Recall and use the equation for the change in pressure beneath the surface of a liquid Δp = ρ g Δh

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IGCSE Physics - 1.8 Pressure

IGCSE Physics - 1.8 Pressure

Objective

Recall and use the equation for the change in pressure beneath the surface of a liquid: $\Delta p = \rho g \Delta h$

Understanding Pressure

Pressure is defined as the force exerted per unit area. In liquids, pressure acts equally in all directions.

The pressure at a certain depth in a liquid depends on the density of the liquid, the acceleration due to gravity, and the depth.

The Formula: $\Delta p = \rho g \Delta h$

Where:

  • $\Delta p$ = The change in pressure (in Pascals, Pa)
  • $\rho$ (rho) = The density of the liquid (in kg/m3)
  • $g$ = The acceleration due to gravity (approximately 9.8 m/s2)
  • $\Delta h$ = The change in depth or height (in meters, m)

This equation states that the pressure at a depth is directly proportional to the density of the liquid and the depth.

How the Formula Works

Consider a liquid with a constant surface area. The pressure at a certain depth is caused by the weight of the liquid above that point. The weight of the liquid is given by mass x gravity. Mass is related to density and volume. Volume is related to area and depth. Combining these relationships leads to the pressure formula.

Example Calculations

Example 1: Calculate the change in pressure at a depth of 2 meters in water, given that the density of water is 1000 kg/m3.

Using the formula: $\Delta p = \rho g \Delta h$


$\Delta p = (1000 \, \text{kg/m}^3) \times (9.8 \, \text{m/s}^2) \times (2 \, \text{m})$


$\Delta p = 19600 \, \text{Pa}$

Example 2: A scuba diver is at a depth of 10 meters in seawater. The density of seawater is approximately 1030 kg/m3. Calculate the pressure on the diver.

Using the formula: $\Delta p = \rho g \Delta h$


$\Delta p = (1030 \, \text{kg/m}^3) \times (9.8 \, \text{m/s}^2) \times (10 \, \text{m})$


$\Delta p = 99940 \, \text{Pa}$

Note: The pressure on the diver is the sum of atmospheric pressure and the pressure due to the water above.

Table of Values

Density ($\rho$) Gravity ($g$) Depth ($\Delta h$) Change in Pressure ($\Delta p$)
1000 kg/m3 9.8 m/s2 1 m 9800 Pa
1000 kg/m3 9.8 m/s2 10 m 98000 Pa
1030 kg/m3 9.8 m/s2 1 m 10094 Pa

Important Considerations

The pressure at a point in a liquid is always in the same direction as the force acting on a small horizontal area at that point.

The pressure is cumulative. The total pressure at a depth is the sum of the pressure due to all the layers of liquid above.