A cylindrical container whose weight is 79 N is inverted and...

A cylindrical container whose weight is 79 N is inverted and pressed into the water, as shown in the figure. Determine the differential height $h$ of the manometer and the force $F$ needed to hold the container at the position shown.
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Key Concepts

Hydrostatic Pressure

This is the pressure in a fluid that increases with depth due to the weight of the fluid overhead. It is a fundamental concept in fluid mechanics and is used to determine the pressure differences in systems such as manometers or submerged containers.

Manometer

A manometer is an instrument used to measure the pressure difference between two points in a fluid. It typically works by comparing the heights of liquid columns, allowing for the calculation of pressure differences based on known fluid densities and gravitational acceleration.

Buoyant Force

Buoyant force is the upward force exerted by a fluid on an object immersed in it, described by Archimedes’ principle. This principle states that the buoyant force is equal to the weight of the fluid displaced by the object, which is key in analyzing the forces on submerged or partially submerged bodies.

Force Balance

Force balance involves the equilibrium analysis where all forces acting on a body are summed and set equal to zero in a static situation. In problems involving fluid pressure and objects in fluids, balancing the gravitational, buoyant, and applied forces is essential for determining unknown values such as applied force or pressure differences.

Pressure Differential

This concept refers to the difference in pressure between two regions, which can create a net force when applied over an area. Understanding how pressure differences translate into forces is crucial when analyzing systems with confined fluids and external forces, such as the scenario with an inverted container in water.

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