Understanding Hydrostatic Pressure, Hydraulics, and Buoyancy

Posted on Mar 15, 2025 in Physics

Hydrostatic Pressure

Hydrostatic pressure is the pressure within a liquid caused by the weight of the liquid itself.

Features of Hydrostatic Pressure:

  • The pressure inside a liquid acts in all directions.
  • The pressure is higher at greater depths.
  • The pressure increases with the density of the liquid.
  • The pressure is not dependent on the shape or width of the container.

The pressure at any point inside a liquid of density d is due to the weight of the liquid above it.

Fundamental Principle of Hydrostatics

The pressure difference between two points of a homogeneous liquid in equilibrium equals the product of the density, gravity, and the height difference between the points.

Superimposed Immiscible Fluids

If the height of each container is the same, the heights of the two liquids are inversely proportional to their respective densities. Pressures at the same horizontal point must be equal:

hA / hB = dB / dA

Pascal’s Principle

  • The pressure at a point in a fluid, understandably contained in a container, is transmitted equally to every point of the liquid and the container walls.
  • The pressure is transmitted equally in all directions.

Hydraulic Press

A hydraulic press consists of two cylinders of different sections, connected by a tube containing a liquid that reaches the same height in both. These cylinders are closed by pistons of different sizes in contact with the liquid.

pA = pB, FA / SA = FB / SB

Barometer

1 atm = 760 mmHg = 1.013 × 105 Pa

[E = V · d · g] Any body wholly or partially submerged in a fluid experiences a vertical upward thrust equal to the weight of the volume of fluid displaced. V = submerged body volume, d = liquid density. Apparent Weight: Pa = PE

Floating Bodies

When a body is immersed in a fluid, it is subjected to two forces in the same direction but opposite:

  • The weight force, applied at the center of gravity, acts downward.
  • The buoyant force, applied at the center of thrust, acts upward.

By immersing a solid in a fluid, three situations may occur:

  • If the weight is greater than the thrust, the body is completely submerged and sinks to the bottom (i.e., it does not float).
  • If the weight is equal to the thrust, the body is submerged in the fluid without reaching the bottom (i.e., it is in equilibrium within the fluid).
  • If the weight is less than the thrust, the body is partially submerged, enough so that the weight of fluid displaced equals the weight of the body (i.e., it floats).

Floating Boat

For a vessel to be in equilibrium, the following must be met:

  • The weight and thrust are equal.
  • The center of gravity (G) and the center of thrust (C) are in the same vertical line; otherwise, a force couple will form, and the boat will rotate.
  • The center of gravity is lower than the center of thrust.

Floating on Air

Unlike rockets, which overcome the force of Earth’s gravity by the force of action provided by combustion gases, a balloon rises because it is full of a gas whose density is lower than the surrounding air. Because its volume is very large, the driving force that the air provides is greater than its weight.