Applications of Hydrostatics

Manometers, hydraulic presses, communicating vessels, and stability of floating bodies.

General idea of the topic

The applications of hydrostatics follow directly from the fact that pressure depends only on depth. A manometer reads a pressure by comparing heights of liquid column, communicating vessels equalize levels because the pressure at a given level is the same, and flotation results from comparing weight and buoyant force.

The topic develops these three cases with their typical setup and numerical examples, and shows how the fundamental equation of hydrostatics becomes a tool for measurement and design.

What you will truly understand

By the end you will be able to read a U-tube manometer, compute levels in communicating vessels with different liquids and determine the submerged fraction of a floating body.

You will also be able to distinguish absolute and gauge pressure.

Recommended learning route

1. Manometers: pressure measurement with liquid columns and gauge versus absolute pressure.
2. Communicating Vessels: equality of pressures at the same level and ratio of heights with immiscible liquids.
3. Flotation: balance between weight and buoyant force and submerged fraction.

Physical criterion you must acquire

The essential criterion is always to compare pressures at points in the same fluid and at the same height, and to follow the path from one point to another by adding ρgh with the appropriate sign. In communicating vessels with two liquids, the heights are in inverse proportion to the densities.

Connection with real problems

• barometers and manometers.
• water tanks and leveling.
• ships and buoys.
• hydrometers.

Final goal of the topic

The final goal is to apply the hydrostatic equation to real measurement and flotation devices and justify each step of the setup.