Review. The tank in Figure P 14.13 is filled with water of...

Review. The tank in Figure $P 14.13$ is filled with water of depth $d=2.00 \mathrm{m} .$ At the bottom of one sidewall is a rectangular hatch of height $h=1.00 \mathrm{m}$ and width $w=2.00 \mathrm{m}$ that is hinged at the top of the hatch. (a) Determine the magnitude of the force the water exerts on the hatch. (b) Find the magnitude of the torque exerted by the water about the hinges. (FIGURE CANT COPY)

Key Concepts

Torque (Moment) Calculation

Torque, or moment, due to a distributed force is calculated by integrating the product of the force density and the lever arm distance over the area. In the context of fluid pressure acting on a surface, this requires summing the contributions of the varying pressures (and their lever arms) to determine the overall rotational effect about a specific axis or point, such as hinges.

Center of Pressure

The center of pressure is the point on a submerged surface where the resultant hydrostatic force effectively acts. It is generally located below the geometric center of the area since pressure increases with depth. Determining the center of pressure is important for assessing the moments produced by the fluid force about a given pivot or hinge.

Force on Submerged Surfaces

The force exerted by a fluid on a submerged surface is determined by integrating the pressure over the area of the surface. Due to the variation in pressure with depth, different parts of the surface experience different pressures, requiring an integration process to sum up the contributions across the entire surface.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the force of gravity. It increases linearly with depth because of the weight of the overlying fluid. This principle is fundamental when calculating the pressure at any given point under a fluid surface and forms the basis for determining the force acting on submerged surfaces.

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