Pressure in static fields

A solid object exerts pressure due to its weight via its base surface only, not from its sides.
A liquid exerts pressure due to its weight against the sides and bottom of its container.
- Molecules in a liquid push against adjacent molecules, exerting pressure in all directions (upward, downward, and sideways).

Fluid: All substances that can flow and have an indefinite shape, including:
- Liquids
- Gases
Not included: Granular items such as sand and sugar (if it can be piled up, it is not classified as a fluid).

The pressure exerted by a liquid at any specific point primarily depends on two factors:
1. Depth of the location
2. Density of the liquid

Pressure in a liquid is directly proportional to depth:
- Pressure ∝ Depth
- Greater depth results in greater total weight force acting on that layer from the layers above it.

Density (ρ): Defined as the mass per unit volume of a substance.
- Greater density means more matter (mass) per unit volume.
- Since the weight force is dependent on mass, greater density results in a greater weight force of each layer pushing down on the liquid below it.
- Pressure ∝ Density

Basic pressure formulation:
- P = \frac{F}{A}
Weight force formation:
- F = mg
Substitute into pressure equation:
- P = \frac{mg}{A}
- Substituting density relation, where
- Density (ρ) is defined as:
  - \rho = \frac{m}{V}
  - V = \text{Area} \times \text{height} = A \times h
  - Therefore, m = \rho \times (A \times h).
Rewriting for the new pressure equation results in:
- P = g \times \frac{m}{A}
From earlier formulations:
- P = g \times \rho \times h
- Hence, for pressure in a liquid, the pressure at any depth (h) can be calculated as:
- P = g \rho h.

Question: What is the pressure at a location that is 1 m below the surface of a lake, given that the density of water is approximately 1000 kg/m³?
- Calculation:
- P = g \rho h
- P = 10 \, m/s^2 \times 1000 \, kg/m^3 \times 1 \, m
- P = 10,000 \, Pascals = 10 \, kPa
- Note: Atmospheric pressure is around 100 kPa, so this pressure is not excessively high.

The discussion covers only the pressure exerted by the liquid on itself.
Total pressure also includes air pressure exerted on the liquid from above.
Fluid pressure is often measured on a relative basis, known as gauge pressure.
- Example: Blood pressure is expressed using the height of a column of mercury.

Pascal’s Principle: For any incompressible fluid at rest in a closed container, a change in pressure is transmitted equally and undiminished in all directions throughout the fluid.

Example scenario:
- When a force is applied against the wall of a closed liquid container, the pressure increase at that wall is transmitted throughout the liquid.
The ratio of force to area (which defines pressure) remains constant, leading to a possible force multiplication.
- A small force applied to a small area can lead to a larger force applied over a larger area.
- Application Example: Hydraulic lift system utilized to elevate a hospital gurney to the desired height.

Context: Pregnant women are encouraged to wear loose-fitting clothing around the abdomen during the later stages of pregnancy.
- The fetus resides in a fluid-filled amniotic sac.
- If external pressure is applied to the amniotic sac, the pressure is uniformly transmitted throughout the fluid, thus affecting the fetus.

Observation: The exit of the urinary bladder, known as the urinary sphincter, is the weakest point of the bladder’s contained pressure.
- Increased pressure can lead to involuntary release or urge to urinate.