface, the pressure varies with depth, and the total force is calculated as $$F = P_{avg} \cdot A$$, where $$P_{avg}$$ is the pressure at the centroid of the submerged area.