The tank in Figure P 14.14 is filled with water 2.00 m deep. At the bottom of one side wall is a

step 1 This question we have d equals to 2 meter H equals to 1 meter W equals to 2 meter okay so we hav

The tank in Figure P 14.14 is filled with water 2.00 m deep....

The tank in Figure $\mathrm{P} 14.14$ is filled with water 2.00 $\mathrm{m}$ deep. At the bottom of one side wall is a rectangular hatch 1.00 $\mathrm{m}$ high and 2.00 $\mathrm{m}$ wide, which is hinged at the top of the hatch. (a) Determine the force the water exerts on the hatch. (b) Find the torque exerted by the water about the hinges.

Key Concepts

Hydrostatic Pressure Distribution

This concept refers to the way pressure varies with depth in a fluid at rest. The pressure increases linearly with depth according to the relation p = ?gh (ignoring atmospheric pressure when appropriate), where ? is the density of the fluid, g is the acceleration due to gravity, and h is the depth. Understanding this varying pressure is crucial when calculating forces on submerged surfaces.

Integration Over a Submerged Surface

Because the pressure on a submerged surface varies with depth, the total force is found by integrating the pressure over the entire area of the surface. This involves summing the infinitesimally small forces (pressure multiplied by an area element dA) across the surface, which results in a net force that is typically not acting through the geometric center.

Center of Pressure

The center of pressure is the point on a submerged surface through which the resultant force can be considered to act. It is determined by calculating the moments produced by the differential forces due to the pressure distribution and is often found by dividing the first moment of the pressure distribution by the total force. This concept is particularly important when determining torques or designing supports for submerged surfaces.

Torque from Distributed Forces

Torque, or moment, in the context of fluid forces, is the rotational effect produced by the force distribution on a surface. When the fluid exerts a distributed force, the torque about a given point (such as a hinge) is calculated by integrating the product of the local pressure force and its lever arm (the distance from the point of rotation). This approach is used to assess the rotational stability or determine the required strength of support structures.

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