The water in a 25-m-deep reservoir is kept inside by a 150-m-wide wall whose cross section is an

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The water in a 25-m-deep reservoir is kept inside by a...

The water in a $25-\mathrm{m}$-deep reservoir is kept inside by a $150-\mathrm{m}$-wide wall whose cross section is an equilateral triangle, as shown in the figure. Determine (a) the total force (hydrosta- tic + atmospheric) acting on the inner surface of the wall and its line of action and (b) the magnitude of the horizontal component of this force. Take $P_{\mathrm{atm}}=100 \mathrm{kPa}$. figure cant copy

The water in a $25-\mathrm{m}$-deep reservoir is kept inside by a $150-\mathrm{m}$-wide wall whose cross section is an equilateral triangle, as shown in the figure. Determine (a) the total force (hydrosta-
tic + atmospheric) acting on the inner surface of the wall and its line of action and (b) the magnitude of the horizontal component of this force. Take $P_{\mathrm{atm}}=100 \mathrm{kPa}$.
figure cant copy

Key Concepts

Force Component Decomposition

In many hydrostatic force problems, it is necessary to decompose the resultant force into its horizontal and vertical components. This is done by resolving the vector into components, which is particularly useful when determining the magnitude of the horizontal component of the force acting on inclined or curved surfaces.

Center of Pressure

This is the point on the submerged surface at which the total resultant force can be considered to act. It is determined by taking the moments produced by the pressure distribution about a reference axis. The center of pressure is typically located below the centroid of the area for vertical or inclined surfaces due to the increasing pressure with depth.

Atmospheric Pressure

Atmospheric pressure is the pressure exerted by the weight of the atmosphere. In hydrostatic problems, it is important because it provides a baseline pressure that acts on the free surface of the fluid and on the submerged surfaces, contributing to the total pressure distribution and force calculations.

Hydrostatic Pressure

This concept refers to the pressure exerted by a fluid at rest, which increases linearly with depth due to the weight of the fluid above. It is generally described by the equation p = p? + ?gh, where p? is the atmospheric pressure at the surface, ? is the density of the fluid, g is the acceleration due to gravity, and h is the depth below the free surface.

Resultant Force on a Submerged Surface

The net force acting on a submerged surface is obtained by integrating the pressure distribution over the area of the surface. This integration results in the total force, which accounts for both the hydrostatic pressure and the atmospheric pressure acting on the surface.

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