The pressure due to the weight of a liquid with uniform density is calculated using the formula: p = ρgh.
Here's a breakdown of this formula and its components:
- p: Represents the pressure at a specific depth within the liquid. The SI unit for pressure is the Pascal (Pa), which is equivalent to Newtons per square meter (N/m2).
- ρ (rho): Represents the density of the liquid. Density is a measure of mass per unit volume, typically expressed in kilograms per cubic meter (kg/m3).
- g: Represents the acceleration due to gravity. On Earth, this is approximately 9.81 m/s2.
- h: Represents the depth of the liquid, measured from the surface to the point where the pressure is being calculated. Depth is typically measured in meters (m).
Explanation:
The formula p = ρgh indicates that the pressure at any point within a liquid is directly proportional to the liquid's density, the acceleration due to gravity, and the depth from the surface of the liquid to that point. This means that:
- Denser liquids exert greater pressure at the same depth compared to less dense liquids.
- Pressure increases with depth. The deeper you go into a liquid, the greater the pressure.
- Gravity plays a role: On a planet with higher gravity, the pressure exerted by a liquid at a specific depth would be greater.
Example:
Imagine a swimming pool filled with water (density ≈ 1000 kg/m3). If you want to find the pressure at a depth of 2 meters, you would calculate it as follows:
p = (1000 kg/m3) (9.81 m/s2) (2 m) = 19620 Pa
Therefore, the pressure at a depth of 2 meters in the swimming pool is approximately 19620 Pascals.
Important Considerations:
- This formula assumes that the liquid is incompressible (its density doesn't change with pressure) and that the density is uniform throughout the liquid.
- The pressure calculated by this formula is the gauge pressure, which is the pressure relative to atmospheric pressure. The absolute pressure would be the gauge pressure plus the atmospheric pressure.
